Hindawi Publishing CorporationChinese Journal of EngineeringVolume 2013 Article ID 501587 13 pageshttpdxdoiorg1011552013501587
Review ArticleA Comprehensive Review of Embedded Transmission PricingMethods Based on Power Flow Tracing Techniques
Baseem Khan and Ganga Agnihotri
Department of Electrical Engineering Maulana Azad National Institute of Technology Bhopal 462003 India
Correspondence should be addressed to Baseem Khan baseem khan04yahoocom
Received 2 August 2013 Accepted 22 August 2013
Academic Editors Z Gu and Z Li
Copyright copy 2013 B Khan and G Agnihotri This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Restructuring of electricity supply industry introduced the concept of deregulation After deregulation transmission cost allocationis a vital issue In the available literature various authors have presented different methods for allocation of transmission cost Thispaper presents the review of a variety of methods and algorithm based on the principle of power-flow tracing For a fair andequitable transmission charge allocation it is necessary to know the quantum of power flowing by each generator and load in lineflows Power flow tracing techniques are mainly based on the concepts of proportional sharing principle graph theory circuittheory (Z-bus tracing) optimization approach relative electrical distance concept Equilateral bilateral exchange (EBE) and gametheory This paper presents a comprehensive review of all the available literature on the above
1 Introduction
Restructuring of electricity supply industry (ESI) has takenplace around the world The main aim behind this restruc-turing is to introduce competition to increase efficiency andquality of services in the electricity supply industry Initiallypower sector operated as vertically integrated utility in whichall the functions are governed and controlled by state ownorganization After the restructuring deregulation and openaccess is introduced in the ESI Following deregulation theregulated structure of the ESI is converted into a deregulatedstructure in which all the three major functions are sepa-rated by three companies namely Generation Company Ltd(GENCOS) Transmission Company Ltd (TRANSCO) andDistribution Company Ltd (DISCOMS) Competition isintroduced in the entire system Various independent powerproducers IPPs come in the field of generationThey generatepower and sell to the Central Transmission Utility (CTU)or TRANSCO Competition is introduced in the distributionsector But it is difficult to introduce competition in the trans-mission sector due to itsmonopolistic nature In transmissionsector it is not possible to build a separate transmission linefor every generation facility Hence transmission cost alloca-tion is very complicated task in the deregulated environment
Several methodologies and their variants are presented tosolve this problem
The main aim of any transmission pricing methodologyis to introduce a fair competition in the electricity sectorand provide efficient economic signals Transmission pricingmethods are the overall processes of translating transmissioncosts into overall transmission charges Figure 1 presents thecharging strategy for transmission utility
The main transmission pricing methodologies are classi-fied as in Figure 2
Further the incremental pricing methods are subdividedinto categories as in Figure 3
Colombia UK and Brazil have used long run marginalcost (LRMC) methodology due to its easy implementation
Embedded Transmission Pricing Methods allocate theembedded system costs that is fixed cost among transmis-sion system users These methods can be classified as in Fig-ure 4
Selection of the slack bus greatly influenced the pricingmethodologies for example use of a fixed ldquoslack busrdquo is ade-quate in countries where most of the load is concentrated in asingle center such as the cities Buenos Aires (Argentina) andSantiago (Chile) Hence themarginal participationmethod isapplied in countries like Argentina Chile and Panama
2 Chinese Journal of Engineering
Allowed revenue of transmission company
Marginalincremental charge allocated to loads
and generators
Supplementary charge allocated to the loads
Individual charges (locational)
Common system charge (postage stamp)
Real power loads Reactive power loads
Figure 1 Charging strategy
Most suitable pricing methods
Composite embeddedincremental
Embedded cost
Incremental pricing methods
Compositeembeddedincremental
Figure 2 Various transmission pricing methods
In India themethod which is used so far is postage stampmethod But this method is not distance and direction sen-sitive It is mainly depending on the amount of transactedpower The main advantage of this method is its simplicity inimplementation Due to its various demerits central electric-ity regulatory commissions (CERCs) of India proposed a newtransmission pricing methodology which is the combinationof power flow tracing technique and marginal participationmethodology In the proposed hybrid methodology powerflow tracing is used for selection of the ldquoslack busrdquo while bymarginal participation burden of transmission charges orlosses on each node is computed
This paper presents the review of the variousmethods andtechniques based on power flow tracing which is used for thetransmission embedded cost allocation in the electricitymar-ket For the fair and equitable allocation of the transmissionusage it is necessary to trace the path of power supplied fromthe generator to load though it is difficult but by the power
Incremental transmission
pricing
Short-run Short-runincremental cost
pricing (SRIC)incremental cost
pricing (LRIC)marginal cost
pricing (SRMC)
Long-runLong-runmarginal cost
pricing (LRMC)
Figure 3 Types of incremental transmission pricing methods
Embedded cost transmission
pricing methods
Roll-in methods
Postage stamp method
Contract path method
Network-based methods
MW-Mile method
MVA-Mile method
Flow-based methods
Proportional sharing based
Circuit theory based
Figure 4 Types of embedded transmission pricing methods
flow tracing the flow of electricity can be traced The mainprinciple used in power flow tracing is proportional sharingprinciple According to this principle a network node work asa perfect mixer which follows the Kirchhoff current law thatis total incoming power is equal to total outgoing powerTheprinciple described assumes that each outflow (a flow leavinga node) on a line is dependent only on the voltage gradientand the impedance of the line The contribution of eachinflow (a line flow entering the node) to each outflow is inthe same proportion as the inflow on each line divided by thetotal inflow of all lines at the node However a disadvantageis the fact that the proportional sharing principle for powertransfer between generators and loads is not based on amathematically strict derivation [1]
The rest of the paper is organized as follows fromSections2 to 8 authors present the review of variousmethods based onor using power flow tracing In Section 9 case studies relatedto practical implementation of power flow tracing techniquesare presented Section 10 provides a comparison between var-ious power flow tracing techniques Discussion is also done inthis section followed by the conclusion
2 Power Flow Tracing Techniques Based onProportional Sharing Principle
This approach allocates the charges of each transmission facil-ity to a wheeling transaction based on the extent of use of thatfacility by the transaction This is determined as a function
Chinese Journal of Engineering 3
of magnitude the path and the distance travelled by thetransacted power
21 Topological Generation Distribution Factors Based PowerFlow Tracing (Bialek Tracing) This algorithm works only onlossless flows when the flows at the beginning and end ofeach line are the same The tracing of electricity is done byupstream looking algorithm and downstream looking tracingalgorithm
211 Downstream Looking Algorithm In the downstreamlooking algorithm the nodal power 119875
Note that 119860119889is also sparse and nonsymmetric If 119860minus1
119889
exists then 119875 = 119860minus1119889119875119871and its 119894th element is equal to
119875119894=
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119896
119894 = 1 2 119899 (4)
This equation shows how the nodal power 119875119894distributed
between all the loads in the system On the other hand thesame 119875
119894is equal to the sum of the generation of node 119894 and
all the inflows in lines entering the node Hence the inflow tonode 119894 from line 119894-119895 can be calculated using the proportionalsharing principle as
119889]119894119896119875119894is the topological load distribu-
tion factor that is the portion of 119896th load demand that flowsin line 119894-119895
The generation at a node is also an inflow and can be cal-culated using the proportional sharing principle as
119875119866119894=119875119866119894
119875119894
119875119894=119875119866119894
119875119894
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119870
for 119894 = 1 2 119899(6)
This equation shows that the share of the output of the119894th generator used to supply the 119896th load demand is equal to119875119866119894119875119871119896[119860minus1
119889]119894119896119875119894and can be used to trace where the power of
a particular generator goes to [2]This methodology is proposed by Bialek and Tam in
March 1996 [3] which explained the method for tracing gen-eratorrsquos output They introduce a simple topological methodof tracing the flow of real and reactive power in transmis-sion networks Bialek also explained the topological tracingmethod for apportioning of the total transmission loss toindividual sinks or sources [2 4] whereas in August 1997 [5]explained the topological generation and load distributionfactors for supplement charge allocation in transmissionopen access Also in August 1998 same author [6] explainedthe MW-Mile methodology to allocate the transmissionsupplementary charges to real and reactive power loads
In July 1999 Kattuman et al [7] explained a transmissionloss allocation scheme based on the concept of power flowtracking and also proportionality assumption is analyzed interms of the cooperative game theory Bialek also dealt withthe transmission pricing of cross-border trades [8 9] InOctober 2000 Li et al [10] explained a power flow tracingmethod which is based on topological distribution factorsOn Sep 2001 Su and Liaw [11] explained a newwheeling pric-ing technique called MVA-KM method which applies ACpower flow and considers the apparent power In June 2002Al-Rajhi and Bialek [12] explained the comparison betweenthe marginal and tracing charging of transmission In August2003 Limpasuwan et al [13] investigated the application ofelectricity tracing methodology inThailand In August 2002Bialek [14] explained a range of indices to quantify the incen-tives for gaming the uniform-price spot market In October2002 Shirani and Siahkali [15] explained the application ofpower flow tracing algorithm to allocate the congestion costin the pool market In 2004 Limpasuwan et al [16] explainedthe TransmissionUse of System charge (TUOS)methodologysuggested by Price water house Cooper (PwC) and makes acomparison with a transmission pricing method based on acombination of the electricity tracing and Long Run AverageIncremental Cost (LRAIC) InMay 2004 Kattuman et al [17]explained that the allocation done by the tracing methodol-ogy is equal to the Shapely value of an equivalent cooperativegame In June 2003 Bialek and Ziemianek [18] explained acomparison between the graph based tracing algorithm withthe algorithm based on the solution of linear equations anddeclared that the algorithms are conceptually the same Alsoa practical algorithm is presented to eliminate the cycles fromthe diagraph of flows In July 2004 Bialek and Kattuman [19]rationalized proportional sharing principle of cooperativegame theory and information theory They concluded thatShapely value validates the proportional sharing rule In June2005 Adsoongnoen et al [20] enlightened a unified trans-mission pricing based on electricity tracing methodology
4 Chinese Journal of Engineering
of cross border trades In [21] Nallagownden et al extendsthe methods of proportional sharing and put forward analgorithm to determine the extent of use of a transmissionpath and associated losses In December 2009 Pal et al [22]explained an analytical approach for calculating the incentivecharge for individual participant when the multiple wheelingtransactions are considered simultaneously In May 2010Achayuthakan et al [23] furnished tracing in a new way ofrepresenting the inverted tracing upstream and downstreamdistribution matrices in the form of matrix power seriesIn June 2010 Nallagownden and Lee [24] explained tracingmethodology for the purpose of eliminating problems relatedto the Marginal pricing of transmission costs In July 2010Naresh et al [25] explained the Genetic algorithm basedapproach for power flow tracing and compared with existingapproaches
22 Factors Based on Generators Domain (Kirschen Tracing)The domain of a generator represents a subset 119873 of 119899 buseswhich are supplied by this generator A particular bus belongsto a generator domain if there is a ldquotracerdquo through the trans-mission network for which the direction of power flow isfrom the generator to the bus The generator common is asubset of ldquoneighboredrdquo buses from the subset 119873 which aresupplied by the same generators The subsets of buses whichare not connected andnot supplied by the same generators aretreated as separate commons A bus therefore belongs to onlyone common The branches can be divided in two groupsthose which connect two buses which are part of the samecommon (the internal branches) and those which connecttwo buses which belong to different commons (the externalbranches) External branches are called a link
Knowing the direction of the power flow through thenetwork elements and the commons and the links beingdefined the graph theory can be applied The state graphof the problem studied can be obtained using the followingrepresentation conventions the graph vertices correspond tothe commons graph arcs correspond to links between thecommons and the arc orientation is given by the power flowsThe state graph provides only a qualitative view of the powersystem The inflow of a common is defined as the sum of theinjected power by the sources connected to buses located inthis common and the power imported in this common fromother common by links
The calculus of generator contribution to various com-mons (119863 is the set of commons) is made in the followingmanner [26]
119875119894
119895119896= 119908119894
119895sdot 119875119895119896
119908119894
119896=
sum119895isin119863
119875119894
119895119896
119875119896
119896 isin 119863
119875119896= sum
119895isin119863
119875119895119896 119896 isin 119863 119895
(7)
where119908119894119895is the contribution of the 119894 generator to the load and
the outflow of the 119895 common 119908119894119896is the contribution of the 119894
generator to the load and the outflow of the 119896 common 119875119895119896
is the flow on the link between the 119895 and 119896 commons 119875119894119895119896is
the flow on the link between the 119895 and 119896 commons due to the119894 generator 119875
119896is the inflow of the 119896 common
In February 1997 Kirschen et al [26] explained a powerflow tracing method based on the proportional sharingassumption which introduces the concept of domains com-mons and links On the same track a case study has beendiscussed for normal and network contingency conditionsin [27] by Thukaram et al June 2006 In May 1998 Strbacet al [28] explained the method based on the generatordomain distribution factors to allocate the usage of branchto the load and generators in the maximum flow conditionsIn November 1999 Kirschen and Strbac [29] explained themethod of real and reactive power tracing by converting theall power injections into real and imaginary currents
23 Nodal Generation Distribution Factors In Nov 2000Gubina and Orgie [30] explained the method to determinethe generatorsrsquo contribution to a particular load by using thenodal generation distribution factors (NGDF-s) InDec 2000Grgic and Gubina [31] explained the distribution factorapproach for the reactive power flow tracing Pantos et al in2003-04 worked on transaction based transmission servicepricing techniques based on the Nodal Generation Distribu-tion factor and also proposed an Ex-Ante transmission pric-ing technique They also proposed a new power flow tracingmethod and explained a transmission service pricing Thesame authors further proposed a pattern based transmissionpricing technique [32ndash36]
3 Power Flow Tracing TechniquesBased on Graph Theory
In January 2000 Sun et al [37] explained a new method fortracing AC power flows where the graph theory is used tosolve the tracing problem In April 2000 Xi-Fan et al [38]explained a very efficient algorithm for power flow tracingby proposing two current decomposition axioms in whichGraph theory is used whereas Wei et al [39] used graph the-ory to analyze real power transfer between individual gener-ators and loads In Aug 2000Wu et al [40] explained the useof graph theory to calculate the contributions of individualgenerators and loads to line flows and the real power transferbetween individual generators and loads In March 2001Chai and Sekar [41] explained a methodology using graphtheory to determine the specific generator contributions todifferent loads and the transmission system usage of differentutilities In Dec 2001 Wei et al [42] proposed that the graphtheory is used to detect the existence of circulating powerthen the optimal power flow approach is applied to eliminatecirculating power From 2003 to 2009 Xie et al proposedand explained the power flow tracing algorithms foundedon extended incidence matrix and matrix multiplicationconsidering loop flows [1 43 44] In July 2003 Ghasemi et al[45] explained the closed-form solution for tracing problemby presenting a formula which is obtained by using bothproportionality and averaging criteria From 2004 to 2010Mustafa et al proposed power flow tracing method basedon tracing currents and complex power flows They also
Chinese Journal of Engineering 5
proposed a proportional tree method based method for trac-ing A comparison has also done by the same authors[46ndash48] In Oct 2004 Xiao and Wang [49] explained aproportional tree method to determine the contribution ofan individual generator to loads and also to determinethe nodal-must-run-share In Dec 2005 Wang and Xiao[50] explained proportional tree methods to allocate andprice the transmission usages among the users From 2005to 2008 Lim et al explained power flow tracing and lossallocation method based on loop flow analysis [51ndash53] In2006 Su et al proposed a method to deal with the problemof reactive power decomposition where Graph theory andproportional sharing principle are employed to determine thepower flow tracing sequence [54 55] From 2006 to 2009Abdelkader proposed and explained various power flowtracing techniques and loss allocation algorithms which arebased on physical flow in transmission lines line flowmatrixpower flow topology complex power flow tracing power flowtracing considering loop flows separation of transmissionlosses [56ndash65] In 2011 Nikoukar et al [66] explained thetransmission expansion pricing based on proportional treemethod and economic benefit method
4 Power Flow Tracing TechniquesBased on Circuit Theory
In Feb 1999 Yang and Anderson [67] proposed a power flowcomparison method for power flow tracing and comparethis method with the existing methods In Feb 2001 Liuet al [68 69] proved and extended the proportional sharingrule by network theory and graph theorem In [69] basedon the [68] proportional Sharing principle is incorporatedwith the load-flow tracing method In Nov 2001 Reta andVargas [70] explained a new method for power flow tracingbased on the concept of electric circuit theory in which theinfluence areas are determined In March 2002 Peng andJiang [71 72] explained amethod of power flow tracing basedon the definitions and concepts of total differential and thedefinite integral In [72] Peng and Jiang proposed a principleto trace the complex power flow and the theory proposedin [71] is applied to elementrsquos equivalent circuits to obtain anonlinear relationship between the complex power compo-nents flowing into and out of an element from a powersource In 2002 Chang and Lu [73] explained a node basedstrategy for tracing the current and power flows in a networkIn December 2004 Teng [74] explained method based onthe basic circuit theories equivalent current injection andequivalent impedance to allocate the power flow and loss forderegulated transmission systems In April 2006 Lin et al[75] explained a method to trace the power flow based onthe converged AC power flow solution In December 2007Sulaiman et al [76] explained the power flow tracing methodbased on converged load flow basic circuit theories includingsuperposition theory equivalent impedance and equivalentcurrent injection In June 2007 Meng and Jeyasurya [77]explained a simple transmission pricing scheme using apower flow tracingmethodwhich incorporated transmissionservice cost congestion cost and loss cost In Nov 2009Mohammadi et al [78] explained an approach based on
actual operation of the power network and using a conversionof load model superposition principle In March 2011 Quet al [79] explained a method of power flow tracing whichis based on the concept of the power supply path of sourceunder the constraints of all the basic electrical laws
41 Based on Z-Bus Tracing In Feb 2001 Conejo et al [80]proposed a transmission loss allocation method based onthe Z-bus matrix In Oct 2002 Zhaoxia et al [81] explainedan expression-analysis based power allocation method fortransmission loss allocation in which Generators (loads)are replaced with current sources while loads (generators)are replaced with shunt branches In September 2004Zhao et al [82] explained a redistribution loss allocationmethod for improving Z-Bus loss allocation OnMarch 2005Daniel et wal [83] proposed a method to allocate the activepower transmission loss which is based on the inclusionof the admittances equivalent to bus power injections inthe bus admittance matrix In November 2006 Kazemiand Andami [84] explained the multi-area power systemtransmission loss allocation based on the Z bus matrix InFebruary 2007 Conejo et al [85] explained a method ofnetwork cost allocation based on Z-bus matrix In November2008 Lalitha and Sydulu [86] explained a direct transmissionnetwork cost allocation method by finding the coefficientsof real and reactive power generations and load demandsin the complex line flow From 2008 to 2010 Parastar et alproposed a method to allocate the transmission loss basedon the basic circuit theories equivalent current injectionand modified Z-Bus [87 88] In December 2008 Mustafaet al [89] explained a new method to identify the real powertransfer between generators and load using modified nodalequations In December 2008 Chen and Chu [90] explainedthe redistribution of Z-bus loss allocation for finding the con-tributionattribution of the current flow between generationand load In 2008 Shareef et al [91] explained a method toidentify the real and reactive power transfer between gener-ators and load using modified nodal equations In Sept 2010Kilyeni et al [92] explained a transmission cost allocationmethod using the real and reactive power flow tracing whichis based on the Z-bus system matrix
5 Power Flow Tracing Based onOptimization Techniques
In Nov 2003 Conejo et al [93] explained a procedure for theallocation of the transmission loss cost that is based on deriv-ing a radial networkThis equivalent network is derived solv-ing a simple quadratic optimization problem In Nov 2005Vlachogiannis and Lee [94] explained a method that deter-mined generator contributions to the transmission system byan evolutionary computation technique From 2005 to 2007Abhyankar et al proposed various paradigms of MW powertracing algorithms and real power flow tracing They alsoexplained tracing compliant modified postage stampmethodand transmission service charge based real power flowtracing method Same authors furnished power flow trac-ing methods based on optimization approach and min-max
6 Chinese Journal of Engineering
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
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ortio
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Stable
Stable
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22
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34
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Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
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[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
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[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
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[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
In India themethod which is used so far is postage stampmethod But this method is not distance and direction sen-sitive It is mainly depending on the amount of transactedpower The main advantage of this method is its simplicity inimplementation Due to its various demerits central electric-ity regulatory commissions (CERCs) of India proposed a newtransmission pricing methodology which is the combinationof power flow tracing technique and marginal participationmethodology In the proposed hybrid methodology powerflow tracing is used for selection of the ldquoslack busrdquo while bymarginal participation burden of transmission charges orlosses on each node is computed
This paper presents the review of the variousmethods andtechniques based on power flow tracing which is used for thetransmission embedded cost allocation in the electricitymar-ket For the fair and equitable allocation of the transmissionusage it is necessary to trace the path of power supplied fromthe generator to load though it is difficult but by the power
Incremental transmission
pricing
Short-run Short-runincremental cost
pricing (SRIC)incremental cost
pricing (LRIC)marginal cost
pricing (SRMC)
Long-runLong-runmarginal cost
pricing (LRMC)
Figure 3 Types of incremental transmission pricing methods
Embedded cost transmission
pricing methods
Roll-in methods
Postage stamp method
Contract path method
Network-based methods
MW-Mile method
MVA-Mile method
Flow-based methods
Proportional sharing based
Circuit theory based
Figure 4 Types of embedded transmission pricing methods
flow tracing the flow of electricity can be traced The mainprinciple used in power flow tracing is proportional sharingprinciple According to this principle a network node work asa perfect mixer which follows the Kirchhoff current law thatis total incoming power is equal to total outgoing powerTheprinciple described assumes that each outflow (a flow leavinga node) on a line is dependent only on the voltage gradientand the impedance of the line The contribution of eachinflow (a line flow entering the node) to each outflow is inthe same proportion as the inflow on each line divided by thetotal inflow of all lines at the node However a disadvantageis the fact that the proportional sharing principle for powertransfer between generators and loads is not based on amathematically strict derivation [1]
The rest of the paper is organized as follows fromSections2 to 8 authors present the review of variousmethods based onor using power flow tracing In Section 9 case studies relatedto practical implementation of power flow tracing techniquesare presented Section 10 provides a comparison between var-ious power flow tracing techniques Discussion is also done inthis section followed by the conclusion
2 Power Flow Tracing Techniques Based onProportional Sharing Principle
This approach allocates the charges of each transmission facil-ity to a wheeling transaction based on the extent of use of thatfacility by the transaction This is determined as a function
Chinese Journal of Engineering 3
of magnitude the path and the distance travelled by thetransacted power
21 Topological Generation Distribution Factors Based PowerFlow Tracing (Bialek Tracing) This algorithm works only onlossless flows when the flows at the beginning and end ofeach line are the same The tracing of electricity is done byupstream looking algorithm and downstream looking tracingalgorithm
211 Downstream Looking Algorithm In the downstreamlooking algorithm the nodal power 119875
Note that 119860119889is also sparse and nonsymmetric If 119860minus1
119889
exists then 119875 = 119860minus1119889119875119871and its 119894th element is equal to
119875119894=
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119896
119894 = 1 2 119899 (4)
This equation shows how the nodal power 119875119894distributed
between all the loads in the system On the other hand thesame 119875
119894is equal to the sum of the generation of node 119894 and
all the inflows in lines entering the node Hence the inflow tonode 119894 from line 119894-119895 can be calculated using the proportionalsharing principle as
119889]119894119896119875119894is the topological load distribu-
tion factor that is the portion of 119896th load demand that flowsin line 119894-119895
The generation at a node is also an inflow and can be cal-culated using the proportional sharing principle as
119875119866119894=119875119866119894
119875119894
119875119894=119875119866119894
119875119894
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119870
for 119894 = 1 2 119899(6)
This equation shows that the share of the output of the119894th generator used to supply the 119896th load demand is equal to119875119866119894119875119871119896[119860minus1
119889]119894119896119875119894and can be used to trace where the power of
a particular generator goes to [2]This methodology is proposed by Bialek and Tam in
March 1996 [3] which explained the method for tracing gen-eratorrsquos output They introduce a simple topological methodof tracing the flow of real and reactive power in transmis-sion networks Bialek also explained the topological tracingmethod for apportioning of the total transmission loss toindividual sinks or sources [2 4] whereas in August 1997 [5]explained the topological generation and load distributionfactors for supplement charge allocation in transmissionopen access Also in August 1998 same author [6] explainedthe MW-Mile methodology to allocate the transmissionsupplementary charges to real and reactive power loads
In July 1999 Kattuman et al [7] explained a transmissionloss allocation scheme based on the concept of power flowtracking and also proportionality assumption is analyzed interms of the cooperative game theory Bialek also dealt withthe transmission pricing of cross-border trades [8 9] InOctober 2000 Li et al [10] explained a power flow tracingmethod which is based on topological distribution factorsOn Sep 2001 Su and Liaw [11] explained a newwheeling pric-ing technique called MVA-KM method which applies ACpower flow and considers the apparent power In June 2002Al-Rajhi and Bialek [12] explained the comparison betweenthe marginal and tracing charging of transmission In August2003 Limpasuwan et al [13] investigated the application ofelectricity tracing methodology inThailand In August 2002Bialek [14] explained a range of indices to quantify the incen-tives for gaming the uniform-price spot market In October2002 Shirani and Siahkali [15] explained the application ofpower flow tracing algorithm to allocate the congestion costin the pool market In 2004 Limpasuwan et al [16] explainedthe TransmissionUse of System charge (TUOS)methodologysuggested by Price water house Cooper (PwC) and makes acomparison with a transmission pricing method based on acombination of the electricity tracing and Long Run AverageIncremental Cost (LRAIC) InMay 2004 Kattuman et al [17]explained that the allocation done by the tracing methodol-ogy is equal to the Shapely value of an equivalent cooperativegame In June 2003 Bialek and Ziemianek [18] explained acomparison between the graph based tracing algorithm withthe algorithm based on the solution of linear equations anddeclared that the algorithms are conceptually the same Alsoa practical algorithm is presented to eliminate the cycles fromthe diagraph of flows In July 2004 Bialek and Kattuman [19]rationalized proportional sharing principle of cooperativegame theory and information theory They concluded thatShapely value validates the proportional sharing rule In June2005 Adsoongnoen et al [20] enlightened a unified trans-mission pricing based on electricity tracing methodology
4 Chinese Journal of Engineering
of cross border trades In [21] Nallagownden et al extendsthe methods of proportional sharing and put forward analgorithm to determine the extent of use of a transmissionpath and associated losses In December 2009 Pal et al [22]explained an analytical approach for calculating the incentivecharge for individual participant when the multiple wheelingtransactions are considered simultaneously In May 2010Achayuthakan et al [23] furnished tracing in a new way ofrepresenting the inverted tracing upstream and downstreamdistribution matrices in the form of matrix power seriesIn June 2010 Nallagownden and Lee [24] explained tracingmethodology for the purpose of eliminating problems relatedto the Marginal pricing of transmission costs In July 2010Naresh et al [25] explained the Genetic algorithm basedapproach for power flow tracing and compared with existingapproaches
22 Factors Based on Generators Domain (Kirschen Tracing)The domain of a generator represents a subset 119873 of 119899 buseswhich are supplied by this generator A particular bus belongsto a generator domain if there is a ldquotracerdquo through the trans-mission network for which the direction of power flow isfrom the generator to the bus The generator common is asubset of ldquoneighboredrdquo buses from the subset 119873 which aresupplied by the same generators The subsets of buses whichare not connected andnot supplied by the same generators aretreated as separate commons A bus therefore belongs to onlyone common The branches can be divided in two groupsthose which connect two buses which are part of the samecommon (the internal branches) and those which connecttwo buses which belong to different commons (the externalbranches) External branches are called a link
Knowing the direction of the power flow through thenetwork elements and the commons and the links beingdefined the graph theory can be applied The state graphof the problem studied can be obtained using the followingrepresentation conventions the graph vertices correspond tothe commons graph arcs correspond to links between thecommons and the arc orientation is given by the power flowsThe state graph provides only a qualitative view of the powersystem The inflow of a common is defined as the sum of theinjected power by the sources connected to buses located inthis common and the power imported in this common fromother common by links
The calculus of generator contribution to various com-mons (119863 is the set of commons) is made in the followingmanner [26]
119875119894
119895119896= 119908119894
119895sdot 119875119895119896
119908119894
119896=
sum119895isin119863
119875119894
119895119896
119875119896
119896 isin 119863
119875119896= sum
119895isin119863
119875119895119896 119896 isin 119863 119895
(7)
where119908119894119895is the contribution of the 119894 generator to the load and
the outflow of the 119895 common 119908119894119896is the contribution of the 119894
generator to the load and the outflow of the 119896 common 119875119895119896
is the flow on the link between the 119895 and 119896 commons 119875119894119895119896is
the flow on the link between the 119895 and 119896 commons due to the119894 generator 119875
119896is the inflow of the 119896 common
In February 1997 Kirschen et al [26] explained a powerflow tracing method based on the proportional sharingassumption which introduces the concept of domains com-mons and links On the same track a case study has beendiscussed for normal and network contingency conditionsin [27] by Thukaram et al June 2006 In May 1998 Strbacet al [28] explained the method based on the generatordomain distribution factors to allocate the usage of branchto the load and generators in the maximum flow conditionsIn November 1999 Kirschen and Strbac [29] explained themethod of real and reactive power tracing by converting theall power injections into real and imaginary currents
23 Nodal Generation Distribution Factors In Nov 2000Gubina and Orgie [30] explained the method to determinethe generatorsrsquo contribution to a particular load by using thenodal generation distribution factors (NGDF-s) InDec 2000Grgic and Gubina [31] explained the distribution factorapproach for the reactive power flow tracing Pantos et al in2003-04 worked on transaction based transmission servicepricing techniques based on the Nodal Generation Distribu-tion factor and also proposed an Ex-Ante transmission pric-ing technique They also proposed a new power flow tracingmethod and explained a transmission service pricing Thesame authors further proposed a pattern based transmissionpricing technique [32ndash36]
3 Power Flow Tracing TechniquesBased on Graph Theory
In January 2000 Sun et al [37] explained a new method fortracing AC power flows where the graph theory is used tosolve the tracing problem In April 2000 Xi-Fan et al [38]explained a very efficient algorithm for power flow tracingby proposing two current decomposition axioms in whichGraph theory is used whereas Wei et al [39] used graph the-ory to analyze real power transfer between individual gener-ators and loads In Aug 2000Wu et al [40] explained the useof graph theory to calculate the contributions of individualgenerators and loads to line flows and the real power transferbetween individual generators and loads In March 2001Chai and Sekar [41] explained a methodology using graphtheory to determine the specific generator contributions todifferent loads and the transmission system usage of differentutilities In Dec 2001 Wei et al [42] proposed that the graphtheory is used to detect the existence of circulating powerthen the optimal power flow approach is applied to eliminatecirculating power From 2003 to 2009 Xie et al proposedand explained the power flow tracing algorithms foundedon extended incidence matrix and matrix multiplicationconsidering loop flows [1 43 44] In July 2003 Ghasemi et al[45] explained the closed-form solution for tracing problemby presenting a formula which is obtained by using bothproportionality and averaging criteria From 2004 to 2010Mustafa et al proposed power flow tracing method basedon tracing currents and complex power flows They also
Chinese Journal of Engineering 5
proposed a proportional tree method based method for trac-ing A comparison has also done by the same authors[46ndash48] In Oct 2004 Xiao and Wang [49] explained aproportional tree method to determine the contribution ofan individual generator to loads and also to determinethe nodal-must-run-share In Dec 2005 Wang and Xiao[50] explained proportional tree methods to allocate andprice the transmission usages among the users From 2005to 2008 Lim et al explained power flow tracing and lossallocation method based on loop flow analysis [51ndash53] In2006 Su et al proposed a method to deal with the problemof reactive power decomposition where Graph theory andproportional sharing principle are employed to determine thepower flow tracing sequence [54 55] From 2006 to 2009Abdelkader proposed and explained various power flowtracing techniques and loss allocation algorithms which arebased on physical flow in transmission lines line flowmatrixpower flow topology complex power flow tracing power flowtracing considering loop flows separation of transmissionlosses [56ndash65] In 2011 Nikoukar et al [66] explained thetransmission expansion pricing based on proportional treemethod and economic benefit method
4 Power Flow Tracing TechniquesBased on Circuit Theory
In Feb 1999 Yang and Anderson [67] proposed a power flowcomparison method for power flow tracing and comparethis method with the existing methods In Feb 2001 Liuet al [68 69] proved and extended the proportional sharingrule by network theory and graph theorem In [69] basedon the [68] proportional Sharing principle is incorporatedwith the load-flow tracing method In Nov 2001 Reta andVargas [70] explained a new method for power flow tracingbased on the concept of electric circuit theory in which theinfluence areas are determined In March 2002 Peng andJiang [71 72] explained amethod of power flow tracing basedon the definitions and concepts of total differential and thedefinite integral In [72] Peng and Jiang proposed a principleto trace the complex power flow and the theory proposedin [71] is applied to elementrsquos equivalent circuits to obtain anonlinear relationship between the complex power compo-nents flowing into and out of an element from a powersource In 2002 Chang and Lu [73] explained a node basedstrategy for tracing the current and power flows in a networkIn December 2004 Teng [74] explained method based onthe basic circuit theories equivalent current injection andequivalent impedance to allocate the power flow and loss forderegulated transmission systems In April 2006 Lin et al[75] explained a method to trace the power flow based onthe converged AC power flow solution In December 2007Sulaiman et al [76] explained the power flow tracing methodbased on converged load flow basic circuit theories includingsuperposition theory equivalent impedance and equivalentcurrent injection In June 2007 Meng and Jeyasurya [77]explained a simple transmission pricing scheme using apower flow tracingmethodwhich incorporated transmissionservice cost congestion cost and loss cost In Nov 2009Mohammadi et al [78] explained an approach based on
actual operation of the power network and using a conversionof load model superposition principle In March 2011 Quet al [79] explained a method of power flow tracing whichis based on the concept of the power supply path of sourceunder the constraints of all the basic electrical laws
41 Based on Z-Bus Tracing In Feb 2001 Conejo et al [80]proposed a transmission loss allocation method based onthe Z-bus matrix In Oct 2002 Zhaoxia et al [81] explainedan expression-analysis based power allocation method fortransmission loss allocation in which Generators (loads)are replaced with current sources while loads (generators)are replaced with shunt branches In September 2004Zhao et al [82] explained a redistribution loss allocationmethod for improving Z-Bus loss allocation OnMarch 2005Daniel et wal [83] proposed a method to allocate the activepower transmission loss which is based on the inclusionof the admittances equivalent to bus power injections inthe bus admittance matrix In November 2006 Kazemiand Andami [84] explained the multi-area power systemtransmission loss allocation based on the Z bus matrix InFebruary 2007 Conejo et al [85] explained a method ofnetwork cost allocation based on Z-bus matrix In November2008 Lalitha and Sydulu [86] explained a direct transmissionnetwork cost allocation method by finding the coefficientsof real and reactive power generations and load demandsin the complex line flow From 2008 to 2010 Parastar et alproposed a method to allocate the transmission loss basedon the basic circuit theories equivalent current injectionand modified Z-Bus [87 88] In December 2008 Mustafaet al [89] explained a new method to identify the real powertransfer between generators and load using modified nodalequations In December 2008 Chen and Chu [90] explainedthe redistribution of Z-bus loss allocation for finding the con-tributionattribution of the current flow between generationand load In 2008 Shareef et al [91] explained a method toidentify the real and reactive power transfer between gener-ators and load using modified nodal equations In Sept 2010Kilyeni et al [92] explained a transmission cost allocationmethod using the real and reactive power flow tracing whichis based on the Z-bus system matrix
5 Power Flow Tracing Based onOptimization Techniques
In Nov 2003 Conejo et al [93] explained a procedure for theallocation of the transmission loss cost that is based on deriv-ing a radial networkThis equivalent network is derived solv-ing a simple quadratic optimization problem In Nov 2005Vlachogiannis and Lee [94] explained a method that deter-mined generator contributions to the transmission system byan evolutionary computation technique From 2005 to 2007Abhyankar et al proposed various paradigms of MW powertracing algorithms and real power flow tracing They alsoexplained tracing compliant modified postage stampmethodand transmission service charge based real power flowtracing method Same authors furnished power flow trac-ing methods based on optimization approach and min-max
6 Chinese Journal of Engineering
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Xie J Zhou and W Li ldquoAnalytical model and algorithm fortracing active power flow based on extended incidence matrixrdquoElectric Power Systems Research vol 79 no 2 pp 399ndash4052009
[2] J Bialek ldquoTracing the flowof electricityrdquo IEE ProceedingsmdashGen-eration Transmission and Distribution vol 143 no 4 pp 313ndash320 1996
[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
[5] J Bialek ldquoTopological generation and load distribution factorsfor supplement charge allocation in transmission open accessrdquoIEEE Transactions on Power Systems vol 12 no 3 pp 1185ndash11931997
[6] J Bialek ldquoAllocation of transmission supplementary charge toreal and reactive loadsrdquo IEEE Transactions on Power Systemsvol 13 no 3 pp 749ndash754 1998
[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
[8] J W Bialek ldquoTracing-based unifying framework for transmis-sion pricing of cross-border trades in Europerdquo in Proceedings ofthe International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT rsquo00) pp 532ndash537London UK April 2000
[9] J W Bialek S Ziemianek and R Wallace ldquoA methodology forallocating transmission losses due to cross-border tradesrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1255ndash12622004
[10] Y Z Li S H Zhang Q Liu and Z Qu ldquoElectricity tracingmethod of generation and loss cost allocationrdquo in Proceedings
of the 5th International Conference on Advances in Power SystemControl Operation and Management (APSCOM rsquo00) HongKong China October 2000
[11] C T Su and J H Liaw ldquoPower wheeling pricing using powertracing andMVA-KMmethodrdquo in Proceedings of the IEEE PortoPower Tech vol 1 Porto Portugal September 2001
[12] A N Al-Rajhi and J W Bialek ldquoMarginal and tracing pricingof transmission an empirical comparisonrdquo in Proceedings of the14th Power Systems Computation Conference session 27 paper5 Sevilla Spain June 2002
[13] T Limpasuwan J W Bialek W Ongsakul and B Limmee-chokchai ldquoA proposal for annual power fee in Thailand basedon electricity tracing methodologyrdquo Electric Power SystemsResearch vol 64 no 3 pp 219ndash226 2003
[14] J W Bialek ldquoGaming the uniform-price spot market quantita-tive analysisrdquo IEEE Transactions on Power Systems vol 17 no 3pp 768ndash773 2002
[15] A R Shirani and H Siahkali ldquoTraceable flow method in deter-mination of congestion cost assignment in open access powersystem networkrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exhibition 2002 Asia Pacificvol 2 pp 734ndash738 October 2002
[16] T Limpasuwan JW BialekW Ongsakul and B Limmeechok-chai ldquoA proposal for transmission pricingmethodology inThai-land based on electricity tracing and long-run average incre-mental costrdquo Energy Policy vol 32 no 3 pp 301ndash308 2004
[17] PAKattuman R J Green and JW Bialek ldquoAllocating electric-ity transmission costs through tracing a game-theoretic ration-alerdquoOperations Research Letters vol 32 no 2 pp 114ndash120 2004
[18] JW Bialek and S Ziemianek ldquoTracing based transmission pric-ing of cross-border trades fundamentals and circular flowsrdquo inProceedings of the IEEE Bologna Power Tech Conference vol 3Bologna Italy June 2003
[19] J W Bialek and P A Kattuman ldquoProportional sharing assump-tion in tracing methodologyrdquo IEE ProceedingsmdashGenerationTransmission andDistribution vol 151 no 4 pp 526ndash532 2004
[20] C Adsoongnoen W Ongsakul and H J Haubrich ldquoAllocationof transmission losses and network charges for cross bordertrades in ASEAN power grid based on tracing methodologyrdquoin Proceedings of the IEEE Russia Power Tech pp 1ndash6 StPetersburg Russia June 2005
[21] P Nallagownden R N Mukerjee and S Masri ldquoPower tracingand prediction of losses for deregulated transmission systemrdquoInternational Journal of Electrical and Computer Sciences vol10 no 1
[22] K Pal M Pandit and L Srivastava ldquoIncentive charge calcula-tion for open access transmission systemrdquo in Proceedings of theInternational Conference on Power Systems (ICPS rsquo09) pp 1ndash6Kharagpur India December 2009
[23] C Achayuthakan C J Dent J W Bialek and W OngsakulldquoElectricity tracing in systems with and without circulatingflows physical insights and mathematical proofsrdquo IEEE Trans-actions on Power Systems vol 25 no 2 pp 1078ndash1087 2010
[24] P Nallagownden and T Y Lee ldquoApplication of regression andtracing methodology for efficient operation of generators andretailers in a deregulated systemrdquo in Proceedings of the 4thInternational Power Engineering and Optimization Conference(PEOCO rsquo10) pp 267ndash273 Selangor Malaysia June 2010
[25] B Naresh M S Kumari and M Sydulu ldquoTransmission costallocation using power flow tracing and genetic algorithmrdquo inProceedings of the 5th IEEE International Conference on Intelli-gent Systems (IS rsquo10) pp 432ndash438 London UK July 2010
10 Chinese Journal of Engineering
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
of magnitude the path and the distance travelled by thetransacted power
21 Topological Generation Distribution Factors Based PowerFlow Tracing (Bialek Tracing) This algorithm works only onlossless flows when the flows at the beginning and end ofeach line are the same The tracing of electricity is done byupstream looking algorithm and downstream looking tracingalgorithm
211 Downstream Looking Algorithm In the downstreamlooking algorithm the nodal power 119875
Note that 119860119889is also sparse and nonsymmetric If 119860minus1
119889
exists then 119875 = 119860minus1119889119875119871and its 119894th element is equal to
119875119894=
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119896
119894 = 1 2 119899 (4)
This equation shows how the nodal power 119875119894distributed
between all the loads in the system On the other hand thesame 119875
119894is equal to the sum of the generation of node 119894 and
all the inflows in lines entering the node Hence the inflow tonode 119894 from line 119894-119895 can be calculated using the proportionalsharing principle as
119889]119894119896119875119894is the topological load distribu-
tion factor that is the portion of 119896th load demand that flowsin line 119894-119895
The generation at a node is also an inflow and can be cal-culated using the proportional sharing principle as
119875119866119894=119875119866119894
119875119894
119875119894=119875119866119894
119875119894
119899
sum
119896=1
[119860minus1
119889]119894119896119875119871119870
for 119894 = 1 2 119899(6)
This equation shows that the share of the output of the119894th generator used to supply the 119896th load demand is equal to119875119866119894119875119871119896[119860minus1
119889]119894119896119875119894and can be used to trace where the power of
a particular generator goes to [2]This methodology is proposed by Bialek and Tam in
March 1996 [3] which explained the method for tracing gen-eratorrsquos output They introduce a simple topological methodof tracing the flow of real and reactive power in transmis-sion networks Bialek also explained the topological tracingmethod for apportioning of the total transmission loss toindividual sinks or sources [2 4] whereas in August 1997 [5]explained the topological generation and load distributionfactors for supplement charge allocation in transmissionopen access Also in August 1998 same author [6] explainedthe MW-Mile methodology to allocate the transmissionsupplementary charges to real and reactive power loads
In July 1999 Kattuman et al [7] explained a transmissionloss allocation scheme based on the concept of power flowtracking and also proportionality assumption is analyzed interms of the cooperative game theory Bialek also dealt withthe transmission pricing of cross-border trades [8 9] InOctober 2000 Li et al [10] explained a power flow tracingmethod which is based on topological distribution factorsOn Sep 2001 Su and Liaw [11] explained a newwheeling pric-ing technique called MVA-KM method which applies ACpower flow and considers the apparent power In June 2002Al-Rajhi and Bialek [12] explained the comparison betweenthe marginal and tracing charging of transmission In August2003 Limpasuwan et al [13] investigated the application ofelectricity tracing methodology inThailand In August 2002Bialek [14] explained a range of indices to quantify the incen-tives for gaming the uniform-price spot market In October2002 Shirani and Siahkali [15] explained the application ofpower flow tracing algorithm to allocate the congestion costin the pool market In 2004 Limpasuwan et al [16] explainedthe TransmissionUse of System charge (TUOS)methodologysuggested by Price water house Cooper (PwC) and makes acomparison with a transmission pricing method based on acombination of the electricity tracing and Long Run AverageIncremental Cost (LRAIC) InMay 2004 Kattuman et al [17]explained that the allocation done by the tracing methodol-ogy is equal to the Shapely value of an equivalent cooperativegame In June 2003 Bialek and Ziemianek [18] explained acomparison between the graph based tracing algorithm withthe algorithm based on the solution of linear equations anddeclared that the algorithms are conceptually the same Alsoa practical algorithm is presented to eliminate the cycles fromthe diagraph of flows In July 2004 Bialek and Kattuman [19]rationalized proportional sharing principle of cooperativegame theory and information theory They concluded thatShapely value validates the proportional sharing rule In June2005 Adsoongnoen et al [20] enlightened a unified trans-mission pricing based on electricity tracing methodology
4 Chinese Journal of Engineering
of cross border trades In [21] Nallagownden et al extendsthe methods of proportional sharing and put forward analgorithm to determine the extent of use of a transmissionpath and associated losses In December 2009 Pal et al [22]explained an analytical approach for calculating the incentivecharge for individual participant when the multiple wheelingtransactions are considered simultaneously In May 2010Achayuthakan et al [23] furnished tracing in a new way ofrepresenting the inverted tracing upstream and downstreamdistribution matrices in the form of matrix power seriesIn June 2010 Nallagownden and Lee [24] explained tracingmethodology for the purpose of eliminating problems relatedto the Marginal pricing of transmission costs In July 2010Naresh et al [25] explained the Genetic algorithm basedapproach for power flow tracing and compared with existingapproaches
22 Factors Based on Generators Domain (Kirschen Tracing)The domain of a generator represents a subset 119873 of 119899 buseswhich are supplied by this generator A particular bus belongsto a generator domain if there is a ldquotracerdquo through the trans-mission network for which the direction of power flow isfrom the generator to the bus The generator common is asubset of ldquoneighboredrdquo buses from the subset 119873 which aresupplied by the same generators The subsets of buses whichare not connected andnot supplied by the same generators aretreated as separate commons A bus therefore belongs to onlyone common The branches can be divided in two groupsthose which connect two buses which are part of the samecommon (the internal branches) and those which connecttwo buses which belong to different commons (the externalbranches) External branches are called a link
Knowing the direction of the power flow through thenetwork elements and the commons and the links beingdefined the graph theory can be applied The state graphof the problem studied can be obtained using the followingrepresentation conventions the graph vertices correspond tothe commons graph arcs correspond to links between thecommons and the arc orientation is given by the power flowsThe state graph provides only a qualitative view of the powersystem The inflow of a common is defined as the sum of theinjected power by the sources connected to buses located inthis common and the power imported in this common fromother common by links
The calculus of generator contribution to various com-mons (119863 is the set of commons) is made in the followingmanner [26]
119875119894
119895119896= 119908119894
119895sdot 119875119895119896
119908119894
119896=
sum119895isin119863
119875119894
119895119896
119875119896
119896 isin 119863
119875119896= sum
119895isin119863
119875119895119896 119896 isin 119863 119895
(7)
where119908119894119895is the contribution of the 119894 generator to the load and
the outflow of the 119895 common 119908119894119896is the contribution of the 119894
generator to the load and the outflow of the 119896 common 119875119895119896
is the flow on the link between the 119895 and 119896 commons 119875119894119895119896is
the flow on the link between the 119895 and 119896 commons due to the119894 generator 119875
119896is the inflow of the 119896 common
In February 1997 Kirschen et al [26] explained a powerflow tracing method based on the proportional sharingassumption which introduces the concept of domains com-mons and links On the same track a case study has beendiscussed for normal and network contingency conditionsin [27] by Thukaram et al June 2006 In May 1998 Strbacet al [28] explained the method based on the generatordomain distribution factors to allocate the usage of branchto the load and generators in the maximum flow conditionsIn November 1999 Kirschen and Strbac [29] explained themethod of real and reactive power tracing by converting theall power injections into real and imaginary currents
23 Nodal Generation Distribution Factors In Nov 2000Gubina and Orgie [30] explained the method to determinethe generatorsrsquo contribution to a particular load by using thenodal generation distribution factors (NGDF-s) InDec 2000Grgic and Gubina [31] explained the distribution factorapproach for the reactive power flow tracing Pantos et al in2003-04 worked on transaction based transmission servicepricing techniques based on the Nodal Generation Distribu-tion factor and also proposed an Ex-Ante transmission pric-ing technique They also proposed a new power flow tracingmethod and explained a transmission service pricing Thesame authors further proposed a pattern based transmissionpricing technique [32ndash36]
3 Power Flow Tracing TechniquesBased on Graph Theory
In January 2000 Sun et al [37] explained a new method fortracing AC power flows where the graph theory is used tosolve the tracing problem In April 2000 Xi-Fan et al [38]explained a very efficient algorithm for power flow tracingby proposing two current decomposition axioms in whichGraph theory is used whereas Wei et al [39] used graph the-ory to analyze real power transfer between individual gener-ators and loads In Aug 2000Wu et al [40] explained the useof graph theory to calculate the contributions of individualgenerators and loads to line flows and the real power transferbetween individual generators and loads In March 2001Chai and Sekar [41] explained a methodology using graphtheory to determine the specific generator contributions todifferent loads and the transmission system usage of differentutilities In Dec 2001 Wei et al [42] proposed that the graphtheory is used to detect the existence of circulating powerthen the optimal power flow approach is applied to eliminatecirculating power From 2003 to 2009 Xie et al proposedand explained the power flow tracing algorithms foundedon extended incidence matrix and matrix multiplicationconsidering loop flows [1 43 44] In July 2003 Ghasemi et al[45] explained the closed-form solution for tracing problemby presenting a formula which is obtained by using bothproportionality and averaging criteria From 2004 to 2010Mustafa et al proposed power flow tracing method basedon tracing currents and complex power flows They also
Chinese Journal of Engineering 5
proposed a proportional tree method based method for trac-ing A comparison has also done by the same authors[46ndash48] In Oct 2004 Xiao and Wang [49] explained aproportional tree method to determine the contribution ofan individual generator to loads and also to determinethe nodal-must-run-share In Dec 2005 Wang and Xiao[50] explained proportional tree methods to allocate andprice the transmission usages among the users From 2005to 2008 Lim et al explained power flow tracing and lossallocation method based on loop flow analysis [51ndash53] In2006 Su et al proposed a method to deal with the problemof reactive power decomposition where Graph theory andproportional sharing principle are employed to determine thepower flow tracing sequence [54 55] From 2006 to 2009Abdelkader proposed and explained various power flowtracing techniques and loss allocation algorithms which arebased on physical flow in transmission lines line flowmatrixpower flow topology complex power flow tracing power flowtracing considering loop flows separation of transmissionlosses [56ndash65] In 2011 Nikoukar et al [66] explained thetransmission expansion pricing based on proportional treemethod and economic benefit method
4 Power Flow Tracing TechniquesBased on Circuit Theory
In Feb 1999 Yang and Anderson [67] proposed a power flowcomparison method for power flow tracing and comparethis method with the existing methods In Feb 2001 Liuet al [68 69] proved and extended the proportional sharingrule by network theory and graph theorem In [69] basedon the [68] proportional Sharing principle is incorporatedwith the load-flow tracing method In Nov 2001 Reta andVargas [70] explained a new method for power flow tracingbased on the concept of electric circuit theory in which theinfluence areas are determined In March 2002 Peng andJiang [71 72] explained amethod of power flow tracing basedon the definitions and concepts of total differential and thedefinite integral In [72] Peng and Jiang proposed a principleto trace the complex power flow and the theory proposedin [71] is applied to elementrsquos equivalent circuits to obtain anonlinear relationship between the complex power compo-nents flowing into and out of an element from a powersource In 2002 Chang and Lu [73] explained a node basedstrategy for tracing the current and power flows in a networkIn December 2004 Teng [74] explained method based onthe basic circuit theories equivalent current injection andequivalent impedance to allocate the power flow and loss forderegulated transmission systems In April 2006 Lin et al[75] explained a method to trace the power flow based onthe converged AC power flow solution In December 2007Sulaiman et al [76] explained the power flow tracing methodbased on converged load flow basic circuit theories includingsuperposition theory equivalent impedance and equivalentcurrent injection In June 2007 Meng and Jeyasurya [77]explained a simple transmission pricing scheme using apower flow tracingmethodwhich incorporated transmissionservice cost congestion cost and loss cost In Nov 2009Mohammadi et al [78] explained an approach based on
actual operation of the power network and using a conversionof load model superposition principle In March 2011 Quet al [79] explained a method of power flow tracing whichis based on the concept of the power supply path of sourceunder the constraints of all the basic electrical laws
41 Based on Z-Bus Tracing In Feb 2001 Conejo et al [80]proposed a transmission loss allocation method based onthe Z-bus matrix In Oct 2002 Zhaoxia et al [81] explainedan expression-analysis based power allocation method fortransmission loss allocation in which Generators (loads)are replaced with current sources while loads (generators)are replaced with shunt branches In September 2004Zhao et al [82] explained a redistribution loss allocationmethod for improving Z-Bus loss allocation OnMarch 2005Daniel et wal [83] proposed a method to allocate the activepower transmission loss which is based on the inclusionof the admittances equivalent to bus power injections inthe bus admittance matrix In November 2006 Kazemiand Andami [84] explained the multi-area power systemtransmission loss allocation based on the Z bus matrix InFebruary 2007 Conejo et al [85] explained a method ofnetwork cost allocation based on Z-bus matrix In November2008 Lalitha and Sydulu [86] explained a direct transmissionnetwork cost allocation method by finding the coefficientsof real and reactive power generations and load demandsin the complex line flow From 2008 to 2010 Parastar et alproposed a method to allocate the transmission loss basedon the basic circuit theories equivalent current injectionand modified Z-Bus [87 88] In December 2008 Mustafaet al [89] explained a new method to identify the real powertransfer between generators and load using modified nodalequations In December 2008 Chen and Chu [90] explainedthe redistribution of Z-bus loss allocation for finding the con-tributionattribution of the current flow between generationand load In 2008 Shareef et al [91] explained a method toidentify the real and reactive power transfer between gener-ators and load using modified nodal equations In Sept 2010Kilyeni et al [92] explained a transmission cost allocationmethod using the real and reactive power flow tracing whichis based on the Z-bus system matrix
5 Power Flow Tracing Based onOptimization Techniques
In Nov 2003 Conejo et al [93] explained a procedure for theallocation of the transmission loss cost that is based on deriv-ing a radial networkThis equivalent network is derived solv-ing a simple quadratic optimization problem In Nov 2005Vlachogiannis and Lee [94] explained a method that deter-mined generator contributions to the transmission system byan evolutionary computation technique From 2005 to 2007Abhyankar et al proposed various paradigms of MW powertracing algorithms and real power flow tracing They alsoexplained tracing compliant modified postage stampmethodand transmission service charge based real power flowtracing method Same authors furnished power flow trac-ing methods based on optimization approach and min-max
6 Chinese Journal of Engineering
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Xie J Zhou and W Li ldquoAnalytical model and algorithm fortracing active power flow based on extended incidence matrixrdquoElectric Power Systems Research vol 79 no 2 pp 399ndash4052009
[2] J Bialek ldquoTracing the flowof electricityrdquo IEE ProceedingsmdashGen-eration Transmission and Distribution vol 143 no 4 pp 313ndash320 1996
[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
[5] J Bialek ldquoTopological generation and load distribution factorsfor supplement charge allocation in transmission open accessrdquoIEEE Transactions on Power Systems vol 12 no 3 pp 1185ndash11931997
[6] J Bialek ldquoAllocation of transmission supplementary charge toreal and reactive loadsrdquo IEEE Transactions on Power Systemsvol 13 no 3 pp 749ndash754 1998
[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
[8] J W Bialek ldquoTracing-based unifying framework for transmis-sion pricing of cross-border trades in Europerdquo in Proceedings ofthe International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT rsquo00) pp 532ndash537London UK April 2000
[9] J W Bialek S Ziemianek and R Wallace ldquoA methodology forallocating transmission losses due to cross-border tradesrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1255ndash12622004
[10] Y Z Li S H Zhang Q Liu and Z Qu ldquoElectricity tracingmethod of generation and loss cost allocationrdquo in Proceedings
of the 5th International Conference on Advances in Power SystemControl Operation and Management (APSCOM rsquo00) HongKong China October 2000
[11] C T Su and J H Liaw ldquoPower wheeling pricing using powertracing andMVA-KMmethodrdquo in Proceedings of the IEEE PortoPower Tech vol 1 Porto Portugal September 2001
[12] A N Al-Rajhi and J W Bialek ldquoMarginal and tracing pricingof transmission an empirical comparisonrdquo in Proceedings of the14th Power Systems Computation Conference session 27 paper5 Sevilla Spain June 2002
[13] T Limpasuwan J W Bialek W Ongsakul and B Limmee-chokchai ldquoA proposal for annual power fee in Thailand basedon electricity tracing methodologyrdquo Electric Power SystemsResearch vol 64 no 3 pp 219ndash226 2003
[14] J W Bialek ldquoGaming the uniform-price spot market quantita-tive analysisrdquo IEEE Transactions on Power Systems vol 17 no 3pp 768ndash773 2002
[15] A R Shirani and H Siahkali ldquoTraceable flow method in deter-mination of congestion cost assignment in open access powersystem networkrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exhibition 2002 Asia Pacificvol 2 pp 734ndash738 October 2002
[16] T Limpasuwan JW BialekW Ongsakul and B Limmeechok-chai ldquoA proposal for transmission pricingmethodology inThai-land based on electricity tracing and long-run average incre-mental costrdquo Energy Policy vol 32 no 3 pp 301ndash308 2004
[17] PAKattuman R J Green and JW Bialek ldquoAllocating electric-ity transmission costs through tracing a game-theoretic ration-alerdquoOperations Research Letters vol 32 no 2 pp 114ndash120 2004
[18] JW Bialek and S Ziemianek ldquoTracing based transmission pric-ing of cross-border trades fundamentals and circular flowsrdquo inProceedings of the IEEE Bologna Power Tech Conference vol 3Bologna Italy June 2003
[19] J W Bialek and P A Kattuman ldquoProportional sharing assump-tion in tracing methodologyrdquo IEE ProceedingsmdashGenerationTransmission andDistribution vol 151 no 4 pp 526ndash532 2004
[20] C Adsoongnoen W Ongsakul and H J Haubrich ldquoAllocationof transmission losses and network charges for cross bordertrades in ASEAN power grid based on tracing methodologyrdquoin Proceedings of the IEEE Russia Power Tech pp 1ndash6 StPetersburg Russia June 2005
[21] P Nallagownden R N Mukerjee and S Masri ldquoPower tracingand prediction of losses for deregulated transmission systemrdquoInternational Journal of Electrical and Computer Sciences vol10 no 1
[22] K Pal M Pandit and L Srivastava ldquoIncentive charge calcula-tion for open access transmission systemrdquo in Proceedings of theInternational Conference on Power Systems (ICPS rsquo09) pp 1ndash6Kharagpur India December 2009
[23] C Achayuthakan C J Dent J W Bialek and W OngsakulldquoElectricity tracing in systems with and without circulatingflows physical insights and mathematical proofsrdquo IEEE Trans-actions on Power Systems vol 25 no 2 pp 1078ndash1087 2010
[24] P Nallagownden and T Y Lee ldquoApplication of regression andtracing methodology for efficient operation of generators andretailers in a deregulated systemrdquo in Proceedings of the 4thInternational Power Engineering and Optimization Conference(PEOCO rsquo10) pp 267ndash273 Selangor Malaysia June 2010
[25] B Naresh M S Kumari and M Sydulu ldquoTransmission costallocation using power flow tracing and genetic algorithmrdquo inProceedings of the 5th IEEE International Conference on Intelli-gent Systems (IS rsquo10) pp 432ndash438 London UK July 2010
10 Chinese Journal of Engineering
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
of cross border trades In [21] Nallagownden et al extendsthe methods of proportional sharing and put forward analgorithm to determine the extent of use of a transmissionpath and associated losses In December 2009 Pal et al [22]explained an analytical approach for calculating the incentivecharge for individual participant when the multiple wheelingtransactions are considered simultaneously In May 2010Achayuthakan et al [23] furnished tracing in a new way ofrepresenting the inverted tracing upstream and downstreamdistribution matrices in the form of matrix power seriesIn June 2010 Nallagownden and Lee [24] explained tracingmethodology for the purpose of eliminating problems relatedto the Marginal pricing of transmission costs In July 2010Naresh et al [25] explained the Genetic algorithm basedapproach for power flow tracing and compared with existingapproaches
22 Factors Based on Generators Domain (Kirschen Tracing)The domain of a generator represents a subset 119873 of 119899 buseswhich are supplied by this generator A particular bus belongsto a generator domain if there is a ldquotracerdquo through the trans-mission network for which the direction of power flow isfrom the generator to the bus The generator common is asubset of ldquoneighboredrdquo buses from the subset 119873 which aresupplied by the same generators The subsets of buses whichare not connected andnot supplied by the same generators aretreated as separate commons A bus therefore belongs to onlyone common The branches can be divided in two groupsthose which connect two buses which are part of the samecommon (the internal branches) and those which connecttwo buses which belong to different commons (the externalbranches) External branches are called a link
Knowing the direction of the power flow through thenetwork elements and the commons and the links beingdefined the graph theory can be applied The state graphof the problem studied can be obtained using the followingrepresentation conventions the graph vertices correspond tothe commons graph arcs correspond to links between thecommons and the arc orientation is given by the power flowsThe state graph provides only a qualitative view of the powersystem The inflow of a common is defined as the sum of theinjected power by the sources connected to buses located inthis common and the power imported in this common fromother common by links
The calculus of generator contribution to various com-mons (119863 is the set of commons) is made in the followingmanner [26]
119875119894
119895119896= 119908119894
119895sdot 119875119895119896
119908119894
119896=
sum119895isin119863
119875119894
119895119896
119875119896
119896 isin 119863
119875119896= sum
119895isin119863
119875119895119896 119896 isin 119863 119895
(7)
where119908119894119895is the contribution of the 119894 generator to the load and
the outflow of the 119895 common 119908119894119896is the contribution of the 119894
generator to the load and the outflow of the 119896 common 119875119895119896
is the flow on the link between the 119895 and 119896 commons 119875119894119895119896is
the flow on the link between the 119895 and 119896 commons due to the119894 generator 119875
119896is the inflow of the 119896 common
In February 1997 Kirschen et al [26] explained a powerflow tracing method based on the proportional sharingassumption which introduces the concept of domains com-mons and links On the same track a case study has beendiscussed for normal and network contingency conditionsin [27] by Thukaram et al June 2006 In May 1998 Strbacet al [28] explained the method based on the generatordomain distribution factors to allocate the usage of branchto the load and generators in the maximum flow conditionsIn November 1999 Kirschen and Strbac [29] explained themethod of real and reactive power tracing by converting theall power injections into real and imaginary currents
23 Nodal Generation Distribution Factors In Nov 2000Gubina and Orgie [30] explained the method to determinethe generatorsrsquo contribution to a particular load by using thenodal generation distribution factors (NGDF-s) InDec 2000Grgic and Gubina [31] explained the distribution factorapproach for the reactive power flow tracing Pantos et al in2003-04 worked on transaction based transmission servicepricing techniques based on the Nodal Generation Distribu-tion factor and also proposed an Ex-Ante transmission pric-ing technique They also proposed a new power flow tracingmethod and explained a transmission service pricing Thesame authors further proposed a pattern based transmissionpricing technique [32ndash36]
3 Power Flow Tracing TechniquesBased on Graph Theory
In January 2000 Sun et al [37] explained a new method fortracing AC power flows where the graph theory is used tosolve the tracing problem In April 2000 Xi-Fan et al [38]explained a very efficient algorithm for power flow tracingby proposing two current decomposition axioms in whichGraph theory is used whereas Wei et al [39] used graph the-ory to analyze real power transfer between individual gener-ators and loads In Aug 2000Wu et al [40] explained the useof graph theory to calculate the contributions of individualgenerators and loads to line flows and the real power transferbetween individual generators and loads In March 2001Chai and Sekar [41] explained a methodology using graphtheory to determine the specific generator contributions todifferent loads and the transmission system usage of differentutilities In Dec 2001 Wei et al [42] proposed that the graphtheory is used to detect the existence of circulating powerthen the optimal power flow approach is applied to eliminatecirculating power From 2003 to 2009 Xie et al proposedand explained the power flow tracing algorithms foundedon extended incidence matrix and matrix multiplicationconsidering loop flows [1 43 44] In July 2003 Ghasemi et al[45] explained the closed-form solution for tracing problemby presenting a formula which is obtained by using bothproportionality and averaging criteria From 2004 to 2010Mustafa et al proposed power flow tracing method basedon tracing currents and complex power flows They also
Chinese Journal of Engineering 5
proposed a proportional tree method based method for trac-ing A comparison has also done by the same authors[46ndash48] In Oct 2004 Xiao and Wang [49] explained aproportional tree method to determine the contribution ofan individual generator to loads and also to determinethe nodal-must-run-share In Dec 2005 Wang and Xiao[50] explained proportional tree methods to allocate andprice the transmission usages among the users From 2005to 2008 Lim et al explained power flow tracing and lossallocation method based on loop flow analysis [51ndash53] In2006 Su et al proposed a method to deal with the problemof reactive power decomposition where Graph theory andproportional sharing principle are employed to determine thepower flow tracing sequence [54 55] From 2006 to 2009Abdelkader proposed and explained various power flowtracing techniques and loss allocation algorithms which arebased on physical flow in transmission lines line flowmatrixpower flow topology complex power flow tracing power flowtracing considering loop flows separation of transmissionlosses [56ndash65] In 2011 Nikoukar et al [66] explained thetransmission expansion pricing based on proportional treemethod and economic benefit method
4 Power Flow Tracing TechniquesBased on Circuit Theory
In Feb 1999 Yang and Anderson [67] proposed a power flowcomparison method for power flow tracing and comparethis method with the existing methods In Feb 2001 Liuet al [68 69] proved and extended the proportional sharingrule by network theory and graph theorem In [69] basedon the [68] proportional Sharing principle is incorporatedwith the load-flow tracing method In Nov 2001 Reta andVargas [70] explained a new method for power flow tracingbased on the concept of electric circuit theory in which theinfluence areas are determined In March 2002 Peng andJiang [71 72] explained amethod of power flow tracing basedon the definitions and concepts of total differential and thedefinite integral In [72] Peng and Jiang proposed a principleto trace the complex power flow and the theory proposedin [71] is applied to elementrsquos equivalent circuits to obtain anonlinear relationship between the complex power compo-nents flowing into and out of an element from a powersource In 2002 Chang and Lu [73] explained a node basedstrategy for tracing the current and power flows in a networkIn December 2004 Teng [74] explained method based onthe basic circuit theories equivalent current injection andequivalent impedance to allocate the power flow and loss forderegulated transmission systems In April 2006 Lin et al[75] explained a method to trace the power flow based onthe converged AC power flow solution In December 2007Sulaiman et al [76] explained the power flow tracing methodbased on converged load flow basic circuit theories includingsuperposition theory equivalent impedance and equivalentcurrent injection In June 2007 Meng and Jeyasurya [77]explained a simple transmission pricing scheme using apower flow tracingmethodwhich incorporated transmissionservice cost congestion cost and loss cost In Nov 2009Mohammadi et al [78] explained an approach based on
actual operation of the power network and using a conversionof load model superposition principle In March 2011 Quet al [79] explained a method of power flow tracing whichis based on the concept of the power supply path of sourceunder the constraints of all the basic electrical laws
41 Based on Z-Bus Tracing In Feb 2001 Conejo et al [80]proposed a transmission loss allocation method based onthe Z-bus matrix In Oct 2002 Zhaoxia et al [81] explainedan expression-analysis based power allocation method fortransmission loss allocation in which Generators (loads)are replaced with current sources while loads (generators)are replaced with shunt branches In September 2004Zhao et al [82] explained a redistribution loss allocationmethod for improving Z-Bus loss allocation OnMarch 2005Daniel et wal [83] proposed a method to allocate the activepower transmission loss which is based on the inclusionof the admittances equivalent to bus power injections inthe bus admittance matrix In November 2006 Kazemiand Andami [84] explained the multi-area power systemtransmission loss allocation based on the Z bus matrix InFebruary 2007 Conejo et al [85] explained a method ofnetwork cost allocation based on Z-bus matrix In November2008 Lalitha and Sydulu [86] explained a direct transmissionnetwork cost allocation method by finding the coefficientsof real and reactive power generations and load demandsin the complex line flow From 2008 to 2010 Parastar et alproposed a method to allocate the transmission loss basedon the basic circuit theories equivalent current injectionand modified Z-Bus [87 88] In December 2008 Mustafaet al [89] explained a new method to identify the real powertransfer between generators and load using modified nodalequations In December 2008 Chen and Chu [90] explainedthe redistribution of Z-bus loss allocation for finding the con-tributionattribution of the current flow between generationand load In 2008 Shareef et al [91] explained a method toidentify the real and reactive power transfer between gener-ators and load using modified nodal equations In Sept 2010Kilyeni et al [92] explained a transmission cost allocationmethod using the real and reactive power flow tracing whichis based on the Z-bus system matrix
5 Power Flow Tracing Based onOptimization Techniques
In Nov 2003 Conejo et al [93] explained a procedure for theallocation of the transmission loss cost that is based on deriv-ing a radial networkThis equivalent network is derived solv-ing a simple quadratic optimization problem In Nov 2005Vlachogiannis and Lee [94] explained a method that deter-mined generator contributions to the transmission system byan evolutionary computation technique From 2005 to 2007Abhyankar et al proposed various paradigms of MW powertracing algorithms and real power flow tracing They alsoexplained tracing compliant modified postage stampmethodand transmission service charge based real power flowtracing method Same authors furnished power flow trac-ing methods based on optimization approach and min-max
6 Chinese Journal of Engineering
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Xie J Zhou and W Li ldquoAnalytical model and algorithm fortracing active power flow based on extended incidence matrixrdquoElectric Power Systems Research vol 79 no 2 pp 399ndash4052009
[2] J Bialek ldquoTracing the flowof electricityrdquo IEE ProceedingsmdashGen-eration Transmission and Distribution vol 143 no 4 pp 313ndash320 1996
[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
[5] J Bialek ldquoTopological generation and load distribution factorsfor supplement charge allocation in transmission open accessrdquoIEEE Transactions on Power Systems vol 12 no 3 pp 1185ndash11931997
[6] J Bialek ldquoAllocation of transmission supplementary charge toreal and reactive loadsrdquo IEEE Transactions on Power Systemsvol 13 no 3 pp 749ndash754 1998
[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
[8] J W Bialek ldquoTracing-based unifying framework for transmis-sion pricing of cross-border trades in Europerdquo in Proceedings ofthe International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT rsquo00) pp 532ndash537London UK April 2000
[9] J W Bialek S Ziemianek and R Wallace ldquoA methodology forallocating transmission losses due to cross-border tradesrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1255ndash12622004
[10] Y Z Li S H Zhang Q Liu and Z Qu ldquoElectricity tracingmethod of generation and loss cost allocationrdquo in Proceedings
of the 5th International Conference on Advances in Power SystemControl Operation and Management (APSCOM rsquo00) HongKong China October 2000
[11] C T Su and J H Liaw ldquoPower wheeling pricing using powertracing andMVA-KMmethodrdquo in Proceedings of the IEEE PortoPower Tech vol 1 Porto Portugal September 2001
[12] A N Al-Rajhi and J W Bialek ldquoMarginal and tracing pricingof transmission an empirical comparisonrdquo in Proceedings of the14th Power Systems Computation Conference session 27 paper5 Sevilla Spain June 2002
[13] T Limpasuwan J W Bialek W Ongsakul and B Limmee-chokchai ldquoA proposal for annual power fee in Thailand basedon electricity tracing methodologyrdquo Electric Power SystemsResearch vol 64 no 3 pp 219ndash226 2003
[14] J W Bialek ldquoGaming the uniform-price spot market quantita-tive analysisrdquo IEEE Transactions on Power Systems vol 17 no 3pp 768ndash773 2002
[15] A R Shirani and H Siahkali ldquoTraceable flow method in deter-mination of congestion cost assignment in open access powersystem networkrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exhibition 2002 Asia Pacificvol 2 pp 734ndash738 October 2002
[16] T Limpasuwan JW BialekW Ongsakul and B Limmeechok-chai ldquoA proposal for transmission pricingmethodology inThai-land based on electricity tracing and long-run average incre-mental costrdquo Energy Policy vol 32 no 3 pp 301ndash308 2004
[17] PAKattuman R J Green and JW Bialek ldquoAllocating electric-ity transmission costs through tracing a game-theoretic ration-alerdquoOperations Research Letters vol 32 no 2 pp 114ndash120 2004
[18] JW Bialek and S Ziemianek ldquoTracing based transmission pric-ing of cross-border trades fundamentals and circular flowsrdquo inProceedings of the IEEE Bologna Power Tech Conference vol 3Bologna Italy June 2003
[19] J W Bialek and P A Kattuman ldquoProportional sharing assump-tion in tracing methodologyrdquo IEE ProceedingsmdashGenerationTransmission andDistribution vol 151 no 4 pp 526ndash532 2004
[20] C Adsoongnoen W Ongsakul and H J Haubrich ldquoAllocationof transmission losses and network charges for cross bordertrades in ASEAN power grid based on tracing methodologyrdquoin Proceedings of the IEEE Russia Power Tech pp 1ndash6 StPetersburg Russia June 2005
[21] P Nallagownden R N Mukerjee and S Masri ldquoPower tracingand prediction of losses for deregulated transmission systemrdquoInternational Journal of Electrical and Computer Sciences vol10 no 1
[22] K Pal M Pandit and L Srivastava ldquoIncentive charge calcula-tion for open access transmission systemrdquo in Proceedings of theInternational Conference on Power Systems (ICPS rsquo09) pp 1ndash6Kharagpur India December 2009
[23] C Achayuthakan C J Dent J W Bialek and W OngsakulldquoElectricity tracing in systems with and without circulatingflows physical insights and mathematical proofsrdquo IEEE Trans-actions on Power Systems vol 25 no 2 pp 1078ndash1087 2010
[24] P Nallagownden and T Y Lee ldquoApplication of regression andtracing methodology for efficient operation of generators andretailers in a deregulated systemrdquo in Proceedings of the 4thInternational Power Engineering and Optimization Conference(PEOCO rsquo10) pp 267ndash273 Selangor Malaysia June 2010
[25] B Naresh M S Kumari and M Sydulu ldquoTransmission costallocation using power flow tracing and genetic algorithmrdquo inProceedings of the 5th IEEE International Conference on Intelli-gent Systems (IS rsquo10) pp 432ndash438 London UK July 2010
10 Chinese Journal of Engineering
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
proposed a proportional tree method based method for trac-ing A comparison has also done by the same authors[46ndash48] In Oct 2004 Xiao and Wang [49] explained aproportional tree method to determine the contribution ofan individual generator to loads and also to determinethe nodal-must-run-share In Dec 2005 Wang and Xiao[50] explained proportional tree methods to allocate andprice the transmission usages among the users From 2005to 2008 Lim et al explained power flow tracing and lossallocation method based on loop flow analysis [51ndash53] In2006 Su et al proposed a method to deal with the problemof reactive power decomposition where Graph theory andproportional sharing principle are employed to determine thepower flow tracing sequence [54 55] From 2006 to 2009Abdelkader proposed and explained various power flowtracing techniques and loss allocation algorithms which arebased on physical flow in transmission lines line flowmatrixpower flow topology complex power flow tracing power flowtracing considering loop flows separation of transmissionlosses [56ndash65] In 2011 Nikoukar et al [66] explained thetransmission expansion pricing based on proportional treemethod and economic benefit method
4 Power Flow Tracing TechniquesBased on Circuit Theory
In Feb 1999 Yang and Anderson [67] proposed a power flowcomparison method for power flow tracing and comparethis method with the existing methods In Feb 2001 Liuet al [68 69] proved and extended the proportional sharingrule by network theory and graph theorem In [69] basedon the [68] proportional Sharing principle is incorporatedwith the load-flow tracing method In Nov 2001 Reta andVargas [70] explained a new method for power flow tracingbased on the concept of electric circuit theory in which theinfluence areas are determined In March 2002 Peng andJiang [71 72] explained amethod of power flow tracing basedon the definitions and concepts of total differential and thedefinite integral In [72] Peng and Jiang proposed a principleto trace the complex power flow and the theory proposedin [71] is applied to elementrsquos equivalent circuits to obtain anonlinear relationship between the complex power compo-nents flowing into and out of an element from a powersource In 2002 Chang and Lu [73] explained a node basedstrategy for tracing the current and power flows in a networkIn December 2004 Teng [74] explained method based onthe basic circuit theories equivalent current injection andequivalent impedance to allocate the power flow and loss forderegulated transmission systems In April 2006 Lin et al[75] explained a method to trace the power flow based onthe converged AC power flow solution In December 2007Sulaiman et al [76] explained the power flow tracing methodbased on converged load flow basic circuit theories includingsuperposition theory equivalent impedance and equivalentcurrent injection In June 2007 Meng and Jeyasurya [77]explained a simple transmission pricing scheme using apower flow tracingmethodwhich incorporated transmissionservice cost congestion cost and loss cost In Nov 2009Mohammadi et al [78] explained an approach based on
actual operation of the power network and using a conversionof load model superposition principle In March 2011 Quet al [79] explained a method of power flow tracing whichis based on the concept of the power supply path of sourceunder the constraints of all the basic electrical laws
41 Based on Z-Bus Tracing In Feb 2001 Conejo et al [80]proposed a transmission loss allocation method based onthe Z-bus matrix In Oct 2002 Zhaoxia et al [81] explainedan expression-analysis based power allocation method fortransmission loss allocation in which Generators (loads)are replaced with current sources while loads (generators)are replaced with shunt branches In September 2004Zhao et al [82] explained a redistribution loss allocationmethod for improving Z-Bus loss allocation OnMarch 2005Daniel et wal [83] proposed a method to allocate the activepower transmission loss which is based on the inclusionof the admittances equivalent to bus power injections inthe bus admittance matrix In November 2006 Kazemiand Andami [84] explained the multi-area power systemtransmission loss allocation based on the Z bus matrix InFebruary 2007 Conejo et al [85] explained a method ofnetwork cost allocation based on Z-bus matrix In November2008 Lalitha and Sydulu [86] explained a direct transmissionnetwork cost allocation method by finding the coefficientsof real and reactive power generations and load demandsin the complex line flow From 2008 to 2010 Parastar et alproposed a method to allocate the transmission loss basedon the basic circuit theories equivalent current injectionand modified Z-Bus [87 88] In December 2008 Mustafaet al [89] explained a new method to identify the real powertransfer between generators and load using modified nodalequations In December 2008 Chen and Chu [90] explainedthe redistribution of Z-bus loss allocation for finding the con-tributionattribution of the current flow between generationand load In 2008 Shareef et al [91] explained a method toidentify the real and reactive power transfer between gener-ators and load using modified nodal equations In Sept 2010Kilyeni et al [92] explained a transmission cost allocationmethod using the real and reactive power flow tracing whichis based on the Z-bus system matrix
5 Power Flow Tracing Based onOptimization Techniques
In Nov 2003 Conejo et al [93] explained a procedure for theallocation of the transmission loss cost that is based on deriv-ing a radial networkThis equivalent network is derived solv-ing a simple quadratic optimization problem In Nov 2005Vlachogiannis and Lee [94] explained a method that deter-mined generator contributions to the transmission system byan evolutionary computation technique From 2005 to 2007Abhyankar et al proposed various paradigms of MW powertracing algorithms and real power flow tracing They alsoexplained tracing compliant modified postage stampmethodand transmission service charge based real power flowtracing method Same authors furnished power flow trac-ing methods based on optimization approach and min-max
6 Chinese Journal of Engineering
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
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[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
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[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
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[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
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[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
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[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
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[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
fairness criteria [95ndash102] In Dec 2008 Amoli and Jadid [103]used a proportional tracing and optimal real power tracingmethod for allocation of loss From 2009 to 2011 Hamidet al proposed methods for allocating the losses and gener-ated power by means of Evolutionary Programming (EP)algorithm [104 105] In Aug 2010 Rao et al [106] explainedthe Min-Max fair allocation criteria for transmission systemusage allocation In Dec 2010 Basak et al [107] explained amodification in the existing pool based nodal charging tech-nique by accommodating the bilateral transactions alsowhich is done by posing the problem of creating virtualexchanges as an optimization problem
6 Power Flow Tracing Based onthe Relative Electrical Distance Concept
Consider a system where 119899 is the total number of buses with1 2 119892 119892 is number of generator buses and 119892 + 1 sdot sdot sdot 119899remaining (119899-119892) load buses For a given system we can write
[119868119866
119868119871
] = [119884119866119866
119884119866119871
119884119871119866
119884119871119871
] [119881119866
119881119871
] (8)
where 119868119866 119868119871and119881119866119881119871represent complex current and voltage
vectors at the generators nodes and load nodes[119884119866119866] [119884119866119871] [119884119871119871] and [119884
119871119866] are corresponding parti-
tioned portions of network 119884-bus matrix Rearranging theequation we get
[119881119871
119868119866
] = [119885119871119871
119865119871119866
119870119866119871
119884119866119866
] [119868119871
119881119866
] (9)
where [119865119871119866] = minus[119884
119871119871]minus1[119884119871119866] This matrix gives the relation
between load bus voltages and source bus voltages It alsogives information about the location of load nodes withrespect to generator nodes that is termed as relative electricaldistance (RED) between load nodes and generator nodes
The relative electrical distances that is the relative loca-tions of load nodes with respect to the generator nodes areobtained from the [119865
119871119866]matrix and is given by (10)
[119877119871119866] = 1 minus abs [119865
119871119866] (10)
The desired proportions of generation for the desiredload sharinggeneration scheduling are also obtained fromthe [119865
119871119866]matrix and is given by
[119863119871119866] = abs [119865
119871119866] (11)
In 2003 Visakha et al proposed amethod of transmissioncharge allocation based on the RED concept [108 109] In2008-2009 Thukaram et al proposed and explained powerflow tracing and transmission loss charge allocationmethodsbased on aREDconceptThey also furnished aT-indexwhichis used for ranking new generation expansion locations [110ndash112]
7 Power Flow Tracing Based onCooperative Game Theory
InMay 1996 Tsukamoto and Iyodo [113] described amethod-ology to allocate the cost of transmission network facilities It
is based on the combination of MW-Mile method with coop-erative game theory Kattuman et al [114] presented a tracingtechnique for pricing inter-area electricity trades In Aug1999 Yeung and Poon [115] explained a multi agent modelin conjunction with game theory to resolve the coalitionformation in multilateral trades In Oct 2000 Yu et al [116]presented amethod for transmission line embedded cost allo-cation using cooperative game theory They also presented acomparison between themethods of transmission embeddedcost allocation [117] In Jan 2002 Tan and Lie [118] appliedShapley value of cooperative game theory for allocation oftransmission cost to loads and generators In May 2002 Yu etal [119] proposed transmission line embedded cost allocatedmethod accounting line capacity use and reliability benefitsIn Nov 2002 Zolezzi and Rudnick [120] explained coopera-tive game theory based transmission cost allocation methodIn this work cooperative game theory solution such asShapley value and nucleolus are compared with conventionalmethods InMay 2004 Stamtsis andErlich [121] implementedthe game theory solutions such as Shapley value and Nucle-olus for the power system fixed cost allocation in the pooland bilateral market InMarch 2005 Bjorndal et al [122] pre-sented amethod for computing the nucleolus of a cooperativegame by which several usage-based methods may be com-bined to produce allocations that are in or as close as possibleto the core In Nov 2007 Junqueira et al [123] presenteda methodology based on the Aumann-Shapley scheme forenergy transmission costs allocation between network usersin energy markets In Dec 2008 Bhakar et al [124] provideda game theoretic model that allocates the transmission anddistribution network costs based on Nucleolus and ShapleyValue approaches In 2009 Bhakar et al [125] proposed a vari-ety of probabilistic cooperative game theory approaches InJune 2003 Juan Zolezzi and Rudnick [126] proposed a trans-mission cost allocation method based on cooperative gametheory and transmission network capacity use of consumeragents Singh et al [127] dealt with the problem of allocatingcommon costs in electric power networks using principlesfrom cooperative game theory In 2011 Balagopalan andAnooja [128] applied cooperative game theory for sharingtransmission charges in electricity markets
8 Equilateral Bilateral Exchange
The term equivalent bilateral exchange represents a powerinjection and an offtake of the same entity It suggests theexistence of a generator and a demand with the same realpower but in opposite directions Assuming a generator 119875
119892at
bus 119894 and a demand119875119889at bus 119895 the bilateral exchange between
generator and demand is given by
119866119863119894119895=
119875119892119894119875119889119895
119875sys119889
(12)
where in a lossless network the system demand 119875sys119889
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Xie J Zhou and W Li ldquoAnalytical model and algorithm fortracing active power flow based on extended incidence matrixrdquoElectric Power Systems Research vol 79 no 2 pp 399ndash4052009
[2] J Bialek ldquoTracing the flowof electricityrdquo IEE ProceedingsmdashGen-eration Transmission and Distribution vol 143 no 4 pp 313ndash320 1996
[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
[5] J Bialek ldquoTopological generation and load distribution factorsfor supplement charge allocation in transmission open accessrdquoIEEE Transactions on Power Systems vol 12 no 3 pp 1185ndash11931997
[6] J Bialek ldquoAllocation of transmission supplementary charge toreal and reactive loadsrdquo IEEE Transactions on Power Systemsvol 13 no 3 pp 749ndash754 1998
[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
[8] J W Bialek ldquoTracing-based unifying framework for transmis-sion pricing of cross-border trades in Europerdquo in Proceedings ofthe International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT rsquo00) pp 532ndash537London UK April 2000
[9] J W Bialek S Ziemianek and R Wallace ldquoA methodology forallocating transmission losses due to cross-border tradesrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1255ndash12622004
[10] Y Z Li S H Zhang Q Liu and Z Qu ldquoElectricity tracingmethod of generation and loss cost allocationrdquo in Proceedings
of the 5th International Conference on Advances in Power SystemControl Operation and Management (APSCOM rsquo00) HongKong China October 2000
[11] C T Su and J H Liaw ldquoPower wheeling pricing using powertracing andMVA-KMmethodrdquo in Proceedings of the IEEE PortoPower Tech vol 1 Porto Portugal September 2001
[12] A N Al-Rajhi and J W Bialek ldquoMarginal and tracing pricingof transmission an empirical comparisonrdquo in Proceedings of the14th Power Systems Computation Conference session 27 paper5 Sevilla Spain June 2002
[13] T Limpasuwan J W Bialek W Ongsakul and B Limmee-chokchai ldquoA proposal for annual power fee in Thailand basedon electricity tracing methodologyrdquo Electric Power SystemsResearch vol 64 no 3 pp 219ndash226 2003
[14] J W Bialek ldquoGaming the uniform-price spot market quantita-tive analysisrdquo IEEE Transactions on Power Systems vol 17 no 3pp 768ndash773 2002
[15] A R Shirani and H Siahkali ldquoTraceable flow method in deter-mination of congestion cost assignment in open access powersystem networkrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exhibition 2002 Asia Pacificvol 2 pp 734ndash738 October 2002
[16] T Limpasuwan JW BialekW Ongsakul and B Limmeechok-chai ldquoA proposal for transmission pricingmethodology inThai-land based on electricity tracing and long-run average incre-mental costrdquo Energy Policy vol 32 no 3 pp 301ndash308 2004
[17] PAKattuman R J Green and JW Bialek ldquoAllocating electric-ity transmission costs through tracing a game-theoretic ration-alerdquoOperations Research Letters vol 32 no 2 pp 114ndash120 2004
[18] JW Bialek and S Ziemianek ldquoTracing based transmission pric-ing of cross-border trades fundamentals and circular flowsrdquo inProceedings of the IEEE Bologna Power Tech Conference vol 3Bologna Italy June 2003
[19] J W Bialek and P A Kattuman ldquoProportional sharing assump-tion in tracing methodologyrdquo IEE ProceedingsmdashGenerationTransmission andDistribution vol 151 no 4 pp 526ndash532 2004
[20] C Adsoongnoen W Ongsakul and H J Haubrich ldquoAllocationof transmission losses and network charges for cross bordertrades in ASEAN power grid based on tracing methodologyrdquoin Proceedings of the IEEE Russia Power Tech pp 1ndash6 StPetersburg Russia June 2005
[21] P Nallagownden R N Mukerjee and S Masri ldquoPower tracingand prediction of losses for deregulated transmission systemrdquoInternational Journal of Electrical and Computer Sciences vol10 no 1
[22] K Pal M Pandit and L Srivastava ldquoIncentive charge calcula-tion for open access transmission systemrdquo in Proceedings of theInternational Conference on Power Systems (ICPS rsquo09) pp 1ndash6Kharagpur India December 2009
[23] C Achayuthakan C J Dent J W Bialek and W OngsakulldquoElectricity tracing in systems with and without circulatingflows physical insights and mathematical proofsrdquo IEEE Trans-actions on Power Systems vol 25 no 2 pp 1078ndash1087 2010
[24] P Nallagownden and T Y Lee ldquoApplication of regression andtracing methodology for efficient operation of generators andretailers in a deregulated systemrdquo in Proceedings of the 4thInternational Power Engineering and Optimization Conference(PEOCO rsquo10) pp 267ndash273 Selangor Malaysia June 2010
[25] B Naresh M S Kumari and M Sydulu ldquoTransmission costallocation using power flow tracing and genetic algorithmrdquo inProceedings of the 5th IEEE International Conference on Intelli-gent Systems (IS rsquo10) pp 432ndash438 London UK July 2010
10 Chinese Journal of Engineering
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
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[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
is a generation shift factor through network ele-ment 119896 corresponding to changes in generator at bus 119894
In Nov 2003 Galiana et al [129] present a methodologyfor allocating the cost of a transmission network to its usersbased on the principle of equivalent bilateral exchanges InOct 2005 Silva et al [130] presented a new strategy designedwith the purpose of achieving revenue adequacy in congestednetworks that use financial transmission rights (FTR) mar-kets In 2008 [131] same authors presented a new strategybased on the principle of equivalent bilateral exchanges forthe allocation of costs related to electric network congestionmanagement In Nov 2005 Mateus and Franco [132] pre-sented a new loss allocation scheme based on equivalent bilat-eral exchanges In Dec 2008 Nouri and Jadid [133] pro-posed a loss allocation method based on equivalent bilateralexchanges and genetic algorithm
9 Case Studies
Case studies presented the suitability and practicability ofvarious methods to be implemented on practical systemsThis section deals with those publications which are relatedto restructuring or deregulation experience in differentcountries
In April 2000 Bialek [8] applied tracing-based unifiedframework for transmission pricing of cross-border tradesin the European interconnected network In August 2002Limpasuwan et al [13] implemented tracing methodology onElectricity Generating Authority ofThailand (EGAT) systemIn June 2006 Thukaram et al [27] presented a case studyon an equivalent 11-bus system a part of Indian SouthernGrid based on the concepts of circuit flowdirections In 2004Pantos and Gubina [33] presented an Ex-ante transmission-service pricing via power-flow tracing on 194 nodes Slovenianpower system In April 2000 Xi-Fan et al [38] presented
a power tracing analysis on UK 30 node system In August2008 Lim et al [52] applied loop based tracing method onmodified CIGRE Nordic32 bus system In December 2008Mustafa et al [89] implemented a new method of real powerflow tracing on practical 25 bus equivalent power system ofsouth Malaysia In 2005 Abhyankar et al [97] implementeda power flow tracing algorithm on a Western regional gridof India In [100] Abhyankar et al Applied optimizationapproach in power flow tracing on aWestern regional grid ofIndia In November 2007 Junqueira et al [123] implementeda transmission cost allocation method based on the AumannShapley approach of game theory on the Brazilian powersystem In June 2003 Zolezzi and Rudnick [126] proposeda method based on cooperative game theory and transmis-sion network capacity use They implemented the proposedmethod on the main Chilean interconnected system
10 Discussion
A review of various methods based on power flow tracing ispresented Tracing based on proportional sharing principle isvery simple and easy to understand But it does not provideefficient economic signals Also it is not based on any fairnesscriteria Hence it has some degree of arbitrariness [2]
Optimization approach is most suitable for large powersystem [106] But it is complex and time consuming Theobjective function is formed which is optimized and givesoptimum results
In the game theory the participants make rational deci-sions in a conflicting competitive solution This approachgives efficient economic signals It is most suitable for thepresent competitive scenario But its applicability is limitedto large power system due to cumbersome calculation [118]
Equilateral bilateral exchange (EBE) is a reasonable wayto determine the combination of each generator to eachdemand The main advantage of this method is its indepen-dence on selection of slack bus In this method slack busis created for each EBE But EBE is a purely mathematicalconcept which does not exist in reality But by this way we canobserve all the different configurations of generator demand[129]
Circuit theory based methods depends on exact networkequation which is defined by the complex impedance matrixAll the calculations based on the sparse admittance matrixThese methods are easy to formulate [85]
Graph theory is widely used for allocation of transmissionusage to loads and generators Various matrixes such as inci-dence matrix adjacency matrix are used for tracing purposeThese methods are simple and easy to implement But thismethodology also follows the proportional sharing principle[1]
Relative electrical distance method allocates the trans-mission charges based on the relative location of the loadnode with respect to generator node It is simple and canbe implemented using the network configuration and gen-erationload conditions It does not require performing loadflow analysis whenever each contracttransaction is exer-cised The main advantage of the developed method lies inits applicability to consider multiple contractstransactionssimultaneously [109]
8 Chinese Journal of Engineering
Table1Com
paris
onbetweenvario
uspo
wer
flowtracingmetho
ds
Characteris
tics
Metho
dscompared
Prop
ortio
nal
sharing
Graph
theory
Circuit
theory
Optim
ization
approach
Relativ
eelectric
aldistance
Gam
etheory
EBE
Basic
approach
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
prop
ortio
nality
principle
Tracingbasedon
networkmatric
es
Tracingbasedon
optim
ization
approach
Tracingbasedon
networkmatric
esBa
sedon
econ
omic
principles
Everyload
issupp
lied
byeverygeneratorin
apropo
rtionate
manner
Quantity
depend
ency
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Networkdepend
ency
No
No
Yes
No
Yes
No
Yes
Slackbu
sdependency
No
No
No
Yes
No
No
No
Effecto
fcou
nter
flow
No
No
No
No
Yes
Yes
Yes
Volatility
No
No
No
No
No
No
No
Isiteasy
toun
derstand
Yes
Yes
Yes
No
Yes
Yes
Yes
Simplicity
44
22
33
3
Fairn
essc
riteria
Show
simmun
ityShow
simmun
ityShow
simmun
ityObjectiv
efun
ction
canbe
defin
edShow
simmun
ityObjectiv
efun
ction
defin
edShow
simmun
ity
Power
flowmod
elAC
DCMeasures
data
ACD
CMeasures
data
ACD
CMeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
ACD
Cmeasures
data
DC
Prices
ignal
Follo
wthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eFo
llowthep
attern
ofmarginalschem
eMay
disto
rtsig
nalsof
prop
ortio
natetracing
Stable
Stable
Dam
ped
Com
putatio
nTime
22
34
34
3Minim
um1m
axim
um5
Chinese Journal of Engineering 9
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
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[2] J Bialek ldquoTracing the flowof electricityrdquo IEE ProceedingsmdashGen-eration Transmission and Distribution vol 143 no 4 pp 313ndash320 1996
[3] J Bialek andD B Tam ldquoTracing the generatorsrsquo outputrdquo in Pro-ceedings of the International Conference on Opportunities andAdvances in International Electric Power Generation pp 133ndash136 Durham NC USA March 1996
[4] J Bialek ldquoIdentification of source-sink connections in transmis-sion networksrdquo in Proceedings of the 4th International Confer-ence on Power System Control and Management pp 200ndash204April 1996
[5] J Bialek ldquoTopological generation and load distribution factorsfor supplement charge allocation in transmission open accessrdquoIEEE Transactions on Power Systems vol 12 no 3 pp 1185ndash11931997
[6] J Bialek ldquoAllocation of transmission supplementary charge toreal and reactive loadsrdquo IEEE Transactions on Power Systemsvol 13 no 3 pp 749ndash754 1998
[7] P A Kattuman J W Bialek and N Abi-Samra ldquoElectricitytracing and co-operative game theoryrdquo in Proceedings of the 13thPower System Computation Conference pp 238ndash243 Trond-heim Norway June 1999
[8] J W Bialek ldquoTracing-based unifying framework for transmis-sion pricing of cross-border trades in Europerdquo in Proceedings ofthe International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT rsquo00) pp 532ndash537London UK April 2000
[9] J W Bialek S Ziemianek and R Wallace ldquoA methodology forallocating transmission losses due to cross-border tradesrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1255ndash12622004
[10] Y Z Li S H Zhang Q Liu and Z Qu ldquoElectricity tracingmethod of generation and loss cost allocationrdquo in Proceedings
of the 5th International Conference on Advances in Power SystemControl Operation and Management (APSCOM rsquo00) HongKong China October 2000
[11] C T Su and J H Liaw ldquoPower wheeling pricing using powertracing andMVA-KMmethodrdquo in Proceedings of the IEEE PortoPower Tech vol 1 Porto Portugal September 2001
[12] A N Al-Rajhi and J W Bialek ldquoMarginal and tracing pricingof transmission an empirical comparisonrdquo in Proceedings of the14th Power Systems Computation Conference session 27 paper5 Sevilla Spain June 2002
[13] T Limpasuwan J W Bialek W Ongsakul and B Limmee-chokchai ldquoA proposal for annual power fee in Thailand basedon electricity tracing methodologyrdquo Electric Power SystemsResearch vol 64 no 3 pp 219ndash226 2003
[14] J W Bialek ldquoGaming the uniform-price spot market quantita-tive analysisrdquo IEEE Transactions on Power Systems vol 17 no 3pp 768ndash773 2002
[15] A R Shirani and H Siahkali ldquoTraceable flow method in deter-mination of congestion cost assignment in open access powersystem networkrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exhibition 2002 Asia Pacificvol 2 pp 734ndash738 October 2002
[16] T Limpasuwan JW BialekW Ongsakul and B Limmeechok-chai ldquoA proposal for transmission pricingmethodology inThai-land based on electricity tracing and long-run average incre-mental costrdquo Energy Policy vol 32 no 3 pp 301ndash308 2004
[17] PAKattuman R J Green and JW Bialek ldquoAllocating electric-ity transmission costs through tracing a game-theoretic ration-alerdquoOperations Research Letters vol 32 no 2 pp 114ndash120 2004
[18] JW Bialek and S Ziemianek ldquoTracing based transmission pric-ing of cross-border trades fundamentals and circular flowsrdquo inProceedings of the IEEE Bologna Power Tech Conference vol 3Bologna Italy June 2003
[19] J W Bialek and P A Kattuman ldquoProportional sharing assump-tion in tracing methodologyrdquo IEE ProceedingsmdashGenerationTransmission andDistribution vol 151 no 4 pp 526ndash532 2004
[20] C Adsoongnoen W Ongsakul and H J Haubrich ldquoAllocationof transmission losses and network charges for cross bordertrades in ASEAN power grid based on tracing methodologyrdquoin Proceedings of the IEEE Russia Power Tech pp 1ndash6 StPetersburg Russia June 2005
[21] P Nallagownden R N Mukerjee and S Masri ldquoPower tracingand prediction of losses for deregulated transmission systemrdquoInternational Journal of Electrical and Computer Sciences vol10 no 1
[22] K Pal M Pandit and L Srivastava ldquoIncentive charge calcula-tion for open access transmission systemrdquo in Proceedings of theInternational Conference on Power Systems (ICPS rsquo09) pp 1ndash6Kharagpur India December 2009
[23] C Achayuthakan C J Dent J W Bialek and W OngsakulldquoElectricity tracing in systems with and without circulatingflows physical insights and mathematical proofsrdquo IEEE Trans-actions on Power Systems vol 25 no 2 pp 1078ndash1087 2010
[24] P Nallagownden and T Y Lee ldquoApplication of regression andtracing methodology for efficient operation of generators andretailers in a deregulated systemrdquo in Proceedings of the 4thInternational Power Engineering and Optimization Conference(PEOCO rsquo10) pp 267ndash273 Selangor Malaysia June 2010
[25] B Naresh M S Kumari and M Sydulu ldquoTransmission costallocation using power flow tracing and genetic algorithmrdquo inProceedings of the 5th IEEE International Conference on Intelli-gent Systems (IS rsquo10) pp 432ndash438 London UK July 2010
10 Chinese Journal of Engineering
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
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[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
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[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
A comparison between various power flow tracing meth-odologies is presented Table 1
11 Conclusion
This paper presents an overview of transmission pricingmethods based on or using power flow tracing techniquesin a deregulated environment of the power systemThe mainprinciple used in power flow tracing is the proportional shar-ing principle which is based on the Kirchhoff rsquos current lawThe other approaches are based on graph theory circuit the-ory optimization techniques Z-bus matrix relative electricaldistance and EBEThis paper makes overall systematic sum-mary and analysis of the existing allocation methods whichare classified according to different tracing techniques
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
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[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
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[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
[26] D K Ron and A G Strbac ldquoContributions of individual gener-ators to loads and flowsrdquo IEEE Transactions on Power Systemsvol 12 no 1 pp 52ndash60 1997
[27] DThukaram H P Khincha B Ravikumar andG YesuratnamldquoGenerators contribution towards loads and line flowsmdasha casestudyrdquo in Proceedings of the IEEE Power India Conference NewDelhi India April 2006
[28] G Strbac D Kirschen and S Ahmed ldquoAllocating transmissionsystem usage on the basis of traceable contributions of gener-ators and loads to flowsrdquo IEEE Transactions on Power Systemsvol 13 no 2 pp 527ndash534 1998
[29] D Kirschen and G Strbac ldquoTracing active and reactive powerbetween generators and loads using real and imaginary cur-rentsrdquo IEEE Transactions on Power Systems vol 14 no 4 pp1312ndash1319 1999
[30] F Gubina and D Orgie ldquoA method for determining the gener-atorsrsquo share in a consumer loadrdquo IEEE Transactions on PowerSystems vol 15 no 4 pp 1376ndash1381 2000
[31] D Grgic and F Gubina ldquoGenerator contribution to a line reac-tive power flowrdquo in Proceedings of the International Conferenceon Power System Technology (PowerCon rsquo00) vol 3 pp 1587ndash1590 Perth Wash USA 2000
[32] M Pantos D Grgic and F Gubina ldquoNew transmission servicepricing technique based on actual power flowsrdquo in Proceedingsof the IEEE Bologna Power Tech Conference vol 3 BolognaItaly June 2003
[33] M Pantos and F Gubina ldquoEx-ante transmission-service pricingvia power-flow tracingrdquo International Journal of Electrical Powerand Energy System vol 26 no 7 pp 509ndash518 2004
[34] M Pantos and F Gubina ldquoEx-ante transmission service pricingvia load distribution factorsrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 p 4 July 2003
[35] M Pantos and F Gubina ldquoAllocation of production to con-sumersrdquo in Proceedings of the IEEE EUROCON vol 2 pp 301ndash304 September 2003
[36] M Pantos and F Gubina ldquoEx-ante transmission-service pricingbased on load-flow patternsrdquo IEEE Transactions on PowerSystems vol 19 no 2 pp 796ndash801 2004
[37] H SunD C Yu andQ Zheng ldquoACpower flow tracing in trans-mission networksrdquo inProceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1715ndash1720 January 2000
[38] W Xi-Fan W Xin-Li and J Bin ldquoPower tracing analysis inwheeling costingrdquo in Proceedings of the International Conferenceon Electric Utility Deregulation and Restructuring and PowerTechnologies (DRPT rsquo00) pp 173ndash178 London UK 2000
[39] P Wei B Yuan Y Ni and F F Wu ldquoPower flow tracing fortransmission open accessrdquo in Proceedings of the InternationalConference on Electric Utility Deregulation and Restructuringand Power Technologies (DRPT rsquo00) pp 476ndash481 London UK2000
[40] F F Wu Y Ni and P Wei ldquoPower transfer allocation for openaccess using graph theorymdashfundamentals and applications insystemswithout loopflowrdquo IEEE Transactions on Power Systemsvol 15 no 3 pp 923ndash929 2000
[41] S K Chai and A Sekar ldquoGraph theory application to deregu-lated power systemrdquo in Proceedings of the 33rd SoutheasternSymposium on System Theory pp 117ndash121 Athens Ohio USAMarch 2001
[42] P Wei Y Ni and F F Wu ldquoLoad flow tracing in power systemswith circulating powerrdquo International Journal of Electrical Powerand Energy Systems vol 24 no 10 pp 807ndash813 2002
[43] K Xie and J Zhou ldquoPower flow tracing algorithm for electricnetworks with loopflowrdquo Science in China E vol 46 no 1 pp93ndash103 2003
[44] K Xie C Li and Y Liu ldquoTracing power flow from generatorsto loads and branches using incidence matrix multiplicationrdquoin Proceedings of the IEEE Power and Energy Society GeneralMeeting (PES rsquo09) pp 1ndash7 Calgary Canada July 2009
[45] H Ghasemi C Canizares and G Savage ldquoClosed-form solu-tion to calculate generator contributions to loads and line flowsin an open access marketrdquo in Proceedings of the IEEE PowerEngineering Society General Meeting vol 2 July 2003
[46] M W B Mustafa and H Shareef ldquoAn alternative power tracingmethod for transmission open accessrdquo httpiteeuqeduausimaupecaupec05AUPEC2005Volume1S091pdf
[47] M W Mustafa and M H Sulaiman ldquoTransmission loss allo-cation in deregulated power system via superposition and pro-portional tree methodsrdquo in Proceedings of the 2nd IEEE Interna-tional Power and Energy Conference (PECon rsquo08) pp 988ndash993Johor Baharu Malaysia December 2008
[48] M W Mustafa M H Sulaiman H Shareef and S N AbdKhalid ldquoDetermination of generatorsrsquo contributions to loadsin pool based power system using least squares support vectormachinerdquo in Proceedings of the 4th International Power Engi-neering andOptimization Conference (PEOCO rsquo10) pp 226ndash231Selangor Malaysia June 2010
[49] Y Xiao and P Wang ldquoTracing nodal market power usingproportional treemethodrdquo inProceedings of the IEEEPES PowerSystems Conference and Exposition vol 1 pp 196ndash200 October2004
[50] P Wang and Y Xiao ldquoTransmission cost allocation using pro-portional tree methodsrdquo in Proceedings of the 7th InternationalPower Engineering Conference (IPEC rsquo05) pp 1ndash126 SingaporeDecember 2005
[51] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo in Proceedings of the 7th International Power EngineeringConference (IPEC rsquo05) vol 2 pp 1013ndash1018 Singapore Decem-ber 2005
[52] V S C Lim J D F McDonald and T K Saha ldquoDevelopmentof a new loss allocation method for a hybrid electricity marketusing graph theoryrdquo Electric Power Systems Research vol 79 no2 pp 301ndash310 2009
[53] V S C Lim J D F McDonald and T K Saha ldquoApplication ofloop frame of reference to power flow tracing and loss alloca-tionrdquo International Journal of Emerging Electric Power Systemsvol 5 no 2 article 3 2006
[54] C T Su J H Liaw andCM Li ldquoPower-flow tracing andwheel-ing costing considering complex power and convection linesrdquoIEE ProceedingsmdashGeneration Transmission and Distributionvol 153 no 1 pp 1ndash10 2006
[55] C T Su and J H Liaw ldquoComplex power flow tracing consid-ering convection lines using nominal-T modelrdquo InternationalJournal of Electrical Power and Energy Systems vol 29 no 1 pp28ndash35 2007
[56] S Abdelkader ldquoTransmission loss allocation in a deregulatedelectrical energy marketrdquo Electric Power Systems Research vol76 no 11 pp 962ndash967 2006
[57] S Abdelkader ldquoAllocating generation to loads and line flowsfor transmission open accessrdquo in Proceedings of the IEEE GCCConference pp 1ndash6 Manama Bahrain March 2006
Chinese Journal of Engineering 11
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
[58] S Abdelkader ldquoEfficient computation algorithm for calculatingload contributions to line flows and lossesrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 153 no 4 pp391ndash398 2006
[59] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tracingrdquo in Proceedings of the 11th InternationalMiddle East Power Systems Conference (MEPCON rsquo2006) vol 1pp 310ndash316 Minya Egypt December 2006
[60] S Abdelkader ldquoA method for determining generatorsrsquo shares inloads line flows and lossesrdquo Journal of the Franklin Institute vol344 no 8 pp 1063ndash1074 2007
[61] S M Abdelkader ldquoAllocating transmission loss to loads andgenerators through complex power flow tracingrdquo IET Genera-tion Transmission and Distribution vol 1 no 4 pp 584ndash5952007
[62] S M Abdelkader ldquoTransmission loss allocation through com-plex power flow tacingrdquo IEEE Transactions on Power Systemsvol 22 no 4 pp 2240ndash2248 2007
[63] S Abdelkader ldquoDetermining generatorsrsquo contribution to loadsand line flows amp losses considering loop flowsrdquo InternationalJournal of Electrical Power and Energy Systems vol 30 no 6-7pp 368ndash375 2008
[64] S M Abdelkader ldquoA new method for transmission loss alloca-tion considering the circulating currents between generatorsrdquoin Proceedings of the 12th International Middle East Power Sys-tem Conference (MEPCON rsquo08) pp 282ndash286 Aswan EgyptMarch 2008
[65] S M Abdelkader ldquoComplex power flow tracing for transmis-sion loss allocation considering loop flowsrdquo in Proceedings ofthe IEEE Power and Energy Society General Meeting (PES rsquo09)pp 1ndash9 Calgary Canada July 2009
[66] J Nikoukar M R Haghifam and A Panahi ldquoTransmissionexpansion cost allocation based on economic benefit and use ofsystemrdquo Journal of American Science vol 7 no 4 2011
[67] J Yang andMDAnderson ldquoTracing the flowof power in trans-mission networks for use-of-transmission-system charges andcongestion managementrdquo in Proceedings of the Winter Meetingof IEEE Power Engineering Society vol 1 pp 399ndash405 February1999
[68] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part I theoretic fun-damentrdquo in Proceedings of the IEEE Power Engineering SocietyWinter Meeting vol 3 pp 1244ndash1249 Columbus Ohio USAFebruary 2001
[69] F Liu Y Li and G Tang ldquoA quick and practicable power flowtracing method on electric energy market part II a new prac-ticable methodrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting vol 3 pp 1238ndash1243 Columbus OhioUSA February 2001
[70] R Reta and A Vargas ldquoElectricity tracing and loss allocationmethods based on electric conceptsrdquo IEE ProceedingsmdashGenera-tion Transmission and Distribution vol 148 no 6 pp 518ndash5222001
[71] J C Peng and H Jiang ldquoContributions of individual genera-tors to complex power losses and flowsmdashpart 1 fundamentaltheoryrdquo IEE ProceedingsmdashGeneration Transmission and Distri-bution vol 149 no 2 pp 182ndash185 2002
[72] J C Peng and H Jiang ldquoContributions of individual generatorsto complex power losses and flowsmdashpart 2 algorithm and sim-ulationsrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 2 pp 186ndash190 2002
[73] Y C Chang and C N Lu ldquoElectricity tracing method withapplication to power loss allocationrdquo International Journal ofElectrical Power and Energy System vol 23 no 1 pp 13ndash17 2001
[74] JH Teng ldquoPower flowand loss allocation for deregulated trans-mission systemsrdquo International Journal of Electrical Power andEnergy Systems vol 27 no 4 pp 327ndash333 2005
[75] W M Lin T S Zhan and C H Huang ldquoA circuit theory basedload flow tracing method considering counter-flow contribu-tionrdquo in Proceedings of the 5th WSEAS International Conferenceon InstrumentationMeasurement Circuits and Systems (IMCASrsquo06 ) pp 312ndash317 Hangzhou China April 2006
[76] M H Sulaiman O Aliman MW Mustafa and I Daut ldquoTrac-ing generatorsrsquo output in transmission open accessrdquo in Proceed-ings of the 5th Student Conference on Research and Development(SCORED rsquo07) pp 1ndash6 Selangor Malaysia December 2007
[77] Y Meng and B Jeyasurya ldquoInvestigation of transmission costallocation using a power flow tracing methodrdquo in Proceedingsof the IEEE Power Engineering Society General Meeting pp 1ndash7Tampa Fla USA June 2007
[78] M Mohammadi A Ebrahimi and T Daemi ldquoAccurate deter-mination of active power transmission paths for contributionallocation of generating unitsrdquo in Proceedings of the Interna-tional Conference on Electric Power and Energy Conversion Sys-tems (EPECS rsquo09) pp 1ndash5 November 2009
[79] Z J Qu J H Qin X T Wang H Bao and C Zhou ldquoA powerflow tracing method based on the circuit analysis of powersupply pathrdquo in Proceedings of the Asia-Pacific Power and EnergyEngineering Conference (APPEEC rsquo11) pp 1ndash6 Wuhan ChinaMarch 2011
[80] A J Conejo F DGaliana and I Kockar ldquoZ-bus loss allocationrdquoIEEE Transactions on Power Systems vol 16 no 1 pp 105ndash1102001
[81] J Zhaoxia D Xianzhong and H Yangzan ldquoA new expression-analysis-based losses allocation methodrdquo in Proceedings of theIEEEPES Transmission and Distribution Conference and Exhi-bition 2002 Asia Pacific vol 3 pp 1982ndash1985 October 2002
[82] N Zhao Y H Song Z H Bie S Takahash and Y SekineldquoImproved Z-bus loss allocation method through redistribu-tionrdquo in Proceedings of the 39th International Universities PowerEngineering Conference (UPEC rsquo04) vol 3 pp 1101ndash1105 Sep-tember 2004
[83] J S Daniel R S Salgado andM R Irving ldquoTransmission dlossallocation through a modified Y-Busrdquo IEE ProceedingsmdashGener-ation Transmission andDistribution vol 152 no 2 pp 208ndash2142005
[84] A Kazemi and H Andami ldquoMulti-area power system lossallocation usingZ-busmethodrdquo inProceedings of the 1st Interna-tional Power and Energy Conference (PECon rsquo06) pp 286ndash291Putra Jaya Malaysia November 2006
[85] A J Conejo J Contreras D A Lima and A Padilha-FeltrinldquoZbus transmission network cost allocationrdquo IEEE Transactionson Power Systems vol 22 no 1 pp 342ndash349 2007
[86] S V N L Lalitha andM Sydulu ldquoA directmethod for transmis-sion network cost allocationrdquo in Proceedings of the IEEE TEN-CON Region 10 Conference pp 1ndash6 Hyderabad India Novem-ber 2008
[87] A Parastar A Pirayesh BMozafari B Khaki R Sirjani andAMehrtash ldquoA newmethod for power loss allocation bymodifiedY-Bus matrixrdquo in Proceedings of the IEEE International Confer-ence on Sustainable Energy Technologies (ICSET rsquo08) pp 1184ndash1188 Singapore November 2008
12 Chinese Journal of Engineering
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
[88] A Parastar B Mozafari A Pirayesh andH Omidi ldquoTransmis-sion loss allocation throughmodifiedZ-busrdquoEnergyConversionand Management vol 52 no 1 pp 752ndash756 2011
[89] M W Mustafa S N Khalid H Shareef and A Khairuddin ldquoAnew method for real power transfer allocation using modifiednodal equationsrdquo in Proceedings of the 2nd IEEE InternationalPower and Energy Conference (PECon rsquo08) pp 1306ndash1310 JohorBaharu Malaysia December 2008
[90] Y P Chen and W C Chu ldquoRedistribution of transmission lossbased on z-bus methodrdquo in Proceedings of the 2nd IEEE Inter-national Power and Energy Conference (PECon rsquo08) pp 1016ndash1020 Johor Baharu Malaysia December 2008
[91] H Shareef M W Mustafa S Abd Khalid A Khairuddin AKalam andAMaungThanOo ldquoReal and reactive power trans-fer allocation utilizingmodifiedNodal equationsrdquo InternationalJournal of Emerging Electric Power Systems vol 9 no 6 article4 2008
[92] S Kilyeni O Pop G Prostean and C Craciun ldquoTransmissioncost allocation based on power flow tracing using Z busmatrixrdquoinProceedings of the 14th International Conference onHarmonicsand Quality of Power (ICHQP rsquo10) pp 1ndash6 Bergamo ItalySeptember 2010
[93] A J Conejo N Alguacil and G Fernandez-Ruiz ldquoAllocation ofthe cost of transmission losses using a radial equivalent net-workrdquo IEEE Transactions on Power Systems vol 18 no 4 pp1353ndash1358 2003
[94] J G Vlachogiannis and K Y Lee ldquoDetermining generator con-tributions to transmission system using parallel vector evalu-ated particle swarm optimizationrdquo IEEE Transactions on PowerSystems vol 20 no 4 pp 1765ndash1774 2005
[95] A R Abhyankar S A Soman and S A Khaparde ldquoNew para-digm of tracing algorithms application to fair loss allocation inIndian systemrdquo in Proceedings of the International Conference onFuture Power Systems p 6 November 2005
[96] A R Abhyankar S A Soman and S A Khaparde ldquoAllocationof fixed transmission costs by tracing compliant postage stampmethodrdquo in Proceedings of the 7th International Power Engineer-ing Conference (IPEC rsquo05) pp 1ndash132 Singapore December 2005
[97] A R Abhyankar S A Khaparde S A Soman and P PentayyaldquoA transmission pricing mechanism based on power tracing forcentral transmission utility in Indiardquo International Journal ofEmerging Electric Power Systems vol 2 no 1 article 1033 2005
[98] A R Abhyankar S A Soman and S A Khaparde ldquoReal powertracing an optimization approachrdquo International Journal ofEmerging Electric Power Systems vol 3 no 2 article 1088 2005
[99] A R Abhyankar S A Soman and S A Khaparde ldquoTractabilityof bilateral transactions considering multiplicity of solutionspace in real power tracingrdquo in Proceedings of the IEEE PowerIndia Conference p 8 New Delhi India April 2006
[100] A R Abhyankar S A Soman and S A Khaparde ldquoOptimiza-tion approach to real power tracing an application to transmis-sion fixed cost allocationrdquo IEEE Transactions on Power Systemsvol 21 no 3 pp 1350ndash1361 2006
[101] A R Abhyankar S A Khaparde and S A Soman ldquoMultiplesolutions approach to tackle circular flows in real power trac-ingrdquo in Proceedings of the IEEE Power Engineering Society Gen-eral Meeting p 8 June 2006
[102] A R Abhyankar S A Soman and S A Khaparde ldquoMin-maxfairness criteria for transmission fixed cost allocationrdquo IEEETransactions on Power Systems vol 22 no 4 pp 2094ndash21042007
[103] N A Amoli and S Jadid ldquoAllocation of loss cost by optimal andproportional tracing methodsrdquo in Proceedings of the 2nd IEEEInternational Power and Energy Conference (PECon rsquo08) pp994ndash999 Johor Baharu Malaysia December 2008
[104] Z Hamid I MusirinMMOthman andN A Rahim ldquoEvolu-tionary programming based load tracing optimization in dereg-ulated power systemrdquo httpwwwwseasuse-libraryconferen-ces2011MelonerasACELAEACELAE-27pdf
[105] Z A Hamid I Musirin M M Othman and M N A RahimldquoA novel technique for generation tracing via evolutionary pro-grammingrdquo in Proceedings of the 5th International Power Engi-neering and Optimization Conference (PEOCO rsquo11) pp 381ndash386Selangor Malaysia June 2011
[106] M S S Rao S A Soman P Chitkara R K Gajbhiye N Hem-achandra and B L Menezes ldquoMin-max fair power flow tracingfor transmission system usage cost allocation a large systemperspectiverdquo IEEE Transactions on Power Systems vol 25 no3 pp 1457ndash1468 2010
[107] A Basak S Pal A R Abhyankar and B K Panigrahi ldquoModi-fied equivalent bilateral exchange of transmission pricing usingDIWOrdquo in Proceedings of the Joint International Conference onPower Electronics Drives and Energy Systems (PEDES rsquo10) pp1ndash6 New Delhi India December 2010
[108] K Visakha D Thukaram L Jenkins H P Khincha and P KRoutray ldquoAn approach for evaluation of transmisses chargesbased on desired and deviations of power contracts in openaccessrdquo in Proceedings of the 6th International Conference onAdvances in Power System Control Operation and Management(APSCOM rsquo03) pp 860ndash866 Hong Kong China November2003
[109] K Visakha D Thukaram and L Jenkins ldquoTransmission char-ges of power contracts based on relative electrical distances inopen accessrdquo Electric Power Systems Research vol 70 no 2 pp153ndash161 2004
[110] D Thukaram and C Vyjayanthi ldquoRanking of prospective newgeneration location for a power network in a deregulated sys-temrdquo in Proceedings of the Joint International Conference onPower System Technology (POWERCON rsquo08) pp 1ndash8 NewDelhi India October 2008
[111] D Thukaram and C Vyjayanthi ldquoEvaluation of charges forpower transmission and losses in bilateral power contractsrdquo inProceedings of the IEEE TENCON Region 10 Conference pp 1ndash6Hyderabad India November 2008
[112] D Thukaram and C Vyjayanthi ldquoRelative electrical distanceconcept for evaluation of network reactive power and loss con-tributions in a deregulated systemrdquo IET Generation Transmis-sion and Distribution vol 3 no 11 pp 1000ndash1019 2009
[113] Y Tsukamoto and I Iyoda ldquoAllocation of fixed transmissioncost to wheeling transactions by cooperative game theoryrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 3ndash10 May 1995
[114] P A Kattuman R J Green and J W Bialek ldquoA tracing methodfor pricing inter area electricity tradesrdquo httpwwwdspacecamacukbitstream18102861wp0107pdf
[115] C S K Yeung and A S Y Poon ldquoGame theoretical multi-agentmodelling of coalition formation for multilateral tradesrdquo IEEETransactions on Power Systems vol 14 no 3 pp 929ndash934 1999
[116] CW Yu A K David and Y KWong ldquoThe use of game theoryin transmission embedded cost allocationrdquo in Proceedings of theInternational Conference on Advances in Power System ControlOperation and Management (APSCOM rsquo00) vol 1 pp 139ndash143October 2000
Chinese Journal of Engineering 13
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
[117] C W Yu and Y K Wong ldquoAnalysis of transmission embeddedcost allocation scheme in open electricity marketrdquo ResourceEnergy and Development vol 3 no 1 pp 1ndash11 2006
[118] X Tan and T T Lie ldquoApplication of the shapley value on trans-mission cost allocation in the competitive power market envi-ronmentrdquo IEE ProceedingsmdashGeneration Transmission and Dis-tribution vol 149 no 1 pp 15ndash20 2002
[119] C W Yu A K David C T Tse and C Y Chung ldquoCapacity-use and reliability based transmission embedded cost allocationwith temporal considerationsrdquo International Journal of Electri-cal Power and Energy Systems vol 25 no 3 pp 201ndash208 2003
[120] J M Zolezzi and H Rudnick ldquoTransmission cost allocation bycooperative games and coalition formationrdquo IEEE Transactionson Power Systems vol 17 no 4 pp 1008ndash1015 2002
[121] G C Stamtsis and I Erlich ldquoUse of cooperative game the-ory in power system fixed-cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 151 no 3 pp401ndash406 2004
[122] E Bjorndal G C Stamtsis and I Erlich ldquoFinding core solutionsfor power system fixed cost allocationrdquo IEE ProceedingsmdashGeneration Transmission and Distribution vol 152 no 2 pp173ndash179 2005
[123] M Junqueira L C da Costa Jr L A Barroso G C Oliveira LM Thome and M V Pereira ldquoAn Aumann-Shapley approachto allocate transmission service cost among network users inelectricity marketsrdquo IEEE Transactions on Power Systems vol22 no 4 pp 1532ndash1546 2007
[124] R Bhakar V S SriramN Prasad Padhy andHO Gupta ldquoNet-work embedded cost allocation a game-theoretic approachrdquoin Proceedings of the 32nd National Systems Conference NSCDecember 2008
[125] R Bhakar V S Sriram N P Padhy and H O Gupta ldquoProbabi-listic game approaches for network cost allocationrdquo IEEE Trans-actions on Power Systems vol 25 no 1 pp 51ndash58 2010
[126] J M Zolezzi and H Rudnick ldquoConsumers coordination andcooperation in transmission cost allocationrdquo in Proceedings ofthe IEEE Power Tech Conference vol 3 p 7 Bologna Italy June2003
[127] H Singh S Hao A Papalexopoulos and M Obessis ldquoCostallocation in electric power networks using cooperative gametheoryrdquo httpwwweeeconsultingnetpub 1p1 costallocationpdf
[128] S Balagopalan and V S Anooja ldquoCooperative game theory forsharing transmission charges in electricity marketsrdquo in Proceed-ings of the IETConference on Reliability of Transmission andDis-tribution Networks (RTDN rsquo11) pp 1ndash6 London UK November2011
[129] F D Galiana A J Conejo and H A Gil ldquoTransmission net-work cost allocation based on equivalent bilateral exchangesrdquoIEEE Transactions on Power Systems vol 18 no 4 pp 1425ndash1431 2003
[130] J O F Silva P Cuervo and J C Mateus ldquoRevenue adequacyprocedure in congested networks through equivalent bilateralexchangesrdquo in Proceedings of the CIGREIEEE PES InternationalSymposium pp 44ndash51 New Orleans La USA October 2005
[131] J O F Silva and P Cuervo ldquoAllocating congestion manage-ment costs through use-based principle of equivalent bilateralexchangesrdquo in Proceedings of the 5th International Conference onthe European ElectricityMarket EEM pp 1ndash6 Lisbon PortugalMay 2008
[132] J C Mateus and P C Franco ldquoTransmission loss allocationthrough equivalent bilateral exchanges and economical analy-sisrdquo IEEETransactions on Power Systems vol 20 no 4 pp 1799ndash1807 2005
[133] S Nouri and S Jadid ldquoTransmission network loss allocation viaequivalent bilateral exchanges principle and genetic algorithmrdquoin Proceedings of the 2nd IEEE International Power and EnergyConference (PECon rsquo08) pp 1311ndash1316 Johor Bahru MalaysiaDecember 2008
![Meditation [Dhyan] Versus Relaxation A Review With ...oaji.net/articles/2014/1021-1405155841.pdfA Review With Comprehensive Bibliography Surekha D. Kaundinya*, Dilip V. Kaundinya**](https://static.documents.pub/doc/80x56/5e177d73936f11634063115e/meditation-dhyan-versus-relaxation-a-review-with-oajinetarticles20141021-.jpg)
