Electrical Power and Energy Systems 64 (2015) 398–407

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Congestion management solution under secure bilateral transactionsin hybrid electricity market for hydro-thermal combination

http://dx.doi.org/10.1016/j.ijepes.2014.06.0770142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +91 0172 2534990; fax: +91 1722547986.E-mail addresses: yajvender_verma@yahoo.com, yp_verma@pu.ac.in

(Y.pal Verma), ashwa_ks@yahoo.com (A.K. Sharma).

Yajvender pal Verma a,⇑, Ashwani Kumar Sharma b

a Department of Electrical & Electronics Engineering, UIET, Panjab University, Sector-25, Chandigarh 160014, Indiab Department of Electrical Engineering, NIT Kurukshetra, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 27 June 2013Received in revised form 26 June 2014Accepted 28 June 2014

Keywords:CongestionHybrid marketBilateral transactionRescheduling

The deregulation of power system has created an environment of competitiveness among different mar-ket players and the transmission lines are forced to operate near to their thermal or stability limits. It is achallenge with System Operators (SO) to ensure a secure and reliable transmission of power under theseconditions. This paper proposes a rescheduling based congestion management strategy in hybrid(pool + bilateral) electricity market structure for a combination of hydro and thermal units. The proposedcongestion management problem has been formulated as mixed integer nonlinear programming (MINLP)problem with an objective to minimize the congestion management cost by suitably rescheduling thehydro and thermal units based on their up and down generation cost bids. The hydro units having lowestoperational cost and fast startup time have been used to alleviate the congestion by considering non-con-cave piecewise linear performance curves for them. The secure bilateral transactions have been ensuredwhile rescheduling of the generators for alleviating the congestion. The performance of the proposedmodel has been demonstrated by solving the congestion management problem on modified IEEE-24bus system.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

With advancement in technological research, the installedcapacity of Renewable Energy Sources (RESs) is increasing contin-uously in the generation to meet the growing energy demand. Therise in generation sources combined with increasing demand putadditional burden on our existing transmission infrastructure.The transmission lines capability to transmit the electric power islimited by many factors such as voltage limit, MVA limit, and sta-bility limits. The power system is said to be congested when any ofthese parameters reach to its limit. Further, the deregulation ofelectricity sector has created a competitive environment amongall the market players and increase in number of market playershas added complexity in the operation of the power system [1].In present competitive environment, the transmission lines aremade to operate nearer to their thermal or other stability limits.Sometimes, the congested lines may prevent the market playersto have bilateral contracts leading to increase in the price of theelectricity. Thus, independent system operators (ISO) have a majorchallenge to coordinate among the various market players and

manage a secure and reliable flow of power on the highly burdenedexisting transmission infrastructure [2].

Reactive power support, rescheduling of generation, demandre-adjustment etc. are few approaches which have been appliedto manage the congestion problem. A comprehensive literaturesurvey has been presented on conventional congestion manage-ment techniques in [3]. The congestion management approachesensure that the transfer limits on any transmission line are not vio-lated while keeping the costs of adjustments to minimum possible.The comparison of five congestion management schemes appliedto different electricity markets have been presented in [4].

There are two broad approaches by which the congestion ismanaged; one is technical and the other is financial. The resched-uling based congestion management falls under the category offinancial approach and the methods such as the applications offlexible alternating current transmission systems (FACTS) devicesto provide the reactive power support is a technical approach.The rescheduling based congestion management approach hasbeen applied by various authors for different market set ups con-sidering one or the other issues in competitive electricity market[5–8]. A congestion management method based on real and reac-tive power congestion distribution factor-based zones and genera-tor’s rescheduling has been proposed in [9]. Kumar et al. proposeddistribution factor-based generators’ rescheduling for zonal

List of Symbols

SetsG set of thermal generatorsH Set of hydro generatorsN Set of busesL Set of blocks of non-concave linear characteristics

curves of hydro units

ParametersPmin

gi Pminhi minimum generation from thermal and hydro units

in MWPmax

gi Pmaxhi maximum generation from thermal and hydro units

in MWQmin

gi Qminhi minimum reactive power generation from thermal

and hydro units in MVARQmax

gi Qmaxhi maximum reactive power generation from thermal

and hydro units in MVARVmin

i Vmaxi Min and Max values of the voltages at bus i in per

unitdmin

i dmaxi Min and Max values of the angles at bus i in radians

GDminij GDmax

ij min and max transactions entryPdi load demand at bus i in MWPdb bilateral load demand in MWQdi reactive power demand at bus i MVAR

Cupgi Cup

hi up cost bid by thermal and hydro units in $/MW h

Cdowngi Cdown

hi down cost bid by thermal and hydro units in $/MW h

P0i P0

hi scheduled power for thermal and hydro units in MW

/minhi /max

hi min and max discharge of hydro units in m3/s

rlhi slope of the piecewise-linear unit performance curve

of hydro generator at i th bus in block l MW/m3/sqmax;l

hi maximum water discharge of hydro unit at i th busin block l m3/s

M 0.0036 (Conversion factor to convert m3/s to H m3/h)Whi max water contents allocated to hydro generating

unit iSmax

ij maximum power flow limit in MVA

DPup;rampgi thermal unit up ramp rate limit in MW

DPdown;rampgi thermal unit down ramp rate limit in MW

DPup;ramphi hydro unit up ramp rate limit in MW

DPdown;ramphi hydro unit down ramp rate limit in MW

VariablesPgni rescheduled power generation of the thermal gener-

ating units i in MWPghi rescheduled power generation of the hydro generat-

ing units i in MWPgi power generation of the thermal generating units i in

MWPhi power generation of the hydro generating units i in

MWPgp pool power generated by thermal generating units in

MWPgb bilateral power generated by thermal generating

units in MWQgi reactive power generation of the thermal generating

units i in MVARQhi reactive power generation of the hydro generating

units i in MVARVi voltage at bus i in per unit on 100 kV basedi angle at bus iuhiv l

hi binary variables showing status of hydro unitsub vh binary variable for ensuring generation change either

up or down at any busql

hi water discharge of hydro unit at i th bus in block lm3/s

DPupgi increment of generation by thermal unit i in MW

DPdowngi decrement of generation by thermal unit i in MW

DPuphi increment of generation by hydro unit i in MW

DPdownhi decrement of generation by hydro unit i in MW

;hi water discharge of hydro unit i in m3/s

Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407 399

congestion management [10]. The FACTS controllers’ application inthe transmission line controls the power flow and helps in conges-tion management. A congestion management method based onlocating series FACTS devices in deregulated electricity market tominimize the congestion cost have been presented in [11]. Manyauthors have applied heuristics techniques like particle swarmoptimization (PSO), genetic algorithm (GA) and techniques likeBender’s Decomposition to minimize the cost of congestion duringcongestion management [7,12–14].

The congestion management techniques have been applied tovarious electricity market structures. The common market struc-ture prior to deregulation, which has been studied is the pool mar-ket structure. But post de-regulation, the hybrid (pool + bilateral)market model has become the most favored market structure[15,16]. Kumar et al. have solved congestion management problemin pool and bilateral market structures considering demandresponse based congestion management, using generic load mod-els and FACTS devices ensuring loadability limit [17–20]. Thedetailed modeling how different market players deal in openaccess bilateral market model has been presented in [21]. Thereare few case studies which have been applied to alleviate conges-tion problem in bilateral market, but most of them have ignoredthe secure bilateral transactions during the congestion manage-ment studies. The combination of pool and bilateral model is themost preferred model of future electricity market and the

congestion management can be extended to ensure the securetransactions in a hybrid electricity market.

The RESs due to their unpredictable nature are not preferred formanaging the congestion. They supply power either through firmtransactions or through power pool. Among the cleaner andcheaper sources of energy, hydro is the second largest energyresource available in India. The hydro units have fast turn on char-acteristics and negligible operational cost, which make them suit-able to meet the peak and emergency demand [22]. Hydro unitshave been used along with thermal units to manage the congestionin a pool market structure. The duration considered for the conges-tion management is generally low (1 h) and the characteristics(variations in reservoir level, head etc.) of the hydro units can beused to increase and decrease the generation to manage the con-gestion in such short duration [23]. The hydro generation entitycan also carry out self scheduling of generated energy in day-aheadmarket to maximize their profit. The Market Clearing Price (MCP)is decided by scheduling the thermal units only and the hydrounits are generally considered to be the price takers which helpsin maximizing their revenue by bidding power at a price close tobut lesser than system marginal price [24,25]. However, hydrounits due to their better performance characteristics can be usedto bid in the electricity market along with thermal units to allevi-ate the congestion. The hydro units have been used in combinationwith wind units to bid in the markets as hydro can support the

400 Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407

units during volatilities [22]. However, thermal units are muchreliable than wind power and thus hydro can be used to bid inthe competitive market when used in combination with them. Inthe literature, hydro units have not been used to alleviatecongestion in combination with thermal units considering themunder bilateral contract obligation and ensuring secure bilateraltransaction by bidding in the competitive electricity market.

In this paper, the congestion management approach based onrescheduling of generators has been implemented for a pool andbilateral electricity market. The paper emphasizes on the role ofhydro units in combination with thermal units in congestion man-agement by ensuring secure bilateral contracts. The previouspapers have not incorporated the hydro units for the congestionmanagement with secure bilateral contract. The secure bilateraltransactions between producers and consumers have beenincorporated through transaction matrix GD. The thermal andhydro generating units submit their up and down generation bidsto ISO for congestion management. The operational constraints ofthe thermal and hydro units have been included in the optimiza-tion problem. The participation of hydro units in congestionmanagement is dependent upon the availability of water duringthe congestion. The water discharge, availability of water duringcongestion management has been modeled in the problem. Thecongestion cases have been considered in different lines based ontheir sensitivity towards getting congested. The mixed-integernon-linear congestion management optimization problem hasbeen solved using CONOPT solver of GAMS [26] with interfacingwith MATLAB [27] through rescheduling of generators duringcongestion hour. It is ensured that the rescheduling of generatorskeep the operational parameters like voltage, reactive power andangle within the limits. The results have been obtained forIEEE-24 bus Reliability Test System [28].

The rest of the paper is structured as follows: in section ‘Hybridelectricity market with secure bilateral transaction’ detailed discus-sion on Hybrid (pool + bilateral) market has been presented; thenmodeling of deviations minimizations have been done to facilitatethe secure bilateral transactions. Section ‘Congestion managementbased on rescheduling’ gives the rescheduling based congestionmanagement model. Simulation, results and discussions arecovered in sections ‘Case studies’; Section ‘Conclusions’ carries theconclusions.

Hybrid electricity market with secure bilateral transaction

Hybrid electricity market

The power sector generally carries out many activities whichinclude generation, transmission, distribution, supply and meter-ing of the electricity. Before the restructuring, the power sectorwas constituted by vertically integrated companies. However afterderegulation, the vertically integrated companies were reconsti-tuted as generation, transmission and distribution companies. Asa result, several market structures came up in different countriesaround the world however, electricity pool and bilateral contractsmodel are the two main market arrangements. The pool model is acentralized form of trading electricity with competition focused ongenerators with minimal input from buyers whereas; the bilateralmodel is more market-oriented which encourages moreinteractions between the generators and load centers. Schedulingand dispatch, handling power imbalances and constraints on trans-mission line capacity that may affect the system stability are fewissues which differentiate the two market models from each other.The most preferred practical system that will be adopted in futureis the hybrid electricity market in which pool will co-exist simulta-neously with bilateral and multilateral transactions. The market

participants not only can bid into pool but also can have bilateralagreements with each other [15]. Therefore, this model offers moreflexibility for transmission access. California market model is themost common example of this category.

In pool market model, there are two major entities participatingin the market, supplier (generators) and the buyers (customers).The pool model facilitates competition between generators andthe electricity price offered by the buyers. The generators, ISO,market operator, suppliers etc. are the signatories to a poolingagreement that directs the operation of the pool. The pool operatorcollects the electricity transaction bids and offers from the gener-ators and the customers and prepares the matching bid and MarketClearing Price (MCP) using adopted procedures. The deregulatedenvironment has allowed establishing services contract mutuallybetween the electricity supplier and the customers. The contractsclearly specify the amount and the price of electricity to be traded.If there are no violations of static and dynamic security, the ISOsimply dispatches all the requested transactions and charge forthe services. However, the ISO can curtail contracted power if thereis threat to system security. The ISO does not have the generationcapabilities to balance the system under deviations; the method topay the imbalances is a penalty price. The method is dependent onnumber of factors including the system security. This marketmodel, offers more retail choices for the customers. Thus, bilateraltrading is considered as a suitable model from the point of view ofdynamic incentive to competition and short-term and long-termstability in the supply [15]. The bilateral market model can alsoaccommodate the voluntary power exchange. The bilateral marketmodel permits the generators to decide on the dispatch of theirown generating units. Thus, in pool model the central dispatch isfollowed whereas, the concept of self dispatch is applied to bilat-eral market model.

In this paper, the congestion management solution has beenproposed for a hybrid electricity market having secure bilateralcontracts. The bilateral contract model can be represented as atransaction matrix GD between Generation (G), Demand (D), andany other trading entities (E) [21] as given by Eq. (1).

T �GG GD GEDG DD DE

EG ED EE

264

375 ð1Þ

The diagonal block matrices of transaction matrix are zero, as it isassumed that there are no contracts between any two suppliersor two customers. The elements of the T matrix tij, represents abilateral contract between a supplier Pg of row i with a customerPd of column j.

T � GD �

t11 � � � t1;nd

..

. . .. ..

.

tng;1 � � � tng;nd

2664

3775 ð2Þ

The conventional load flow variables, generation Pg and demand Pd

vectors are expanded into two dimensional matrix as:

Pd

Pg

� �¼ TT 0

0 T

" #ug

ud

� �ð3Þ

where, ug and ud are the column vectors of ones with the dimensionof ng and nd respectively.

The line flow in a DC model can be expressed as below ifud = ug = u:

Pline ¼ DF½Pg � Pd� ð4Þ

where, DF is the distribution factors [29]. The matrix DF dependsupon the configuration and network parameters which generallyare constant.

Pow

er O

utpu

t [M

W]

Water Discharge m3/s

Fig. 1. Non-concave piece-wise linear characteristics curves for hydro units.

Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407 401

Minimization of deviations

Based on the concept of bilateral market model, the deviationsfrom the proposed transactions have to be minimized. This resultsin a new transaction matrix which ensures the secure transactionduring rescheduling of generation. The objective function is:

MinimizeX

i

Xj

bijðGDij � GD0ijÞ

2( )

ð5Þ

Subject to:The power flow equations for real and reactive power are given

by (6) and (7) respectively.

Pi ¼ Pgi þ Phi � Pdi ¼XN

j

ViVjYij cosðdi � dj � hijÞ

8i ¼ 1:2 . . . . . . . . . N ð6Þ

Q i ¼ Q gi þ Q hi � Q di ¼XN

j

ViVjYij sinðdi � dj � hijÞ

8i ¼ 1:2 . . . . . . . . . N ð7Þ

The power balance equations for generation and demand usingbilateral transaction matrix GD for hybrid market model are givenby (8)–(11)

Pdb ¼X

j

GDij ð8Þ

Pgb ¼X

i

GDij ð9Þ

Pg ¼ Pgb þ Pgp ð10ÞPd ¼ Pdb þ Pdp ð11Þ

The power flow equations for the bilateral power is given by (12)

Pfb ¼ DFðPgb � PdbÞ ð12Þ

The power flow equations for the pool power is given by (13)

Pfbp ¼ DFðPgp � PdpÞ ð13Þ

The net power flow is given by (14)

Pf ¼ Pfb þ Pfp ð14Þ

Each generator can generate between its generation capacities only.The real and reactive power generation capacities of thermal andhydro generators are given (15) and (16).

Pmingi 6 Pgi 6 Pmax

gi ; 8i 2 G ð15ÞPmin

hi 6 Phi 6 Pmaxhi ; 8i 2 H ð16Þ

The reactive power limits of the units must also be abided andspecified by (17) and (18) for thermal and hydro units respectively.

Q mingi 6 Q gi 6 Q max

gi ; 8i 2 G ð17Þ

Q minhi 6 Q hi 6 Q max

hi ; 8i 2 H ð18Þ

The voltage and angle limits on the buses are incorporated as givenby (19) and (20) respectively.

Vmini 6 Vi 6 Vmax

i ð19Þdmin

i 6 di 6 dmaxi ð20Þ

The transaction limits between the seller bus-i and buyer bus-j isgiven by (21)

GDminij 6 GDij 6 GDmax

ij 6 min Pmaxgi ; Pdj

� �ð21Þ

The apparent power flow from bus-i to bus-j is given by Eqs. (22)and (23)

Pij ¼ V2i Gii � ViVj½Gii cosðdi � djÞ þ Bii sinðdi � djÞ� ð22Þ

Qij ¼ �V2i Bii þ ViVj½Bii cosðdi � djÞ � Gii sinðdi � djÞ� ð23Þ

The MVA limit for the lines are expressed by (24)

jMVAijj 6MVAmaxij ð24Þ

The line voltage variations have been allowed between 1.05 p.u and0.95 p.u. A new bilateral transaction matrix GD is obtained by solv-ing the objective function (5) under the constraints given by theabove equations. This transaction matrix ensures the secure bilat-eral transactions during the congestion cost optimization problem.

Congestion management based on rescheduling

Here, day-ahead hybrid electricity market has been consideredfor problem formulation. The hydro and thermal generators havesome bilateral contract obligations and rest of the power is con-tributed towards pool market. The objective of the congestionmanagement problem formulation is to minimize the cost of con-gestion in a system containing hydro and thermal units subject totheir equality and inequality operational constraints ensuringsecure bilateral transactions for them. The components of the con-gestion management cost are the up and down costs and the powerof the hydro and thermal generating units. Mathematically theproblem can be stated as:

Minimize

CC ¼Xi2g

ðCupgi DPup

gi Þ þ Cdowngi DPdown

gi

� �þXi2h

Cuphi DPup

hi

� �

þ Cdownhi DPdown

hi

� �ð25Þ

Subject to the constraints:(i) Equality constraintsEqs. (6) and (7) give the real and reactive power injections at

each bus. The total up and down generation during congestionmanagement should be equal and is given by (26)

XN

i

DPupgi

� ��XN

i

DPdowngi

� �þXN

i

DPuphi

� ��XN

i

DPdownhi

� �¼ 0; 8i 2 N

ð26Þ

The rescheduled generation on generator i is equal to day-aheadschedule and the up and down in generation by that unit duringcongestion management and given by (27).

Table 1Day-ahead schedule and incremental/decremental cost bids of IEEE-24 bus system.

Busno.

Generatortype

P0g

(MW)Q0

g

(MVAR)

Incremental costbids ($/MW h)

Decremental costbids ($/MW h)

1 Thermal 152 41.42 18 202 Thermal 152 45.51 14 157 Thermal 150 120.00 15 178 Hydro 240 192.08 10 12

13 Hydro 236 200.00 12 1315 Thermal 450 46.00 12 1516 Thermal 150 16.00 7 918 Hydro 350 10.00 10 1221 Thermal 300 10.00 16 1822 Thermal 310 36.00 12 12.523 Thermal 350 92.00 12.5 15.5

402 Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407

Pgni ¼ P0i þ DPup

gi � DPdowngi 8i 2 N ð27Þ

Pghi ¼ P0hi þ DPup

hi � DPdownhi : 8i 2 H ð28Þ

The injected real and reactive power can thus be given by (29) and(30) respectively.

Pi ¼ Pgni þ Pghi � Pdi ð29ÞQ i ¼ Q gi þ Q hi � Q di ð30Þ

The performance of the hydro units has been modeled by piece-wise linear non-concave curves as shown in Fig. 1. The binary vari-ables uhi and v l

hi represent the status and discharge of the hydrounits. The first variable denotes the status of hydro generating unit.The variable uhi is equal to 1, if the unit is committed during conges-tion management. The variable v l

hi is 1, if the water discharge of thei th unit exceeds the limit in lth block. Being a short term congestionmanagement solution the head variations effect on the hydro unitperformance can be neglected.

P0hi þ DPup

hi � DPdownhi ¼ Pmin

hi uhi þXL

l¼1

qlhir

lhi; 8i 2 H ð31Þ

;hi ¼ ;minhi þ

XL

l¼1

qlhi; 8i 2 H ð32Þ

The DPuphi and DPdown

hi generation in hydro units is dependent uponthe minimum power generation Pmin

hi and the power generated bywater discharge ql

hi in total block period of L and given by (31).The water discharge in all block periods l can be calculated by (32).

(ii) Inequality constraints: The system is subjected to manyinequality constraints on thermal and hydro generatingunits. The rescheduled real power on hydro as well as onthermal units must remain within the limits as given by(33) and (34).

Pmingi 6 P0

gi þ DPupgi � DPdown

gi 6 Pmaxgi ; 8i 2 G ð33Þ

Pminhi 6 P0

hi þ DPuphi � DPdown

hi 6 Pmaxhi ; 8i 2 H ð34Þ

The change in generation at any bus can be either up or down bothfor hydro and thermal units. The same has been modeled by (35)and (36).

Pgi ¼ P0gi þ ubDPup

gi � ð1� ubÞDPdowngi ð35Þ

Phi ¼ P0hi þ vhDPup

gi � ð1� vhÞDPdowngi ð36Þ

The reactive power limits of the units and the voltage and anglelimits have been specified by (17)–(20) respectively.

The water discharge for the hydro units should also be withinthe limits as given by (37)–(45)

;minhi uhi 6 ;hi 6 ;max

hi ð37Þql

hi 6 qmax;lhi uhi; 8l ¼ 1; i 2 H ð38Þ

qlhi P qmax;l

hi v lhi; 8l ¼ 1; i 2 H ð39Þ

qlhi 6 qmax;l

hi v l�1hi ; 8l–1; i 2 H ð40Þ

qlhi P qmax;l

hi v lhi; 8l–1; i 2 H ð41Þ

The power generated by the hydro unit during congestion manage-ment is limited by the water contents allocated to the generators.But the available water must be able to meet at least the day-aheadschedule of power generating unit.

M;hi 6Whi; 8i 2 H ð42Þ

Here, M is a conversion factor to convert m3/s into H m3/h. Whi is thewater contents allocated by hydro generator company at ith busduring congestion management for rescheduling. The power flowthrough the congested transmission lines should be limited to theirMVA limit as given by (43) and the formulation for real and reactive

power flow between bus i and j has already been given by Eqs. (22)and (23)

P2ij þ Q 2

ij 6 Smaxij

� �2ð43Þ

In addition to the above constraints, the up and down ramp ratelimits for all the generating units are also used. The ramp ratesfor the thermal and hydro units are specified by (44)–(47)respectively.

0 6 DPupgi 6 DPup;ramp

gi ; 8i 2 G ð44Þ

0 6 DPdowngi 6 DPdown;ramp

gi 8i 2 G ð45Þ0 6 DPup

hi 6 DPup;ramphi ; 8i 2 H ð46Þ

0 6 DPdownhi 6 DPdown;ramp

hi 8i 2 H ð47Þ

The power balance equations for generation and demand usingbilateral transaction matrix GD for hybrid market model have beenmodeled using (8)–(11) and (21).

Case studies

The simulation studies solving congestion management prob-lem have been conducted on modified IEEE-24 bus test system.The hydro plants have been added in the existing system of gener-ators along with thermal plants. The data of day-ahead scheduleand incremental and decremental cost bids for the hydro and ther-mal plants have been given in Table 1.

The IEEE-24 system has eleven generators at bus number1,2,7,8,13,15,16,18,21,22, and 23. The generating units at bus num-ber 8, 13 and 18 have been modeled as the units of hydro compa-nies and the remaining belong to the thermal generationcompanies. The different cases of congestion have been consideredwhich include congestion on single line (15–16), congestion ontwo lines (15–16) and (14–16) and congestion on three lines(15–16), (14–16) and (6–10). The cases for congestion in transmis-sion lines have been considered assuming the power flow maxi-mum ratings in the corresponding lines below their base powerflows assuming there is no threat to the system security. The objec-tive is to minimize the congestion cost as specified by (23) aftersolving the objective specified by (5).

Congestion on line (15–16)

The congestion condition on line (15–16) has been simulated byconsidering the line rating limit to be 150 MVA instead of 500 MVAactual rating. The secure bilateral transactions have been obtainedsolving GD matrix deviation minimization. Fig. 2 shows securetransactions that can take place between the generation companiesand load entities.

04

812

1620

24

05

1015

20

0

0.5

1

1.5

GeneratorsLoads

Pow

er [p

.u.]

Fig. 2. Secure bilateral transaction between generators and loads.

Table 2Hydro generator data.

Busno.

Pmaxh

(MW)Pmin

h

(MW)Qmax

h

(MVAR)Qmin

h

(MVAR)Wf ðHm3=hÞ ;minðm3=sÞ ;maxðm3=sÞ

8 500 40 150 �50 1.4 10 10013 590 81 240 �50 2.5 20 20018 450 68 200 �50 1.5 10 120

Table 3Generators up and down generation for congestion management.

Gen 1L congestion line (15–16) Without bilateral contractAll values in per unit

Pg Pgn DPug DPd

gPg Pgn DPu

g DPdg

1 1.52 1.52 – – 1.52 1.52 – –2 1.52 1.52 – – 1.52 1.52 – –7 1.5 1.5 – – 1.5 1.5 – –8⁄ 2.4 2.4 – – 2.4 2.4 – –13⁄ 2.36 3.067 0.707 2.36 3.067 0.70715 4.5 3.7 – 0.80 4.5 3.7 – 0.8016 1.5 2.3 0.8 – 1.5 2.3 0.8 –18⁄ 3.5 3.5 – – 3.5 3.5 – –21 3.0 2.618 – 0.3824 3.0 2.618 – 0.382422 3.1 2.776 – 0.3246 3.1 2.776 – 0.324623 3.5 3.5 – 3.5 3.5 –

⁄ Hydro units.

0 4 8 12 16 20 240

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Unit No

Pow

er [p

.u.]

Pg

Pgn

Fig. 3. Day-ahead and after congestion management schedule.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240.94

0.96

0.98

1

1.02

1.04

1.06

Bus No

Vol

tage

[p.u

]

V NL

V 2L

Fig. 4. Bus voltage profile for day ahead and rescheduled generation.

Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407 403

The secure transactions have been incorporated by calling GDmatrix in GAMS from the MATLAB environment in the optimiza-tion problem discussed earlier [26,27]. The incremental and decre-mental cost bids of the companies have been fixed considering themarginal locational prices obtained from the power flow solution.Under normal operating condition, the flow through line (15–16)was 226.33 MVA. The line flow limit was reduced to 150 MVAand thus, the line gets congested. The day-ahead schedule for thishour has to be rescheduled for congestion management. The oper-ating costs of the hydro units are small hence; the bids for gener-ation up and down have been fixed lower. The maximum andminimum voltage limits for the buses have been assumed1.05 p.u and 0.95 p.u respectively. The data corresponding to thehydro units (i.e. maximum and minimum MW and MVAR capacitylimits, maximum water available, water discharge limit duringcongestion etc.) are given in Table 2.

The units are already assumed to be operating and hence theirstarts up costs have not been considered. The each generating unitalso has a ramp rate limit and it has been fixed to be 80 MW for allthe generators participating in congestion management. During

congestion management, the bilateral transactions are not allowedto be affected. A case has also been simulated when there are nobilateral transactions between the Gencos and Discos. It has beenobserved that for single line congestion, the bilateral transactionsdo not put additional cost for rescheduling the generation of gen-erators as shown in Table 3. The congestion management cost forsingle line congestion is 3348.7 $/h. The congestion cost mayremain unaffected due to sufficient individual line capacities whichmay settle congestion for the same up and down bids with theleast cost. The hydro units’ characteristics curves have beenassumed piece wise linear in three blocks of slopes 0.3 MW/m3/s,0.7 MW/m3/s, 0.5 MW/m3/s respectively with each block havingmaximum discharge limit of 30 m3/s, 60 m3/s and 30 m3/s forgenerating unit 8, 13 and 18 respectively.

Two line congestion case

The second case of congestion was considered with two con-gested line i.e. line (15–16) & (14–16). The base power flows onthese lines were 226.33 MVA and 332.84 MVA respectively. Thecongestion on these lines was considered by reducing the line flowlimits to 150 MVA and 300 MVA respectively from their respectivelimits of 500 MVA each.

Fig. 3 shows the generators which are participating in thecongestion management with their day ahead and rescheduled gen-eration. It can be observed that the units offering lower bid pricessuch as 8, 13, 15 and 22 reschedule their generation up to their ramplimits. The other adjustments are made on the remaining generatorsin order of their bid prices. It is very important during reschedulingthat none of the parameters violate any limits. The variations ofvoltage with two lines congested having secure bilateral transaction

Table 4Day-ahead and rescheduled generation for two line congestion.

Gen 2 congestion line (15–16) & (14–16) Without bilateral contractAll values in per unit

Pg Pgn DPug DPd

gPg Pgn DPu

g DPdg

1 1.52 1.52 – – 1.52 1.52 – –2 1.52 1.52 – – 1.52 1.52 – –7 1.5 1.5 – – 1.5 1.50 – –8⁄ 2.4 2.847 0.447 – 2.4 2.8641 0.4641 –13⁄ 2.36 3.12 0.762 2.36 3.16 0.80 –15 4.5 3.7 – 0.80 4.5 3.7 – 0.8016 1.5 2.119 0.619 – 1.5 2.0897 0.5897 –18⁄ 3.5 2.997 – 0.5031 3.5 2.9965 – 0.533521 3.0 3.0 – – 3.0 3.0 – –22 3.1 2.575 – 0.5249 3.1 2.579 – 0.52123 3.5 3.5 – – 3.5 3.5 – –

⁄ Hydro units.

0 4 8 12 16 20 240

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Unit No

Pow

er [p

.u]

Pg

Pgn

Fig. 5. Day-ahead and after congestion management schedule.

0 4 8 12 16 20 240

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Unit No

Pow

er [p

.u]

Pdb

Pgb

Pgp

Pdp

Fig. 6. Pool and bilateral generation and load in 3-Line Congested Case.

0 4 8 12 16 20 24240.94

0.96

0.98

1

1.02

1.04

1.06

Bus No

Vol

tage

[p.u

.]

V 3Line congestionV 2 Line congestionV 1Line congestion

Fig. 7. Voltage profile for 3 congestion cases after congestion management.

404 Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407

and with no congestion on any line are shown in Fig. 4. The resched-uling during congestion management on the line does impact thevoltage slightly which can be observed from the figure.

The congestion management case has also been simulatedwithout any bilateral transactions with two congested lines. Dur-ing congestion management on two line congestion, the up and

down rescheduling of the generators get affected when there areany bilateral transactions on the system. Table 4 shows the day-ahead Pg and new generation schedule Pgn along with up and downchange in power by different generators during congestionmanagement. The congestion management cost during bilateraltransaction is 3927.56 $/h whereas, the cost with no bilateraltransaction is 3911.56 $/h. The secure bilateral transactions mayimpact the flow on certain lines and some units may not havebid with the price that they could have quoted without bilateralagreement. Thus, the location and amount of congestion willdecide the effect on congestion management cost, when thereare bilateral contracts between different entities.

Three line congestion case with hydro units

In this case study, the congestion was considered in three differ-ent transmission lines. These are line (15–16), (14–16) and (6–10).The base power flows on these lines are 226.33 MVA, 332.84 MVAand 124.15 MVA respectively. These lines were made congested byreducing the line flow limits of the transmission lines to 150 MVA,300 MVA and 100 MVA from their normal rating of 500 MVA,500 MVA and 175 MVA respectively. The day-ahead Pg and newgeneration schedules Pgn have been depicted in Fig. 5. It can beobserved that the location of congested line affects the up anddown generation change in a generator. Until line (6–10) was con-gested, the unit No. 2 did not participate in the congestion manage-ment but, with congestion in (6–10) line, the rescheduling of unit 2was economical. The cost of congestion management for threelines with secure bilateral transaction is 4537.31 $/h. Fig. 6 showsthe pool and bilateral power generation of different units

0 4 8 12 16 20 24-1.5

-1

-0.5

0

0.5

1

1.5

Bus No

Rea

ctiv

e P

ower

[p.u

.]

Q with Bilateral ContractQ without Bilateral Contract

Fig. 8. Reactive power with and without bilateral contract.

Fig. 9. Cost comparison with and without bilateral contract for different congestedLines.

2 4 6 8 10 12 14 16 18 20 22 240.94

0.96

0.98

1

1.02

1.04

1.06

Bus No

Vol

atag

e [p

.u.]

Voltage Without Hydro Unit

Voltage with Hydro Unit

Fig. 10. Bus voltage profile during congestion management with and without hydrounits.

Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407 405

participating in congestion management along with pool and bilat-erally contracted load during three line congestion situation.

The congestion management process adjusts the bus voltageson the buses with major reshuffle occur in the proximity ofcongested lines. A comparison of voltage profiles for day-aheadschedule and after congestion management is shown in Fig. 7 for

Table 5Results of hydro generators after congestion management.

Bus no. DPuh (MW) DPd

h (MW) Qg (MVAr)

8 31.90 – �19.2213 69.04 – �50.0018 – 80 200.0

Table 6Generation schedule with and without hydro units’ participation.

Gen 3L congestion line with hydroAll in per unit

Pg Pgn DPug DPd

g

1 1.52 1.52 – –2 1.52 1.773 0.2535 –7 1.5 1.5 – –8⁄ 2.4 2.719 0.319 –13⁄ 2.36 3.055 0.6905 –15 4.5 3.7 – 0.816 1.5 2.113 0.6126 –18⁄ 3.5 2.7 – 0.821 3.0 2.824 – 0.175622 3.1 3.0 – 0.1023 3.5 3.5 – –

⁄ Hydro units.

three different cases of congested lines. The results show that morethe congestion lines more are the variations in voltages. The reac-tive power is also very significant in power system as it affects thevoltage profile on the buses. Fig. 8 shows the reactive power flowon various buses during and without Bilateral Contract. The hydrounit 18 generates the reactive power to its limit and tends toreduce the overall reactive power requirement of the system.

The secure bilateral transaction tends to fix the power flow andas a result the scheduling cost of generating units during conges-tion management may be affected. However, the location andamount of congestion on the lines may also change the up anddown rescheduling of the generators and in returns the congestioncost. The variations in the congestion management costs for differ-ent congested lines with and without bilateral transactions havebeen shown in Fig. 9.

The hydro units also tend to participate in congestion manage-ment during three lines congestion case. The hydro units’characteristics curves have been assumed piece wise linear in threeblocks with slopes and discharges as mentioned in section‘Congestion on line (15–16)’ already. The total water contentsallocated to different units during congestion management are1.5 Hm3/s, 2.5 Hm3/s and 1.4 Hm3/s respectively. Out of their

/h (m3/s) q1h (m3/s) q2

h (m3/s) q3h (m3/s)

89.26 30 30 19.26157.12 60 60 17.12

91.78 30 30 21.78

3L congestion without hydro units

Pg Pgn DPug DPd

g

1.52 1.52 – –1.52 1.80 0.28 –1.5 2.03 0.53 –2.4 2.4 – –2.36 2.36 – –4.5 3.7 – 0.801.5 1.865 0.365 –3.5 3.5 – –3.0 2.61 – 0.393.1 2.3 – 0.803.5 4.5 0.8 –

0 4 8 12 16 20 24-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Bus No

Rea

ctiv

e P

ower

[p.u

.]

Q without Hydro Units

Q with Hydro Units

Fig. 11. Reactive power generation with and without hydro units.

0 2 4 6 8 10 12 14 16 18 20 22 240

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Unit No

Gen

erat

ion

[p.u

.] Pg

Pgn

Fig. 12. Thermal unit generation schedule with and without hydro unit duringcongestion management.

406 Y.pal Verma, A.K. Sharma / Electrical Power and Energy Systems 64 (2015) 398–407

maximum generation limits during congestion management thehydro units 8 and 13 increases the generation by 31.90 MW and69.04 MW respectively whereas, the unit 18 decreases the genera-tion by 80 MW. Table 5 shows the results for hydro units after con-gestion management. The water discharge corresponding to threeblocks along with the reactive power generation and maximumdischarge have been shown.

Three line congestion case without hydro units

In this case, the role of hydro units in the congestion manage-ment has been studied. It is assumed that no hydro units are par-ticipating in the congestion management. The comparison ofparticipation of thermal units in rescheduling their generation dur-ing congestion management with and without hydro units isdepicted in Table 6. Figs. 10 and 11 show the voltage and reactivepower profile at buses with and without hydro units participatingin congestion management. The cost of congestion goes up whenhydro units do not participate in congestion management. The con-gestion cost without the participation of hydro unit is 5163.29 $/hand it is 4537.31 $/h when hydro units participate in congestionmanagement. There is an increase of 625.98 $/h when no hydrounits participate in congestion management. There is an overallincrease in the day-ahead schedule of power without the participa-tion of hydro units. Fig. 12 shows the day-ahead Pg and new gener-ation schedule Pgn of thermal generating units when there are nohydro units available for rescheduling. The use of hydro unit incongestion management can play a vital role in the successfulintegration of renewable sources due to proximity of these sourcesin remote areas. By introducing three extra hydro generating units,

hydro or thermal, can relax the solution space of the optimizationproblem and can get a better solution for congestion problem.

Conclusions

In this paper, the rescheduling based congestion managementmethod has been proposed for a system containing hydro and ther-mal units considering their operational constraints for pool andbilateral market. The hydro units performance is included throughpiece-wise linear characteristics curves. The short term wateravailability prediction can be utilized for rescheduling during con-gestion management. The generations of the units have beenrescheduled to manage the congestion for multi-line congestionproblems by ensuring the secure bilateral transactions. The costof the congestion is related with the number of congested linesand the amount of congestion. The secure bilateral transactionsalso affect the cost of congestion which depends upon the locationof congested lines, the amount of congestion and the entities underbilateral contract. The reactive power balance during the conges-tion management ensures that voltage remains within limitsduring rescheduling of generation of the generating units. Thelow operating cost hydro units having quick start up time can playan important role in reliable integration of renewable due to theirlocational proximity and ability to manage the congestion.

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