Allocation of Transmission Fixed Charges- An Overview-96

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IEEE Transactions on Power Systems, Vol. 11,No . 3, August 1996 1409ALLOCATIONOFTRANSMISSIONFIXEDCHARGES:ANOVERVIEW

J W Marangon LimaEsfola Federal de Engenharia de ItajubaBrazil

Abstract - The application of marginal cost in pricing thetransmission services has shown not effective mainly due torevenue reconciliation problems. To overcome this, a set of othermethods derived from the MW-mile rule has been suggested toallocate transmission fixed costs . This paper compares suchmethods known as embedded cost methods in a centralizedtransmission nehyork environment. Although these methodsactually share the total cost and are very simple, they are usuallyrejected due to the lack of a good economic reasoning. Theeconomic issue and the impact on the system expansion planningof such allocation will be addressed in this paper. Some exampleswith the Brazilian transmission system will illustrate the resultsderived from thisanalysis.Keywords - Transmission pricing, Wheeling Transaction, UtilityRegulation

INTRODUCTIONThe new trend toward unbundling of services (i.e., generatio%transmission and distribution) and incorporating some degree ofcompetition in generation are becoming a commonplace indifferent countries [1,2]. Tranmssion open access is one of theessential issues in this process and it thereforeneeds some specialattention. In this way, pricing and investments of transmissionsystem are frequently at the heart of regulation problems.One of the challenges ahead is the development of rules that allowthe shared use of transmission system by utilities and third-partygeneration. Besides ensuring the technical quality of thetransmission service (voltage control, static and dynamic securityconstraints, etc.), these rules should satisfy other criteria,including [3]:

no cross-subsidies00 easy of regulation

0 economic signals for dimensioningcontinuity of the charge

transparency of cost allocation procedureensure an adequate remuneration of present and hturetransmission investments

95 SM 574-4 PWRS A paper recommended and approvedby the IEEE Power Syste m Engineering Committee of th eIEEE Power Engineering Society for presentati on atthe 1995 IEEE/PES Summer Meeting, July 2 3 - 2 1 , 1995,Portland, OR. Manuscript submitted December 28, 1994;made available for printing June 5, 1995.

Some methods have been proposed and may be classified as oneof the following paradigms: embedded cost, incremental cost andcomposite embedddincremental cost. Belonging to the set ofincremental methods, the short term marginal cost [4-6] has beenthe most popular due to its economic basis, that is, it can providethe economic signals for operation and dimension. Somelimitations have been observed in its application to powertransmissionsystems such as: not recovering all the transmissioncosts, the charges obtained may be highly volatile, charges for @transmission system are based on generation costs rather than itsown cost, the transmission system is usually not in the optimalcondition, and so forth.On the other hand, the embedded cost methods provide, ingeneral, an adequate remuneration of transmission systems andare easy to implement. These methods have been criticized due totheir economic grounds.The combined incrementaYembedded cost methods have beenproposed as a solution to this problem. The main goal of thiscombinationis exploiting the properties of both methods. The useof the embedded cost methods as a supplement costcandistort theeconomic signalsprovided by the marginal cost pricing.This paper will focus on the analysis of the embedded costmethods, showing their main features and their ability to providereasoning economic signals. The relation with the transmissionexpansion planning will also be addressed, The analysis will beextended to the peak oad of the Southern Brazilian system.

MAIN EMBEDDED COST METHODSIn these methods all system costs (existing transmission system,operation and expansion) are allocated among the system users inproportion to their "extent of use" of the transmission resources.Allocation methodologies differ on their definition and measure ofthis "extent of use". They can be classified as load flow basedmethods and rolled-in methods [q. he main shortcoming of thelatter methods (such as, Postage Stamp and Contract Path) is thatthey ignore actual system operation. As a result, they are likely tosend incorrect economic signals to transmission customers. Forinstance, in the Postage Stamp method, an agent that uses thesystem lightly (generation and load at short electrical distance)would be subsidizing other one that uses the system heavily.The identification of such cross-subsidies can be made by theanalysis of the pool stability. An allocation rule is said to bestable if each agent pays less as a member of the integrated poolthan as a member of any sub-pool, or as an isolated agent. In otherwords, there should be no incentive for any member to leave theintegrated pool. The pool stability property is important in aderegulated environment.Our attention will be addressed to the load flow based methodsthat will be described next.

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that use thecircuit in the same direction of thk net flow (&chwill be denoted as the positive direction) pay in proportion totheir flow.

The MW-mile method [8] first calculates the flow on each circuitcaused by the generatiodoad pattern of each agent based on apower flow model. Costs are then allocated in proportion to theratio of power flow and circuit capacity:

where:R(u)fdu)

allocated cost to agent Uk-circuit flow caused by agent U

c k Cost O Circuit kk-circuit capacityfk

This method overcomes some limitations of the rolled-in methods,but has been criticized as having no obvious grounding oneconomic theory. However, considering some simplifyingassumptions this method can be intexpreted as a solution to theoptimal transmission planning problem &om a static point of view19,101.As the total circuit power flows are usually smaller than thecircuit capacities, this allocation rule does not recover allembedded costs. In terms of transmission expansioninterpretation, this means that the MW-mile scheme is onlycharging for a "base-case" etwork, but not for the "transmissionreserve", given by the difference between circuit capacity andactual flow.

A simple way to ensure recovery of all embedded costs in theMW-mile method while retaining its advantages is to replace thecircuit capacities by the sum of absolute power flows caused byall agents:

all sFor the transmission expansion interpretatio& this method alsocalled usage method [ill assumes that all agents have to pay forthe actual capacity use and for the additional reserve. This reservemay be due to the need of system meeting reliability, stability andsecuxity criteria or due to system disadjustments (i.e., due toplanning "errors" caused by the inherent uncertainties of theplanning process). However, there is no incentive to the agent thatalleviates the circuit load, improving the system performanceandor postponing transmission investments.

In this method, there is no charge for the agent whose Dower flowis in the opposite direction of the net flow f121. Onlv-the agents

all SQ&(3 )R ( u )= 0

Qk+

for fdu)Iwhereset of participants with positive flows oncircuit k

This method assumes that the net flow reduction is beneficial,even if there is already an "excess" instaIled capacity. Moreover,for a light loaded circuit, there is a discontinuity on the chargeswhen the net flow changes the direction.Dominant Flow Method (DFM)This method is a combination of the last two methods as part ofan attempt to overcome the drawbacks pointed out 191. Thescheme is to divide the circuit cost allocation R(u) into twocomponents,R, (U) nd I$ (U):a) R,(u) is related to the circuit capacity that is actually beingused, called base capacity. This capacity fiaction

corresponds to the circuit net flow and the associated costis borne only by those participants with a positive flow,i.e., which go in the same direction as the net total flow fk.The allocation criterion of this portion is the same asexpression (3), changing the k-circuit total cost c k to C B ~(cost of base capacity) where:

G k = c k x f k / f k (4)b) %(U) is related to the difference fk -&, called additionalcapacity. This capacity corresponds to the circuit reserveand asall participants take advantage of the reliability and

security associated, this corresponding fkaction of total costis borne by all participants, according to the expression (2)changing c k o c~ (cost of additional capacity) where:CAk" ck (J' k-f k) /fk ( 5 )

The total allocationR(u) s then given by the swnR, (U )+R, (U).COMPARI~ON F THE ME THO^^

We will present some relevant features associated with theprevious methods through simple examples.Transaction Amount VariationInthis section we will analyze the charge associated with an agentA that uses a circuit k shown in Figure 1. Without loss ofgenerality, the circuit capacity is 1 pu and the corresponding costis 1 pu. One of the objectives of the embedded cost methods is tocollect the exact amount of the transmission fixed cost which, inthis case, is equal to 1 pu. The circuit k is already fuu loaded byan agent B. The agent A causes a negative flow of x pu on thecircuit. Figure 2shows the variation of the cost allocated to agent



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141A accordingly to its flow. The functions were obtained using theprevious expressions (seeAppendix A).

F=-I/ - x z u l3=Figure1 - Agents Using Circuit k

M W M ,zcM1

0.5

0

Figure 2 - Cost Variation of Agent AThe MWM has a constant average charge (straight line) no matterwhat is happening with the circuit. Therefore no incentive to thecounter flow agent is provided. Also it fails to collect the exactembedded cost. In the MM the average charge decreases as thetransaction amount increases. This seems orrected from the agentviewpoint but it does not make sense when transmission systemexpansion and operation are considered. The ZCM gives anincentive to agent A (charge equal zero) when ts flow is againstto the net flow. When the net flow changes the direction the agentA bares the total cost. One can note the discontinuity when x isequal to the circuit capacity. This can lead to a great variation ofthe charge for a slight variation of x. In the DFM, the agent A hasincentive only when x s close to zero, i.e.,when agent A actuallyalleviates the circuit load. When x approximates to 1and becomesclose to the agent B flow, the incentive decreases.Association EffectIn a competitiveenvironment, he agents always try to minimizetheir costs and one of them is the transmission service charge. Inthe embedded cost methods, as the total cost is distributed amongthe transmission users, the inclusion of a new agent or even anassociation of agents changes the share of this cost, that is,changes the denominator of expressions (2) and (3).An exceptionis the expression (1) for the MWM, but as stated before thismethod does not recover the total cost. In other words, using thesame circuit of the previous item, the sum of all agent charges isnot necessary equal to 1 pu.It is easy to show that the comtertlow agents are the ones thatpromote the pool stability (seeAppendix B) and then the systemshould encourage them, either by granting credits or by Settinglower prices. The ZCM and the DFM follow the secondalternative mainly because the utilities feel uncomfortable toprovide a service and give credits. If no incentives are given tothese agents, it is likely that they will associate with positiveflows. Figure 3 shows an example of a possible association.

-UI I I II

Before Association After AssociationFigure3 - Example of an Association

Agents B and C are on the net flow direction and A is thecounterflow agent. Table 1shows the charges borne by each agentbefore the association and Table 2 shows the charges after it.Table 1 - Charges Before the Association

ZCM 0.11 0.89DFM 0.11One can see fiom the tables that for MWM and MM the agent Awill try to associate to minimize its costs. After the association,the agent B will see an increase of its charge. T h i s increase isgreater for the MM. There is no variation on the change of agentB for the MWM.The charges are the same for MM , ZCM and DFM when there isno counterflow agent (see Table 2).Effect of Discrete InvestmentUp to now, only a static analysis [ 31 has been made supposmgthat in each year it was possible to build a new transmissionsystem adjusted to the ge ndon/L oad pattern of all transmissionusers.The methodologies Will be compared considering a time horizon.A simple example will be used to show the main differences ofthe methods. Figure4shows the simplified network configuration.For the sake of simplicity the circuit capacity is 1 pu and its costis equal to 1 pu. There is a generation at node 1 which feeds aload at node 2. Agent A has a negative flow.

A with7puFigure4 - Network Configuration

Assuming that the load u t ) is a linear function and notconsidering the operational cost, the inclusion of the second and



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1412third lines change the transmission cost allocated to the generatorand to the agent A. For a particular case in which A has 0.3 puand t(t) = 0.8+0.5t pu, we can see in Figure 5 the chargevariation of agent A as a function oft .

T CostorFlow 725

215

1

0 50

Figure5 - Dynamic Variation of the ChargesThe ZCM and the MWM, both not included in the graph of Figure4, have a zero charge and a constant charge of 0.3 pu respectively.For MM and DFM there is a charge discontinuity when thecorridor capacity increases. As continuity along a time horizon isdesirable, one possible solution to that discrete variation is theuse of a levelized annual cost based on a present worth sumobtained from a centralized expansion plan.

CASESTUDYThe comparison will be extended to the peak load codigurationofthe Southern Brazilian system for the year 1992.An equivalent ofthis system (141with 53 buses and 86 circuits was used, as shownin Figure 6. In this example, only the average costs of the maintransmission lines and transformers were taken into account.We evaluated the charges associated with three alternativewheeling transactions, represented in Figure 6:

itaipunnterconnection fJG

-500 kVHG - Hydro GenerationTG - Terrnal Genertation

h ~ l i n ~ransactions

T1.T2.T3Tramaction T1 is in the counterdirection for the 500 kV lineswhich interconnect the hydro plants in the North including Itaipuwith the load center at the South. Besides using the same 500 kVwith positive flows, transaction T2 also uses the lines bemeenbuses 2 and 3 but in the negative direction. T3 is in the reversedirection of T2 but incorporates additional lines. Table 3summarizes the corresponding charges for each method. Asexpected, the DFM is between MM and ZCM and the charges forMWM are the lowest one.

Injection of 50MW at bus 6 and removal at bus 1.Injection of 50MW at bus 3 and removal at bus 6.Injectionof 50 MW at bus 7 and removal at bus 5 .

Supposing an association of the agents responsible for thetransactions T1 and T2, we can see from Table 4 that the chargesof this association decrease substantially. On the other hand, anincrease is observed for transaction T3.

L J , 0.J f 1 I . UAssuming a substantial increase in the amount of transaction T1(case 1 with 1200 MW and case 2 with 1300 MW ) we can seefrom Table 5 a huge deviation on the charges for the ZCM.

CONCLUSIONSThis paper has presented some interesting features of the mainembeddedcost methods showing their advantages and drawbacks.Special attention was devoted to the load flow based methodswhich better represent the actual operation of power transmissionsystems. Some points should be emphasized:e an agent association changes the charge of others notinvolved with it. The association can be minimized givingincentives to the counterflow agents.the original MW-mile method does not hold the pool stabilityproperty This conclusion ~ a $e extended to the postagestamp method.as the generatiodload pattern has inherent uncertainties,small deviation on the line flows should not represent greatchangeson the charges.

0

e



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14130 when a long-term analysis is developed, we can observecharge discontinuitiescausedby new investments. The use oflong-term incremental cost approaches can minimize suchdiscontinuities.Designing a cost allocation rule which encompasses both thecomplexities of power transmission business and the economicand regulation requirements is a topic still open to muchdiscussion.

REFERENCES[11 R D Tabors, "Transmission System Management and Pricing:New Paradigms and International Comparisons",IEEE Transon PWRS, Vol. 9, No. 1, pp 206-215, Feb 1994.[2] I J Pkrez-Aniaga, H Rudinick, W 0 Stadlin, "InternationalPower System Transmission Open Acess Experience", paper489-5 PWRS, presented at the 1994 Summer Meeting, USA.[3] J P Clerfeuille, P Sandrin, P Valentin, "Considerations onPricing of Transmission Services", WZPEDE Conference onPricing of TransmissionServices, Tunis, May 1993.[4] M C Caramanis, R E Bohn, F C Schweppe, "The Cost ofWheeling and Optimal Wheelmg Rates", ZEEE Trans onPFPRS, Vol. 1,No. 1,February 1986.[5] M C Caramaris, N Roukos, F C Schweppe, "WRATES: ATool for Evaluating the Marginal Cost of Wheeling", ZEEETrans on PETS , Vol4, N 2, May 1989.[6] M Rivier, I J P&ez-Arriaga, G Luengo, "JUANAC: A Modelfor Computation of Spot Prices in Interconnected PowerSystems", Proc. 10th PSCC Conference, Graz, Austria,August 1990.[7] H H Happ, "Cost of Wheeling Methodologies", ZEEE Trans

on PWRS, V 9, N 1,pp 147-156, Feb 1994.[8] D Shirmohammadi, P R Gribik, E T K Law, J H Malinowki,R E O'Donnel, "Evaluation of Transmission Network CapacityUse for Wheeling Transactions", ZEEE Trans on PER!$ Vol.4, No. 4, October 1989.[9] J W Marangon Lima, M V F Pereira, J L R Pereira, "AnIntegrated Framework for Cost Allocation in Multi-&Transmission System", paper 503-3 PWRS, presented at 1994ZEEE Summer Me eting , USA[10]M C Calviou, RM Dunnet, P H Plumptre, "Charging for theUse of Transmission System Using Marginal Cost Methods",Proc. 11th PSCC Conference, pp. 385-391, Avignon France,[11]R R Kovacs, A L Leverett, "A Load FlowBased Method forCalculating Embedded, Incremental and Marginal Cost ofTransmission Capacity", IEEE Trans onP K W , Vol. 9, No. 1,pp 272-278, Feb 1994.[12]H Rudinick, R Palma, J E F-dez, "Marginal Pricing andSupplement Cost Allocation in Transmission Open Acess",paper 528-0 PWRS, presented at the 1994 ZEEE SummerMeeting, USA[1311J Perkz-Arriaga, F J Rubio, J F Puerta, J Arceluz, J Marin,"Marginal Pricing of Transmission Services:An Analysis ofCost Recovery", paper 592-6 PWRS, presented at 1994Summer Meetin g, USA[14]Three-year Operation Planning of South and Southeast Inter-connected System - Years 1992-93-94, Technical ReportfromGCOZ-SCEL-GTPM-O1/91, Eletrobrh, April 1991 (inportuguese).

A u ~0 - S q 4,1993.

BIOGRAPHYJ W Marangon Lima (M'94), has B.Sc., M.Sc. and DSc.degrees in Electrical Engineering, respectively from the MilitaryInstitute of Engineering (IME),n 1979, h m he Federal Schoolof Engineering of Itajubi, (EFEI), in 1990 and from the FederalUniversity of Rio de Janeiro (COPPE-UFRJ), in 1994. From 1980to 1992 he was with Eletrobrhs, the Brazilian agency for thepower sector, where he developed studies on stability analysis,probabilistic methods applied to power systems and on powertransmission economics. He is currently an Associate Professor ofElectrical Engineering at EFEI.

APPENDIX ALet's determine the function f(x) which relates the charge to bepaid by agent A due to a wheeling transaction of x pu. Forsimplicity, we assume that:0 the analysis will be held in just one circuit of the

00

0

MW M

transmissionsystemthe circuit capacity is 1 puthe circuit cost is 1pubesides the agent A.there is only one more agent (called B)that uses the circuit in its full capacityagent A is initially in the counter direction

Using expression (l), the desired function f(x), its derivative andthe average charge AC(x) canbe easily obtained:f(x) =x f(x) = 1 AC(x) =?= 1 (Al)MMUsing expression (2) and knowing that agent B has a flow of 1 pu:

In this case here is only one agent that pays for the whole circuitcost as they are in opposite direction. Using expression (3):f(x) = 0 for 0 < x < l

1 for 1


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When agent A is in the same direction(1

It was shown that the pool stability still holds even givingincentives o the counterflow agent.

DFMAs the capacity canbe continuously adjusted there isno additionalcapacity and hence this method becomes the same as the ZCM,which has the pool stability property.



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1415The above discussion shows that both the "zero counter flow"method (ZCM) and the "dominant flow" method @FM) areunfounded from the physical point of view. This being thecase, the talk about the economics of the ZCM and DFMmethods is really a discussion about an imaginary transmissiontransaction which does not take place. It is hard to see howsuch cost methods can provide "economic signals" to any one!Probably the only signal being provided is a messageto existingutilities that they will be robbed! The climax of that messageis the notion that utilities should give credits to the so-called"countexflow agents" for fictitious transmission transactionswhich do not and cannot take place.The paper concludes that an association between two agentschanges the charges payable by third parties. Fig. 2also showsthat the charges are discontinuous with increase in output incase of the ZCM method. The above iindings aremanifestations of the fictitiousness of the ZCM and DFMconcepts.The idea of "association between agents" appears to contradictthe spirit behind the whole exercise. The ultimate applicationof that idea would be for al lpower generatorswithin the subjectservice territory to form one company and lease thetransmission system from the utility on a "wholesale" basis.But that is basically what the utility has been doing in the pastand what the political system is attempting to change in thename of competition. Allowing association between agentsimplies that agents are not required to compete with one otherand only the utility is required to let others compete with it.Hence that idea appears to violate the principle of equality oftreatment.

DISCUSSIONAbdul M. Mousa (British Columbia Hydro, Burnaby, BC,Canada): I wish to congratulate Dr. Lima for an interesting paper.The author's response to the following comments would beappreciated:1. The case discussed in Figs. 1and 2 does not appear to be

realistic. In the majority of cases, the building of a power linewas undertaken because the load, or part of it, in one areacould not be optimally met by local generation, and aneconomical generation source was available else where.Consider Fig. 7A which is a revised version of Fig. 1with theareas at the ends of the line designated as areas 1 and 2; thearea on the left-hand-side being area 1. Based on the openingscenario in the paper, the load in area 1 exceeds the generationin it (L, > GI), hile the opposite occurs in area 2 (G2> L2).Agent "A" who wants to transmit power from area 1 to area 2has presumably built a power station in area 1which is "powerhungry",but can only find a purchaser in area 2 which alreadyhas surplus generation! Apart from the peculiarity of thissituation, the transmission plan of agent "A" is simply notfeasible, because the voltage in area 2 will have a leading powerangle compared to the voltage of area 1. Please see Fig. 7B.Hence power cannot flow from area 1 to area 2. What willhappen in the case in Fig. 1s that the output of agent "A" willsimply go to part of the load in area 1 with whom he has nocontractual arrangements. On the other hand, an approximatelyequal part (not exactly equal because of difference+ osses) ofthe output of agent "B" will be diverted to loads in area 2, withwhom he has no contractual arrangements either.

L1A) SCHEHATIC DIAGRAM

B) PHASOR DIAGRAM

2 .

PANKAJ SAHAY, Christensen Associates, 46 10 UniversityAvenue, Madison, WI 53705 :The author lists many important issues related to

transmission fixed charges recovery. I would like the author'sopinion on the following points that may be useful.1) The author correctly characterizes the three methods forallocation of transmission fixed charges. The paper is alsoaccurate in criticizing postage stamp methods of pricing forsending incorrect economic signals. However, the paper solelyconcentrates on embedded cost methods that offer similar insightsinto embedded costs recovery. Comparisons of the three methodsfor allocating fixed charges is pertinent.2) The assertion that the incremental/embedded cost methods as asupplement can distort the economic signals provided by themarginal cost pricing should be explained further. Many USutilities, constrained by regulation and facing imminentderegulation, are practicing this method and citation if availableshould be provided. Two-part tariffs are commonplace to recoverfixed costs. This is an important tariff design tool and should beconsidered.3) Implications of unbundling on ancillary services is also an issueof topical importance. What are the author's views onmethodologies for recovering ancillary services cost explicitly?Manuscript received August 21, 1995.ig. 7. Practical version of Fig. 1.



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1416odrigo Palma (Universidad Cat6licade Chile, Santiago, Chile). The author is to be congratulatedon his efforts to develop procedures to assess differenttransmission cost allocation methods. Countries with openaccess schemes have used different allocation methods andthere is no clear-cut evidence on which one is better in

providing adequate economic signals to the different players[Al.The author contributes in defining one attribute heconsiders important to assess, pool stability. His assessmentof transaction variations and association effects are mostrelevant. The paper is didactic and well presented, with basicconcepts illustrated with simple examples. Nevertheless, onemust be careful in extrapolating conclusions given thesimplification assumptions. We foresee other attributes thatwill need to be assessed to achieve a sound allocation method,attributesthat will be very much system dependent.We are working on a similar line of research, butattempting to do a dynamic assessment of cost allocationmethods on a long term horizon, using an optimal dynamictransmission plan [B]. The difficulties arise not onnumerically obtaining allocations bu t in interpreting theireconomic impact and in simulating decisions that would betaken by the players over time, given the contributions theywould be required to make to develop the transmissionsystem. The author rated well in his examples what he callsthe zero counterflow method (described in our paper [C] andbasic to the Chilean open access methodology), but we warnagain on extrapolating these general findings.

We will appreciate if the author could give us his viewson the following questions:i) In the dominant flow method the allocation of additionalcapacity is much dependent on circuit reserve, reserve thatwill evolve over time, How will this evolution affect poolstability? How would the reserve requirements be determinedand by whom in a competitive environment?ii)How would the different methods treat transmissionover investment (given planning uncertainties that could leadto imperfect long term decisions)? This issue is linked to the"stranded investment" conceptmuch discussed in the US.iii)The assumption of continuously adjusted circuitcapacity is a particularly critical one, given that optimalinvestments over time do take place in discrete steps, giventhe available technologies. Analysis of the pool stabilityproperty will change drastically with these step investments.Can the author comment on how his conclusions wouldchange?.

Can the author illustrate how the different allocationmethods would perform in the following real situation?. Agenerator is built at the extreme of an existing longitudinaltransmission system, to feed a local new load. Thetransmission system is only used to support the generator inthe case of contingencies and for maintenance, therefore itsreserve capacity increases drastically when the generator iscommissioned. What would that generator pay with thedifferent methodologies? Who would pay for the new reserve

capacity? How stable is the pool in that case?. Please makethenecessary assumptions.[A] PCrez-Arriaga, I, , Rudnick, H., Stadlin, W."International power system transmission open accessexperience". IEEE Transactions on Power Systems, Vol. 10,[B ] Rudnick, H., Palma, R., Cura, E., Silva, C.,"Economically adapted transmission systems in open accessschemes- Application of genetic algorithms", Paper 95 SM576-9 PWRS, IEEEPES 1995 Summer Meeting, Portland,Oregon, July 1995[C] Rudnick, H., Palma, R., Fernbdez, J. "Marginalpricing and supplement cost allocation in transmission openaccess". IEEE Transactions on Power Systems, Vol. 10,

NQ1,Febr~ary 995, pp. 554-564

NP2, May 1995, pp. 1125-1142Manuscript received August 30, 1995.

Dariush Shirmohammadi (Pacific Gas and Electric Company):This paper uses some useful measures to assess the suitabilityvarious cost allocation transmission pricing methodologies. Thepricing methodologies discussed in the paper are based on variousimplementations of the MW-mile methodology as described inReference [8] of the paper. These methodologies are named in thepaper as: "Modulus Method", "Zero Counterflow Method" and"Dominant Flow Method". I have the following questions andcomments regarding the paper:The paper states that Equation (1) is used in the original referenceon MW-mile [8]. In fact, Reference [8] is based on Equation (2 ) ofthe paper ("Modulus Method").Equation (3) Seems to indicate that entire transmission revenue fora transmission transaction under "Zero Counter Flow Method" iszero even if the flow due to the transaction on a single facility isopposite to the net flow on that facility. The author is requested toelaborate on thispoint.The formulae for RI (U) and R2 U) for a specific transmissiontransaction in the 'Dominant Flow Method" are not presented inthe paper. Such formulae, specially for Rz(u), are not obviouslyknown. The author is, hence, requested to include these formulaein his closure of the paper. ,The paper suggests that reduction in average charges when the sizeof transmission transaction increases under "Modulus Method"does no t make sense. The author is requested to elaborate on thisissue.Under the section on ''Association Effect", it is stated that thepricing methodology should assign credits for counterflows. Thisobviously requires that transmission transaction be monitored andpriced on real-time basis. None of the cost allocationmethodologies discussed in the paper have been considered for real-time environment. The author is requested to elaborate on thispoint.Manuscript received September 1, 1995.



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1417which was not included in this paper. The same result can not bereached using Eq. (2) as waspointed out in reference [l 11.In the Eq. 3) , positive direction corresponds to the direction ofthe net flow. To compute the transmission charge of a wheelingtransactionU under ZCM, it is necessary to identify the direction

J W Marangon Lima, we thank the discussers for their valuablecomments and questions allowing clarificationof some points. Wewould like to offer the following comments in response for eachdiscusser.To Dr. Sahay

The assertion that postage stamp method sends incorrecteconomic signals is based on the principle of pool stability.Assuming the same assumptions of Appendix B, it is provedby a counter-example that this method is not stable. In Fig. 8,two agentsA and B use a transmission line that connects bus1 to bus 2.The transmission line cost is equal to 1 pu andboth agents have the same power flow equal to 1 pu. AgentAcollects his power at bus 3 which is between buses 1 and 2.Bus 1 isy miles away from bus 2 and bus 3 is x miles.1 PU 1 PUAgentA AgentA

1-U puw gent=Agent 6-Figure8 - PostageStamp InstabilityAdopting postage stamp, both agents A and B pay 0.5 pu forthe wheeling charge. Not including the ending equipmentcosts, agent A spendsx/y pu to build a new transmission linebetween buses 2 and 3. As this relation varies from 0 to 1, itcanbe less than 0.5 pu, i.e., agent A can spend less operatingisolated than in the integrated pool. Therefore, pool stabilitydoes not hold in this case.Thc two-part tariff seems to be the most appropriatealternative in the current development of pricingmethodologies.In this paper, the focus was on the embeddedcosts which correspond with one of these parts. It isinteresting to note that this part is usually the high portion ofthe tariff mainly if the system is hydrodominated. In thiscase, we have low short-term m a r 4 cost (STMC) and hightransmission fixed charges. This is exactly what happens inBrazil, where regulators are questioning about the inclusion ofSTMC in the tariffof transmission services.Aspart of the unboundling process,ancillary services, such asvoltage control & reactive supply, frequency control & powerflow, security, etc. need to be priced. The problem is thatthere are still many drawbacks in the emerging methodsproposed to price transmission services. The value of suchservices depends mostly on the system performance criteriawhich, inturn,depend on regulation.For instance, these criteria can be included as constraints inan optimization process. Also, the we of interruption cos t sand customer behavior seems to be very promise. We arecurrently working on this field.

of f d u ) in each facility k. f all the directions are negative, thenthe charge for this wheeling transactionis zero.As requested, the formulae of DFM are included here and wereextracted b m eference PI. For a wheeling transaction U, thepower flowf d u ) in each facility k can be obtained by running aDC power flow with only the generatiodoad pattern of U.Thus,

(6)Zfds)R, (U)= I: , kall SEQk+

for all U E Qk+;otherwise,R , (U)= 0where:

f++C,f k

set of'allagents with positive flows at circuit kcost of base capacity which is equal toc k f k / f knet flow in circuit k with all transactions

and

all swhere C ,k is tlie cost of additional capacity which is

equal to c k x ( Tk fk) /&.From Eqs. (6) and (7), one canobserve that if there are no counterflowsthis method produces the same result of MM.From Fig. 2, agent A under MM pays less in terms of averagecosts when the transacted power increases. This relation continueseven if the transmission capacity is reaching its limit (transactedpower close to 2 pu). Under DFM, the wheeling charge ismodulated according to circuit capacity. In the example, agent Apays the whole circuit cost for a transacted power equal to 2 pu.This rationality seems to be correct remembering that if the netflow is close to the circuit capacity it is an indicative of newtransmission investmemt.Different treatment should be given to the counterflow agentwhich is clearly observed when STMC is under consideration. Asthe fixed charge usually corresponds to the major part of the tariffthis treatment should be extended to the allocation of thissupplement charge. If counterflow agents are included in theexpansion planning studies, new investment can be postponed.These studies are not c;uried out on a real-time basis but, instead,they use average power to assess systemperformance.ToDr. MousaTo Dr. Shirmohammadi

The Eq. (2 ) of reference [81 is not exactly the same of@. (I), butit is easy to show that both of them produce the same result. Themain difference is related to revenue reconciliation component1. Although the purpose of this paper was to introduce sometopics on a facility by facility basis, the scenario is notunrealistic. Many c:xamples can be found where counMowagents appear. For instance,a steel company inBrazil plans to



10/10

1418expand the thermal generation connected to bus 6 by 230 kVlines (see Fig. 6) in order to feed its load which is located inthe Southeastern system which is not shown in this Figure. Tothe Southern system, this wheeling transaction is clearlyopposite to the main flow and brings many benefits in termsof postponing transmission investment on the 500 kV sector.It is obvious that the power generated by this company willnot reach its load, but this wheeling transaction will cause adecrease on the 500 kV power flows. Assuming the linearityof power flow and using the superposition theorem, thisdecrease can be exactly calculated running a DC power flowprogram with only the generatidload pattern of thiscompany.

2. We agree that the association between agents should beavoided in order to preserve competition. It is shown in thepaper that this association will be more Seyuently if noincentives are given to the counterflow agents. Therefore, themethods which do not take this effect into account are againstthis new trend toward competition.To Drs. Rudnick& PalmaThe circuit capacity can be divided into three componentsaccording to its use:

base capacity which corresponds to the net flow or actualflow,security capacity which is the necessary circuit reserve tosatisfy reliability and security criteria; and,excess capacity which corresponds to system disadjustments(i.e. due to planning "errors" caused by inherent uncertaintiesof the planning process) or to the discrete natnre of theinvestments,

0

0

The second and third components were defined as additionalcapaci@ in the paper.Many questions were raised concerningpool stability. One of theassumptions made to assess this property (see Appendix B) wasthe continuous adjustment of circuit capacity, i.e. only the basecapacity was considered. Clearly, this is not a practicalassumption because circuits have additional capacities. Theproblem is that all embedded cost methods only see the base case.However, the comparison of the methods based on thisassumption is valid if a relative measure is under consideration.Although the inclusion of security capacity in the analysis of poolstability is very complex, if one assumes that the agents need tosatisfy the same criteria operating or not in the pool, it is possibleto extend the results including this capacity component.As the discussers pointed out, this is not the case when the excesscapacity is under consideration. Pool stability does not hold if thetransmission system is over dimensioned. There is an exceptionrelated to economy of scale where a long-term analysis needs tobe carried out to identify it. On this condition, pool stability canbe tested in a dynamic basis.Fig. 9shows the actual situation proposed by the discussers. Thegenerator of agent B feeds the local new load. Clearly, theinclusion of generatiodload pattern of agent B does not changethe power flows of the transmission system represented here bythe line between buses 1 and 2. Thus, using the load flow basedmethods described in the paper, there wil l be no charge to agentB, i.e., agent B is not a transmission user.

I Q C l +en t Ben t A

Figure9 -Security ChargeHowever, in an emergency condition, agentB may use the circuitadditional capacity an4 also, the generation reserve of agent A.The use of this additional capacity can be interpreted as a securitysewice provided by the transmission company and the generatorsat bus 1.As observed on the Dr. Sahay comment, this is anothermerging area of great interest.p] W Marangon Lima, M V F Pereira, J L R Pereira, "AnIntegrated Framework for Cost Allocation in Multi-OwnedTransmission System", ZEEE Trans.on P m , Vol 10, N 2,pp 971-977, May 1995.Manuscript received October 30 , 1995.

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Allocation of Transmission Fixed Charges- An Overview-96