Usage-Based Transmission Loss Allocation

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Published in IET Generation, Transmission & DistributionReceived on 24th February 2010Revised on 9th May 2010doi: 10.1049/iet-gtd.2010.0143

ISSN 1751-8687

Usage-based transmission loss allocationunder open access in deregulatedpower systemsP.V. Satyaramesh1 C. RadhaKrishna2

1APTRANSCO, Vidyut Soudha, Hyderabad, AP 500062, India2UGC – ASC, J.N.T. University, Hyderabad, AP, IndiaE-mail: [email protected]

Abstract: This study presents a usage-based methodology of transmission loss allocation in deregulated powersystems under open access. This new approach calculates the portion of real power transmission losscontributions from the generators and simultaneously the portion of real power transmission loss allocated tothe loads using their contract obligations with the generators in the open access environment. A power flowprocedure is used to calculate power loss in the system. It is desirable to take network loss effect of injectionpower at each node for calculating contribution of transmission loss by each generator and loss allocated toloads based on its contractual obligations with consumer. In this study, a methodology is proposed tocalculate the total real power loss in transmission network into components to be allocated to the generatorsand loads. This study focuses on development and application of the equivalent loss compensation conceptfor open access environment. Effectiveness of the proposed algorithms has been demonstrated on sample5-bus and IEEE-118 bus power networks.

1 IntroductionIn the open access system, consumers/Discom companiesrequire a fair and equitable pricing structure that reflectsboth the share of power consumed in the network and thecost of active transmission loss, based on loss that theycause. Loss is always present in transmission lines andtransformers because of resistances. Total loss intransmission system typically amounts only to the extent of3–5% of the total generation. Even though this figure issmall, it is significant in terms of accumulated effect onrevenue. Any proposal for restructuring without a solutionto the problems because of loss is incomplete andunacceptable. The loss allocations have influence ondecision making of the electricity-market participants fortheir financial commitments and their profits. There is aneed to find the contribution of loss by each generator anddistribute the same among market participants. In general,each trade should include its share of transmission loss. Inessence, the net generation should equal the sum of thedemands and the transmission loss caused by the trade.

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The total transmission loss caused by all the trades on thenetwork can be either measured or calculated.

Many different loss allocation schemes exist in this area,but no single method gained universal acceptance. Theproblem of allocating the transmission-active power lossamong the power system users has become more importantwith the increase in the competition level in electricitymarkets. Commercial issues related to charges for powerloss are taken into consideration, subject to negotiationsbetween consumers/distribution utilities and generatingcompanies.

In open access system, a non-profit organisation known asindependent grid operator (IGO) usually is responsible forthe operation of the system. In addition to the operationand control of a system, typical tasks of an IGO may alsoinclude accepting schedules from generators, providingaccess to the successful consumers and allocatingtransmission loss among the generators and consumers. AnIGO also plays the role of a supervisor for system planning

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and security. It would keep track of all information related tothe trading and calculate the transmission usage for eachgenerator. In this model, suppliers and consumersindependently arrange trades, setting by themselves underconcurrence of IGO the amount of generation andconsumption and the corresponding financial terms.Coordination is necessary because physical laws dictate theflow of power from the generators to the consumers in atransmission network. The IGO coordinates among theindependent trades, which would not lead to a violation oftransmission network constraints. In addition, power flowsmust be balanced throughout the network and transmissionloss must be included in power balance. The energy loss inthe transmission network is a function of the aggregatetrades, and therefore the trades have to account for theirown loss.

The main other concern of the IGO, with respect totransmission loss, is to allocate loss either to the generatorsor consumers. Based on the allocation of transmission lossand previously agreed terms, a generator or consumer isrequired either to compensate or to pay its share of loss. Ineither case, the allocation of transmission loss is a debatableissue for the simple fact that transmission loss is a complexnon-linear function of power provided by the generatorsand sensitive to state of system. This methodology iscomputationally efficient and can be utilised to calculate theloss contributions from the generators and its allocation toconsumers. The objective is to recover as much of theactive power loss as possible subject to the terms andconditions of agreement. IGO employs loss-compensationapproaches to balance the difference between the totalsystem loss and the recovered loss.

The evaluation of loss allocations by proportional sharingprocedures has been widely discussed in many papers [1–11].Cost-based transmission loss allocation methods arepresented in [12]. These methods are suggested to allocatethe system loss to generators and loads in a pool market orto individual transactions in a bi-lateral contracts market.They are mainly classified into four categories: (i) Pro-ratamethods allocate the transmission system loss to thegenerators and loads proportional to their active powergeneration and load consumption. The main disadvantageof this approach is not taking topology of network intoaccount. It is not fair as it allocates the same amount ofloss when two identical loads are considered, in which onemay be located near to generators and the other is far awayfrom generators. (ii) Incremental transmission loss (ITL)methods utilise the sensitivities with respect to nodalinjections to allocate the loss to generators and loads. TheITL methods depend on the selection of the slack bus andthere is no allocation of loss to the slack bus. (iii)Proportional sharing procedures allocate the system loss byusing the tracing techniques. The main drawback is thatthere is no possibility of allocation of loss to generators andloads at the same time. (iv) Transactional loss allocationmethods are formulated according to bilateral contracts in

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competitive markets. This paper focuses on the allocationof loss where generators jointly maintain the contractualobligations with consumer/Discom companies in an openaccess system.

The transmission loss compensation schemes consideredas ancillary services are presented in [13–16]. A non-profitorganisation known as independent system operator usuallyis responsible for the operation of these ancillary services.

The negative loss allocations are due to counter-flows. It isdue to the power flow that opposes the initial flow in aparticular transmission line [17, 18]. The net effects ofseveral transactions simultaneously reduce the net realsystem loss. It is argued in [15] that negative lossallocations are unreasonable, opting for heuristic allocationin which for each transaction is assigned positive lossallocation.

The content of present paper is organised as follows.Section 2 presents mathematical formation of proposed lossallocation methodology under open access environment.Algorithm for the proposed approach is indicated inSection 3. Sample 5 bus power systems is used as anexample to illustrate the proposed method in Section 4,followed by conclusions in Section 5.

2 Mathematical formulationof loss allocation in open accesssystemA method to allocate transmission loss for simultaneousbilateral transactions in open access is proposed. The paperpresents an approach to allocate total loss of the systembased on

(i) the ‘exact loss formula’, using bus injected powers and

(ii) a set of coefficients (the amounts of generation utilised byconsumers) that measure the participation of each busgenerator in relation to located-bus-contracted demandsand vice versa. These coefficients are named as usagecoefficients. There are no additional approximationsassumed in the proposed approach, resulting in avoidanceof inaccuracies induced during the formulation stages of themethod.

The standard loss formula for power network [19] isexpressed in terms of amount of power utilised by Discomcompanies/consumers from individual generators. Theproposed method illustrates the splitting of total loss asallocations to each generator and each load by using theusage coefficients.

The methodology starts from a converged load flowsolution, which gives the entire information pertaining tothe network such as bus voltages, complex line flows, slack

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bus power generation and total transmission loss etc. Once aload flow solution is obtained, this result is then adopted inthe proposed methodology to allocate transmission loss toeach load and generator using their usage coefficients.

Consider a power system with NGEN generators and NBloads (no. of buses) connected through a transmissionnetwork. It is assumed that all bus loads are suppliedthrough contractual obligations. An attempt is made hereto separate the non-linear system loss into the sum of NBterms (one transaction per allocation of loss to loads) andsimilarly the sum of NGEN terms (one transaction percontribution of loss from generators). The main difficultyin allocating a component of system loss to a generator/consumer arises because of the highly non-linear nature ofloss equation in which the combined set of all usagecoefficients interact through the load flow terms. Otherimportant factors are consideration of mutual interactionsbetween different transactions and interaction of reactivepower flows in the real power loss allocation. Thus, the lossallocation procedure depends on path and the usagecoefficients of generators and loads.

Let the generators set G ¼ {G1, G2, G3, . . ., GNGEN}and the load set L ¼ {L1, L2, L3, . . ., LNB}.

A transmission loss formula using bus injected powers andthe system parameters is given [19] as follows

PL =∑NB

i=1

∑NB

j=1

[Aij(PiPj + QiQj) + Bij(QiPj − PiQj)] (1)

where

Aij =Rij

|Vi||VJ |cos(di − dj)

Bij =Rij

|Vi||VJ |sin(di − dj)

(2)

PL is the real power loss of the power system, Vi is the voltagemagnitude of bus i, di is the voltage phase angle of bus i, Si isthe injected power at bus i (Si ¼ Pi + jQi), Zij ¼ Rij + jXij

and Zij is the (i, j)th element of Zbus.

2.1 Active power loss allocation togenerators

Let aij be the usage coefficient, that is fraction of powergenerated at jth bus received by the load at ith bus.

The load at bus i can be expressed as the sum of usageamounts from different generators that is

PLoadi =∑NGEN

j=1

aijPGj , where i = 1, 2, . . . , NB (3)

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The injected real power at bus i is given as

Pi = PGi − PLoadi (4)

Substituting the above equation (3) in (4), the injectedpowers can be written as

Pi = PGi −∑NGEN

j=1

aijPGj , where i = 1, 2, . . . , NB (5)

The above equations can be rewritten as, by introducing xij,

Pi =∑NGEN

j=1

xijPGj , where i = 1, 2, . . . , NB (6)

where xij ¼ 2aij, for non-generation buses; xij ¼ 1 2 aij,for generator buses.

Rearrange the above equation (1) as components of self-power (active, reactive) and mutual-power components

PL =∑NB

i=1

∑NB

j=1

[Aij(PiPj) + Bij(QiPj − PiQj)] + [AijQiQj]

(7)

The injected active powers at ith and jth bus are written in theform of (8) as shown below

Pi =∑NGEN

k=1

xikPGk, where i = 1, 2, . . . , NB (8)

Pj =∑NGEN

m=1

xjmPGm, where j = 1, 2, . . . , NB (9)

The above equation (7) can be rewritten as

PL = PL1 + PL2 + PL3 (10)

where the terms PL1, PL3 can be treated as the losscomponents because of solely the active and the reactivepower injections, respectively, and PL2 represents as the losscomponent created by interaction between the active andreactive power injections.

Substituting active injected powers expressed in (8) and (9)in the equation

PL1 =∑NB

i=1

∑NB

j=1

AijPiPj (11)

and can be written as

PL1 =∑NGEN

k=1

∑NGEN

m=1

∑NB

i=1

∑NB

j=1

AijxkixmjPGkPGm

( )[ ](12)

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Substituting injected powers expressed in (8) and (9) in

PL2 =∑NB

i=1

∑NB

j=1

Bij(−PiQj + QiPj) (13)

and can be written as

PL2 =∑NGEN

k=1

∑NB

i=1

∑NB

j=1

Bij(−xkiQj + Qixkj)PGk

[ ](14)

The active power loss because of purely reactive powerinjection at each bus also may be taken as PL3, where

PL3 =∑NB

i=1

∑NB

j=1

[AijQiQj] (15)

It is observed that the active power loss caused because ofinteraction of reactive power injections is around 2% oftotal active power loss. Hence, it is assumed thatreallocation of the active power loss because of interactionof reactive power injections to kth generator is

PGk∑NGENk=1 PGk

PL3 (16)

Substitute the above equations (12), (14), (16) in (10) andrearrange to decompose into self-terms and interactive terms.

The loss contribution component because of individualgenerator kth alone is expressed as

P (k,k)L = PGk∑NGEN

k=1 PGk

PL3 +∑NB

i=1

∑NB

j=1

AijxkixmjPGkPGk

+∑NB

i=1

∑NB

j=1

Bij(−xkiQj + Qixkj)PGk (17)

PL(k,k) is a part of total loss that completely depends on power

generation of kth generator.

The loss component because of interaction of generator kand generator m is expressed as

P (k,m)L =

∑NB

i=1

∑NB

j=1

Aij(xkixmj +xmixkj)PGkPGm, k=m (18)

PL(k,m) is a part of total loss that arises from interaction

between kth generator and other generators of network.

It is common practice to allocate the above term as half ofthe absolute value of PL

(k,m) to each generator of pair (k, m)


rather than the total amount to the individual generators.

P (k)L = P (k,k)

L +∑NGEN

m=1,m=k

1

2P (k,m)

L (19)

and the same computation can be applied to the other termsof the generators.

Total active power loss is

PL =∑NGEN

k=1

PkL (20)

2.2 Active power loss allocation to loads

Alternately, in similar lines to that of Section 2.1 above forgenerators, the active power loss allocations to loads arederived.

Let bij be usage coefficient, that is the fraction of loadpower at jth bus supplied by the generation at the ith bus.

The generation at bus i can be expressed as the sum ofusage amounts from different loads, that is

PGi =∑NB

j=1

bijPLoadj , where i = 1, 2, . . . , NGEN (21)

Substituting the above equations (21) in (4), the injectedpowers can be written as

Pi =∑NB

j=1

bijPLoadj − PLoadi , where i = 1, 2, . . . , NGEN

(22)

The above equations can be rewritten as, by introducing hij

Pi =∑NB

j=1

hijPLoadj , where i = 1, 2, . . . , NGEN (23)

where hij ¼ bij where j ¼ 1, . . . ,NB and j = i or j distinct i

hij = bij − 1 for j = i

The injected active powers at ith and jth bus are written in theform of (24) and (25) as shown below

Pi =∑NB

k=1

hikPLoadk, where i = 1, 2, . . . , NGEN (24)

Pj =∑NB

m=1

hjmPLoadm, where j = 1, 2, . . . , NGEN (25)


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Equation (1) is split into

PL = P ′L1 + P ′

L2 + P ′L3 (26)

where the terms P ′L1, P ′

L3 can be treated as the losscomponents because of purely active and reactive powerinjections, respectively, and P ′

L2 represents the losscomponents created by interaction between the active andreactive power injections.

Rearrange and decompose into self-terms and interactiveterms in similar lines of procedure described for generators.

The active loss component because of individual load kthalone is expressed as

P ′(k,k)L = PLoadk∑NGEN

k=1 PLoadk

PL3 +∑NB

i=1

∑NB

j=1

AijhkihmjPLoadkPLoadk

+∑NB

i=1

∑NB

j=1

Bij(−hkiQj + Qihkj)PLoadk (27)

The loss component because of interaction of load k withload m is expressed as

P ′(k,m)L =

∑NB

i=1

∑NB

j=1

Aij(hkihmj + hmihkj)PLoadkPLoadm, k = m

(28)

The loss contribution to the kth load is given by reallocatinghalf of the amount of loss component because of interactionof load k with load m

P ′(k)L = P ′(k,k)

L +∑NB

m=1,m=k

1

2P ′(k,m)

L (29)

Total active power loss is

PL =∑NB

k=1

P ′kL (30)

2.3 Modification of slack bus elements

The injected power at slack bus is embedded with the totalloss of the system, which are not evident at the outset. Theinjected power given in (6) and (23) at the slack bus doesnot tally with the corresponding elements of aij, bij forslack bus for this reason. Therefore there is a need tomodify these elements corresponding to the slack bus inorder to make injected power at the slack bus power tallywith (6) and (23).

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Actually, the injected power at slack bus, s is

Ps = PGs + PL − PLoads (31)

and (20) can be written as PL =∑NGEN

k=1 (PkL/PGk)PGk.

Substituting the above equation in (31) and the modifiedvectors related to slack bus are

Ps = PGs +∑NGEN

k=1

PkL

PGk

PGk −∑NGEN

k=1

askPGk (32)

for slack bus

xsk = −ask +Pk

L

PGk

if slack bus is a non-generator bus

(33)

xsk = 1 − ask +Pk

L

PGk

if slack bus is a generator bus (34)

In similar lines, elements of h for slack bus can be modified as

hsk = bsk +P ′k

L

PLoadk

if slack bus is a non-generator bus

(35)

hsk = bsk − 1 + P ′kL

PLoadk

if slack bus is a generator bus

(36)

2.4 Presence of counter-flows

In a deregulated electrical power system network, everytransaction of electricity between a generator and a customerresults in some transmission loss. However, in some cases, agenerator while supplying its load may actually decrease thetransmission loss by opposing an initial flow. This flow iscommonly called as ‘counter-flow’. A generator can causedecrease in transmission loss only when there exists an initialflow in the opposite direction by another generator. Thecounter-flow in the system will be dependent on relativeposition of the generators and loads’ in the system.

As counter-flows cannot exist with a singe source in thenetwork and requires at least two sources in network, it isobvious to divide the benefit of counter-flow among thegenerators. As mentioned in the above section, it iscommon practice to allocate the cross terms as half of thevalues rather than the total amount to the individualgenerators.

Counter-flows indicate only the relative magnitudes offlow contributions in a line by the generators in a system.The concept of counter-flow stems from the relativeposition of suppliers (generating utilities) and buyers

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(loads) with respect to each other. This relative positionmakes a difference in the overall transmission loss allocation.

Thus a user who causes more network loss must be chargedmore whereas a user who helps to reduce the loss, because ofcounter-flow, must be rewarded.

3 Computational procedure forallocation of lossThe computational procedure of the proposed concept isbriefly described here. First, an IGO acquires all therequired contractual information and quantity of poweragreement from the participants. The IGO developspreferred values of xij, hij considering the utilisation ofpower by all participants. Then, the IGO performsfeasibility studies using power flow tools. In case of nocongestion, the preferred trading with generators is feasibleand the IGO has to evaluate the loss caused by eachgenerator or load because of its utilisation and allocate theloss to all the participants. In presence of congestion,however, the preferred trading with generators is infeasibleand the IGO has to find other solutions, for examplegeneration rescheduling to relieve the congestion. Since lossmanagement for the congestion case, which may occur fora short period compared to normal operation period, is notin the scope of this paper, only the loss allocation methodfor the feasible trading is reported. The proposed methodcan be utilised to allocate transmission loss among thegenerators and loads in a deregulated network. Thealgorithm presented for loss allocation for the generators isdescribed in detail below. Alternately, in similar lines analgorithm for loss allocation for loads is also developed.

In the first step of iteration, the loss has been assumed tobe zero. This makes the required generation equal to the loadat the beginning.

Then the program computes loss allocation to thegenerators by using (19) and total loss by (20) and updatesthe usage coefficients of slack bus by using (33) and (34)with this computed loss.

In second iteration, the program computes the loss allocationof generators with updated usage coefficients, total loss andcompares the total loss with the loss in first iteration. Ifdifference is not within the specified tolerance, the usagecoefficients of generators are updated again and the programproceeds for next iteration. The process is repeated untilspecified tolerance is obtained. The detailed algorithm forcomputing loss allocation to generators is given below.

Algorithm overview

1. Read power system data and bus voltages, complex lineflows and slack bus power generation and total transmissionloss of converged load flow.


2. Calculate the injected powers from solution of the powerflow, by using (4).

3. Form the matrices A, B as per (2).

4. Read the amount of specified contracted generations forthe loads, that is aij, bij, respectively.

5. Find the loss because of own interaction of reactivepowers, PL3, according to (15). Allocate the PL3 to therespective generators according to the amount of generationby (16).

6. Set the iteration count i ¼ 1.

7. Set dp loss ¼ 0, [PL](i) ¼ 0.0 and set d ¼ 1028.

8. Calculate PL(k,k), PL

(k,m) where k and m ¼ 1, 2, . . . , NGENas per (17) and (18), respectively.

9. Calculate loss shared by all generators by PLk where k ¼ 1,

2, . . . , NGEN as per (19).

10. Calculate the total loss PL, as per (20).

11. Set [PL](i+1) ¼ PL.

12. dp loss ¼ [PL]i+1 2 [PL]i.

13. Update the contributions of loss for PLk where k ¼ slack

bus according to (33) and (34).

14. Check dploss ≤ d.

15. If ‘No’ increment i ¼ i + 1 and go to 8.

16. Print allocation of loss to the generators.

17. Stop.

Similarly, the same algorithm is used for allocation of lossto loads by replacing NGEN with NB and applying therelevant equations.

4 Loss compensation scheme foractive powerThe proposed approach for loss compensation to be utilisedby IGO is presented in this section. The section presentsan approach that every trading arrangement is required tohave, with each individual generator/load for taking care ofits own loss or required to compensate the loss in openaccess. To perform this task, a loss compensation scheme isdeveloped in this section. The advantage of this approach isthat once an agreement in the open access is so defined,results derived in the previous sections become valid. Theloss allocation formulae defined in previous section are used


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to determine the allocation of loss for each generator/load.Having identified the allocation of loss, the approachcalculates the equivalent loss compensation required togenerate at the slack bus because of the specified injectionof real power at other buses. The IGO then suggests tocompensate specified amount of loss by either increasingthe generation or reducing the load. The methodology ispresented in the following.

The power balance equation including loss before injectioncan be shown as

Ps +∑NB

i=1,i=s

Pi = PL (37)

where Ps is the active power injection at slack bus, Pi is theactive power injection at ith bus and PL is the active powerloss of system.

The total transmission loss is expressed as a function ofinitial power loss P0

L and the change in total transmissionloss as DPL because of small injection of active power atbuses, that is

PL = P0L + DPL (38)

The equivalent loss compensation for active power with theinjection of real power, DPi at ith bus generally results indecreasing the injection at the slack bus with all contractson the system remaining unchanged, that is with theadditional amount of power DPi injected at bus i into thesystem to off load the loss compensation at the slack bus,the power balance equation becomes

Ps − DPs +∑NB

i=1,i=s

(Pi + DPi) = PL + DPL (39)

−DPs +∑NB

i=1,i=s

DPi = DPL (40)

The exact transmission loss using bus injected powers andsystem parameters are given in (1). Now the active powerloss of system can be expressed as Taylor series about initialactive power loss PL

0 , before injection, where the terms inTaylor series expansion are the injected power DPi at eachbus with only the linear terms retained

PL = P0L +

∑NB

i=1,i=s

∂PL

∂Pi

DPi (41)

The term (∂PL/∂Pi) represents the loss sensitivity factor,which is defined as an incremental change of real powerloss by an incremental change of scheduled power injectedinto bus. This loss sensitivity factor can be obtained by

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differentiating (1) w.r.t. Pi, that is

∂PL

∂Pi

= 2AiiPi +∑NB

j=1,j=i

[(Aij + Aji)Pj + (Bij − Bji)Qj] (42)

By rearranging (44–46)

PL − P0L =

∑NB

i=1,i=s

∂PL

∂Pi

DPi = DPL = −DPs +∑NB

i=1,i=s

DPi

(43)

DPs =∑NB

i=1,i=s

1 − ∂PL

∂Pi

[ ]DPi (44)

Let

gi = 1 − ∂PL

∂Pi

( )(45)

gi is called as the loss compensation index at bus i. Thephysical interpretation of gi is as follows. gi MW injectedat ith bus is equivalent to reducing loss compensation by1 MW at the slack bus

DPs =∑NB

i=1,i=s

giDPi (46)

The equivalent loss compensation at ith bus is given byDPi ¼ (DPs/gi).

The proposed approach is classified into three categories:

1. Total system loss is compensated by slack bus as explainedin the computational procedure above (loss allocationmethodology).

2. Loss compensation scheme

(a) Each generator uses its own generation to compensate forits allocated loss i.e. the generators are self-compensatingwith their specified compensation fractions (self-losscompensating scheme).

(b) All consumers buy IGO compensation service with leastsystem loss optimisation or least loss cost optimisation.

3. Combination of both (a) and (b) mentioned in (2) above.

4.1 Self-loss compensating scheme

Slight increase in the generation at generator bus to share lossfrom the slack bus results in a small change of loss. The smallchange of loss in the system assuming no changes in loadsafter increasing DPGi of each generator bus to compensate

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the loss, becomes

DPs =∑NGEN

Gi=1,Gi=s

gGiDPGi (47)

where gGi = (1 − (∂PL/∂PGi)) and

∂PL

∂PGi

= 2AiiPGi +∑NGEN

j=1,j=i

[(Aij + Aji)PGj + (Bij − Bji)QGj]

(48)

4.2 IGO-acquired loss compensation

The IGO corrects the generation dispatch for losscompensation at designated buses using the proposedmethodology. The corrective ‘generation dispatch’ with losscompensation must also take into consideration thetransmission line overload and voltage violations. The OPFprogram has been executed by changing the generatorlimits corresponding to the loss compensation along withother constraints such as voltage, overloads of transmissionline etc. Then OPF model for the optimal loss allocationminimises the cost or price or total loss, while satisfying allthe necessary network limits

min∑NGEN

i

ciDPi (49)

subject to the constraints

Sij ≤ Smaxij

DPi ≤ Pmaxi − P0

i

DPi ≤ P0i − Pmin

i

V mini ≤ Vi ≤ V max

i

(50)

4.3 Combination method

The combination method involves the use of both thealgorithms described above.

5 Case studies5.1 Loss allocation methodology

To demonstrate the effectiveness of the proposedtransmission loss allocation methodology for bilateralenergy transactions in open access, the proposedmethodology is applied to three cases such as a sample5-bus system, IEEE-118-bus system and Indian practicalpower system.

The sample system with five nodes, seven branches andthree generators is shown in Fig. 1. The total trading ofsystem is 330 MW and three generators have bilateral


trading agreements with individual loads. Thecorresponding usage coefficients are shown in Table 1. Thetotal trading operates with these three suppliers G1, G2and G3 to supply the five loads according to the contractedamount of MW using the whole network, that is thereexists five simultaneous trades corresponding to threegenerators and five loads.

Test calculations have been performed on sample 5-bussystem and the results are tabulated in Table 1. Acomputer program is developed on Matlab to implementthe proposed approach. Table 1 shows the allocation of lossto generators/loads and the corresponding values of losscompensation indices gi, obtained through the applicationof proposed approach. The total network loss(7.5135 MW) is successfully allocated to all users and theresults are presented in Table 1. The generation at bus-1(slack bus) supplies the system loss of 7.5135 MW. Usingthe algorithm presented in the previous sections, theprocess of contribution of loss from generators convergeswithin five iterations. It is observed that active power lossbecause of purely reactive power injection isPL3 ¼ 0.0137 MW. It is around 0.0182% of the total loss.It is observed that the developed methodology gives rise toloss allocations to both generators/loads, which are alwayspositive in absence of counter-flows.

5.1.1 Impact of the proposed usage coefficientsin loss allocation: The impact of proposed usagecoefficients, alpha and beta used in formulae is studiedfrom the point of view of the fairness to all users and fromthe economic signal to the market. This is because, for thesame scenario of generation, demand, network andcorresponding loss, the loss allocation between users maybe very different, depending on usage between generatorsand loads.

Five different cases are carried out in order to show theimpact of alpha. The same power flow solution is utilisedfor all cases and hence the total system loss is the same forall five cases.

Case 1: From Table 2, one observes that generator 1 trades anamount of 90 MW to supply the customer loads at buses 3and 4, whereas generator 2 trades an amount of 120 MWto supply the customer load at bus 5 and the generator 3supplies to buses 2 and 3.

Figure 1 Sample 5-buses test system


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Table 1 Usage coefficients of sample 5-bus test system and loss allocations to thegenerators and loads

Node no. Percentage MVAcontracted agreement of

consumers with thegenerators

Loss allocatedto loads

Loss allocatedto generator

Gamma value, gi

G1, % G2, % G3, %

1 0 0 0 0 2.0717 1

2 0 33.3333 0 0.1676 2.7662 0.989233

3 100 0 0 2.0717 2.6756 0.982985

4 0 66.667 0 2.5986 1.018831

5 – – 100 2.6756 1.089155

total 100 100 100 7.5135 7.5135

Under these conditions the loss allocation can be obtainedas follows:

P (1,1)L = 2.98 MW, P (2,2)

L = 5.30 MW, P (3,3)L = 0.35 MW

P (1,2)L = 0.14 MW, P (1,3)

L = 0.26 MW, P (2,3)L = 1.24 MW

P1L = 3.05 MW, P2

L = 4.61 MW, P3L = 0.14 MW

It is observed from the above results that the cross termbetween G1 and G2 is negative. This means that lossallocated to G1 and G2 decreases when the trading of bothgenerators G1 and G2 coexist.

The negative sign further signifies that generator 1 causes aflow in the same direction as the net whereas generator 2causes a flow in the opposite direction. The same analogywill be applicable to the cross terms between G2 and G3. Itis also observed that the calculated loss contribution fromG3 is negative. This means that the trading amount of G3causes only counter-flow, which helps generally to reducethe system loss. Hence, generator 3 will receive a negativeloss allocation, which has to be rewarded.

It is observed that depending on usage coefficients ofsuppliers (generators) and consumers (loads), the allocationof transmission loss gets changed abruptly. Since counter-flow would increase the allocated loss of some generatorsand decrease the allocated loss of other generators, thechoice of usage coefficients becomes a subject ofimportance. This fact will be illustrated under five differentcases assuming the following conditions:

1. System state condition remains unchanged.

2. The delivered amounts for utilisation from the generator 3are varied.

3. The corresponding changes are made in generator 1.

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4. Keeping all bilateral contracts and usage from generator 2fixed,

5. Case 1 is taken as base.

Case 2: As an illustration, the amount of trading by generator1 with load 3 is increased and load 4 is decreased in steps of10 MW (to maintain generation at bus constant). Thismeans that the relative positions of load 3 and load 4 arechanged w.r.t. generator 1.

Simultaneously the amount of trading by G3 with load 3 isincreased by 10 MW (to maintain load at bus 3 constant) andcorresponding changes made for the amount of trading byG3. The load 4 is entered into utilisation of power fromG3 newly (to maintain load at bus 4 constant). It isunderstood that the relative distance for load 4 is somewhat decreased with respect to G1. The revised usagecoefficients of generators and loads are shown in Table 2.

The loss allocation obtained is as follows

P (1,1)L = 2.75 MW, P (2,2)

L = 5.30 MW, P (3,3)L = 0.46 MW

P (1,2)L = −0.03 MW, P (1,3)

L = 0.37 MW,

P (2,3)L = −1.34 MW

P1L = 2.92 MW, P2

L = 4.61 MW, P3L = −0.02 MW

The loss allocated to the generator 1 has slightly decreasedbecause of decrease of relative distances of its contracts.

Case 3: With further increase of amount of trading by load 3and decrease of load 4 with generator 1 and correspondingchanges made in the amount of trading by generator 3 forload 3 and load 4, the relative distances of loads 3 and load4 are reduced. The revised usage coefficients of generatorsand loads are shown in Table 2.

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Table 2 Usage coefficients data for Cases 1–5 and allocation results

Case no. Generator Consumer 2 Consumer 3 Consumer 4 Consumer 5 Allocation Total loss, MW

Case 1 No MW (aij) MW (aij) MW (aij) MW (aij)

G1 0 10(0.11111) 80(0.88889) 0 3.0435 7.5135

G2 0 0 0 120 (1) 4.61

G3 40(0.333) 80(0.666) 0 0 20.14

Case 2 G1 0 20(0.2222) 70(0.7778) 0 2.9235 7.5135

G2 0 0 0 120 (1) 4.61

G3 40(0.333) 70(0.5833) 10(0.08333) 0 20.02

Case 3 G1 0 30(0.3333) 60(0.667) 0 2.8 7.5135

G2 0 0 0 120 (1) 4.61

G3 40(0.333) 60(0.5) 20(0.16667) 0 0.125

Case 4 G1 0 40(0.44444) 50(0.55556) 0 2.6805 7.5135

G2 0 0 0 120 (1) 4.61

G3 40(0.33333) 50(0.41667) 30(0.25) 0 0.223

Case 5 G1 0 50(0.55556) 40(0.44444) 0 2.5587 7.5135

G2 0 0 0 120 (1) 4.6097

G3 40(0.33333) 40(0.33333) 40(0.33333) 0 0.3451

Loss allocation obtained is as follows

P (1,1)L = 2.56 MW, P (2,2)

L = 5.30 MW, P (3,3)L = 0.62 MW

P (1,2)L = 0.08 MW, P (1,3)

L = 0.41 MW,

P (2,3)L = −1.45 MW

P1L = 2.80 MW, P2

L = 4.61 MW, P3L = 0.1 MW

This in turn results in decrease of loss allocation ofgenerator 1. The counter-flow because of coexistenceof G1 and G3 coincides with dominant flow (notethe value of PL

3 ) and results in increase of loss allocationto G3.

Case 4: The influence in loss allocation because offurther change of amount of trading by G1 and G3 is shownin below:

P (1,1)L = 2.40 MW, P (2,2)

L = 5.30 MW, P (3,3)L = 0.81 MW

P (1,2)L = 0.19 MW, P (1,3)

L = 0.38 MW, P (2,3)L =−1.56 MW

P1L = 2.6805 MW, P2

L = 4.6067 MW, P3L = 0.2233 MW

Note the revised value of PL3.


Case 5: The influence in loss allocation because of furtherchange is given below

P (1,1)L = 2.27MW, P (2,2)

L = 5.30 MW, P (3,3)L = 1.04MW

P (1,2)L = 0.29MW, P (1,3)

L = 0.28 MW, P (2,3)L =−1.67MW

P1L = 2.5587 MW, P2

L = 4.6097 MW, P3L = 0.3451 MW

The loss allocation to G3 became positive which is asignificant change.

Table 3 shows consolidated loss allocations to generatorsfor all the five cases. It is observed that loss allocation togenerator 1 is decreased from base case to case 5 whereasfor generator 3 it is increased. This will be true until aturning point is reached. Such a result is due to the fact

Table 3 Comparison of loss allocations to generators for fivecases

Generator Case 1 Case 2 Case 3 Case 4 Case 5

1 3.0435 2.9235 2.8 2.6805 2.5587

2 4.61 4.61 4.61 4.61 4.61

3 20.14 20.02 0.125 0.223 0.3448

7.5135 7.5135 7.535 7.5135 7.5135


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that the transactions of G3 initially are on the counter-flowdirection helping to reduce the loss allocation to generator3. At some point, the transactions of G3 will becomealigned with the dominant flow causing the loss allocationsto increase.

5.1.2 Case study on IEEE-118 bus system: Anothercase study is also carried out on a larger system by consideringIEEE-118 bus system with 118 nodes, 186 branches and 19generators for testing the proposed approach. The totaltrading of system is 4242 MW. In order to simplify thecontents of IEEE-118 bus system, the bilateral tradingagreements with individual load nodes and correspondinggenerator nodes are only shown in Table 4. It becomesvoluminous to mention Table 4 in the form of Table 1.

For example, take second row of Table 4. The generationat bus 10 is given as 450 MW and the load at bus 1 as51 MW in IEEE-118 bus system. It is assumed that theload bus 1 has a bilateral trading agreement with generatorat bus 10. The coefficients of a, b are computed as follows:a1,10 ¼ 51/450 ¼ 0.1133 and b10, 1 ¼ 1.0, that is 100%of its load is met from generator 10. In similar lines, thecoefficients of a, b are computed for remaining generatorand load nodes, respectively.

T Gener. Transm. Distrib., 2010, Vol. 4, Iss. 11, pp. 1261–1274i: 10.1049/iet-gtd.2010.0143

The results are tabulated in Tables 4 and 5. Tables 4 and 5show the loss allocation to generators and loads, respectively,corresponding values of loss compensation indices gi,obtained through the application of proposed approach forIEEE-118 bus system. The total trading operates withthese 19 generators to supply 99 consumers according tothe contracted amount of MW using the whole network. Itis assumed that the generation at bus-69 (slack-bus)supplies the system loss of 132.863 MW.

It is observed from the above case study that there is nocounter-flow in the system.

5.2 Loss compensation

The proposed categories of loss compensation allocationmethodologies presented in the previous section are testedon IEEE-118 bus system in this paper. They are mainly(a) self-loss compensating scheme, (b) IGO-acquired losscompensation scheme and (c) both (a) and (b) together.The results are tabulated subsequently.

The compensating capacities and the prices of the playersthat bid to provide loss compensation services are shown inTable 6.The test results show that the self-acquisition and

Table 4 Contracted load data from generators of IEEE-118 bus test system and loss allocation to generators

S. no. Bus no. Participation of buying nodes in the transaction with the generator Allocated loss gi

1 10 1 2 3 4 6 7 8 11 12 13 14 41 0.2533 0.922632

2 12 16 18 0.02513 1.00146

3 25 15 17 19 20 21 23 43 50 0.01428 0.99268

4 26 24 27 28 29 31 32 33 35 36 0.08406 0.961766

5 31 102 108 0.0002 0.99842

6 46 84 109 0.00074 0.99985

7 49 34 39 104 106 118 0.02426 1.003071

8 54 46 48 0.00039 1.00717

9 59 42 45 73 0.00288 1.01835

10 61 44 47 49 53 0.00851 0.989152

11 65 59 60 72 85 0.03696 1.00065

12 66 51 52 54 55 56 62 83 0.05708 0.99164

13 69 66 67 70 74 80 107 0.09504 0.938287

14 80 75 76 77 78 79 90 114 117 0.19346 0.94378

15 89 22 40 57 58 82 88 91 92 93 94 95

96 99 100 101 103 105 110 115 0.48657 0.91149

16 100 112 116 0.08289 0.971498

17 103 98 113 0.00252 0.99883

18 111 86 97 0.00155 0.99708

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Table 5 Loss allocation to the loads for IEEE-118 bus system

Busno.

Allocatedloss

gi Busno.

Allocatedloss

gi Busno.

Allocatedloss

gi Busno.

Allocatedloss

gi Busno

Allocatedloss

gi

1 0.02829 0.96857 2 0.01108 0.968724 3 0.0216 0.97546 4 0.0219 1.0021 6 0.02919 1.05584

7 0.01162 1.02974 8 0.01679 1.042086 11 0.03915 1.03397 12 0.02616 1.0015 13 0.01885 0.97994

14 0.00787 0.97958 41 0.0208 1.084766 16 0.00739 0.99671 18 0.01774 0.9961 15 0.00569 0.9859

17 0.00078 1.04556 19 0.00286 0.984473 20 0.00117 1.00325 21 0.00098 1.0405 23 0.00048 1.04367

43 0.00117 0.9826 50 0.00115 1.006053 24 0.00352 1.06583 27 0.01901 1.0222 28 0.00459 1.0348

29 0.00645 1.00481 31 0.01153 0.998416 32 0.01589 1.04435 33 0.0061 0.9771 35 0.00875 0.9698

36 0.00822 0.97027 102 0.00014 0.995756 108 0.00006 1.00877 84 0.00046 1.0713 109 0.00028 1.00438

34 0.00707 0.97235 39 0.00335 1.053988 104 0.0046 0.992 106 0.00528 1.0141 118 0.00396 1.05618

46 0.00023 0.99985 48 0.00016 1.010088 42 0.00176 1.05438 45 0.00101 1.0165 73 0.00011 1.03781

44 0.00088 1.02022 47 0.00181 1.017666 49 0.00458 1.00307 53 0.00124 1.0215 59 0.02622 1.01835

60 0.00734 0.98781 72 0.00117 1.082888 85 0.00223 0.98216 51 0.00243 1.0078 52 0.00258 1.02727

54 0.01722 1.00717 55 0.00904 1.016109 56 0.01205 1.01312 62 0.01101 0.9928 83 0.00275 0.95551

66 0.00945 0.99164 67 0.00685 1.018839 70 0.01582 0.98914 74 0.01853 1.0858 80 0.03216 0.94378

107 0.01223 1.0262 75 0.01873 0.955515 76 0.02722 1.06518 77 0.02571 1.0734 78 0.02874 1.08255

79 0.01573 1.07308 90 0.06615 0.960219 114 0.00323 1.05716 117 0.00795 0.9631 22 0.00785 0.97323

40 0.05314 1.09777 57 0.00945 1.002757 58 0.00945 1.02116 82 0.04247 1.0208 88 0.03793 1.0452

91 0.0078 0.95991 92 0.05174 0.942535 93 0.00951 1.04043 94 0.0235 0.9679 95 0.03389 0.99497

96 0.02979 1.00789 99 0.03302 1.01685 100 0.02902 0.9715 101 0.01736 1.0167 103 0.0181 0.99883

105 0.02439 1.00795 110 0.0307 0.993747 115 0.01746 1.05776 112 0.02235 1.0509 116 0.06054 1.04006

98 0.00211 1.01363 113 0.00041 1.047313 86 0.00101 1.1013 97 0.00054 0.9918

IGO provided compensation procedures developed in thispaper are effective and provide good flexibility in arrangingfor loss compensation service in usage-based schemes ofopen access.

5.2.1 Self compensation by generators: The losscontributions of generators and loss compensation indicesare calculated by using (47) and (48) for IEEE-118 bussystem is shown in Table 6. The self-acquisition option isexercised in a straightforward manner by a generator asshown in Table 6. The equivalent generation required atgenerator bus will be calculated by using the losscompensation indices to compensate its share of loss. Theloss compensation capacities along with their costsdetermined by this procedure for self-loss compensation aresummarised in Table 6. The cost incurred because of theself-loss compensation scheme is 2556.8 $/h.

5.2.2 Least-price loss compensation methodology:The generators make use of least-price loss compensationservice acquired by IGO. The IGO-acquired least-priceloss compensation scheme for generators is the solution ofthe modified OPF problem formulated with the specifieddata. Since at the optimal solution, the IGO calculates losscompensation for each of the generators, the total costs willbe distributed accordingly to generator. The results forleast-price loss compensation are shown in Table 6. The


least cost price for the loss compensation is 3897.5 $/h.The major portion of loss compensation is taken place from89th generator bus, as it is a nearby generator for the majorloads. It is observed that the schemes depend on thelocation of generators and loads, which participated inleast-price compensation of the loss. It is observed fromTable 6, even if the compensation capacities available at25th, 49th and 61st generator buses, IGO could not utilisetheir compensation capacities because of the process ofoptimal prices for loss compensation. This is mainlybecause of consideration of the limits imposed on theloading of transmission lines interconnected to the saidgenerators. Thus, the limits on the transmission loadingshave an impact on evaluation of the least-price losscompensation.

5.2.3 Self compensation and least-price losscompensation methodologies: In this case generators10, 12, 31, 46, 89, 100, 103 and 111 undertake self-acquisition for loss compensation and the remaininggenerators make use of least-price loss compensation serviceacquired by the IGO, shown in Table 6. Since at the optimalsolution, the IGO calculates loss compensation for each ofthe generator, the total costs will be distributed accordinglyto generators. The generators are able to obtain their losscompensation at the designated slack bus, bus 69; the cost is3897.5/MWh. It is observed that even if there is provision


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Table 6 Costs of compensation data in the IEEE-118 bus system and results for compensation schemes

Bus compensation data A. Self-compensation B. Leastcompensation

C. Self and least compensation

Compensationnode

Ck,$/MWH

Max Dpk,MW

Dpk,MW

Total cost,$/h

Dpk,MW

Total cost,$/h

Mode Dpk,MW

Total cost,$/h

10 12.5 30 27.454 343.18 30 375 self 27.45 343.125

12 15 5 2.509 37.64 5 75 self 2.5093 37.6395

25 30 30 1.44 43.2 0 0 self 1.439 43.17

26 14 10 8.7402 122.36 10 140 self 8.74 122.36

31 15 2 0.02 0.3 2 30 self 0 0

46 19 5 0.0742 1.41 5 95 self 0.074 1.406

49 27 20 2.4186 65.3 0 0 IGO 0 0

54 13 20 0.04 0.52 20 260 IGO 20 260

59 12 10 0.2828 3.39 10 120 IGO 10 120

61 30 50 0.86 25.8 0 0 IGO 0 0

65 20 10 3.7 74 10 200 IGO 10 200

66 22.5 35 5.8 130.5 35 787.5 IGO 35 787.5

69 15 15 9.5 142.5 15 225 IGO 25 375

80 20 10 20.5 410 10 200 IGO 10 200

89 20 60 53.382 1067.64 60 1200 IGO 50 1000

100 10 10 8.5 85 10 100 self 8.53 85.3

103 10 4 0.3 3 4 40 self 0.252 2.52

111 15 4 0.155 2.33 4 60 self 0.1555 2.3325

2558.06 3907.5 3580.353

for compensation of loss by generators 49 and 61, they couldnot be participated because of the optimal solution.

6 ConclusionsThe paper presents a new method for loss allocations toconsumers/Discoms in power systems under open accessmarkets environment. The proposed approach has beendemonstrated on a sample 5-bus and IEEE-118 bussystems. The approach proposed here enables thecalculation of actual active power loss contributions fromgenerators and allocation of loss to consumers. This usefultool is expected to be effectively suitable for planning theloss contributions from generators under open accessenvironment. Once market has defined a set of proposedcontractual agreements among generators and loads, theapproach systematically calculates the loss componentsallocated to each individual generator and loads by usingexact loss equation. The loss compensation techniquespresented in the paper are very effective and expected tobe highly useful in open access environment. The loss

T Gener. Transm. Distrib., 2010, Vol. 4, Iss. 11, pp. 1261–1274i: 10.1049/iet-gtd.2010.0143

compensation by loads is under future work. The proposedapproach for loss allocation is tested for large practicalpower system that is an Indian state power system andsimilar results can be expected for large practical systems.Then proposed methodology is tested on Indian statesystem, which comprises of 481 buses with 29 generatingplants, 399 load buses and 854 branches. The totalgeneration and total load of the system are 7576.938 and7237.239 MW, respectively, and total loss obtainedthrough load flow studies is 342.818 MW. The usagecoefficients are calculated according to their utilisationsbased on their bilateral contracts.

7 AcknowledgmentsThe authors acknowledge the support and encouragementextended to them by their respective organisations.However, the views expressed in this paper are of theauthors in their individual capacity and not necessarily thatof APTRANSCO of Andhra Pradesh.

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[3] KIRSCHEN D., ALLAN R., STRBAC G.: ‘Contributions ofindividual generators to loads and flows’, IEEE Trans.Power Syst., 1997, 12, (1), pp. 52–60

[4] KIRSCHEN D., STRBAC G.: ‘Tracing active and reactive powerbetween generators and loads using real and imaginarycurrents’, IEEE Trans. Power Syst., 1999, 14, (4),pp. 1312–1318

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Usage-Based Transmission Loss Allocation

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