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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 4, NOVEMBER 2007 1

Evaluation of Three Methods Proposed for theComputation of Inter-TSO Payments in the Intern

Electricity Market of the European UnionLuis Olmos and Ignacio J. Prez-Arriaga

Abstract Parties to the Internal Electricity Market of the Eu-ropean Union (IEM) decided in 2001 to abolish the method of pan-caking of transmission tariffs for cross-border transactions thatwas originally in place. Instead, they have agreed to implement asystem whereby national transmission tariffs provide access to theentire IEM. This system is supplemented by a scheme of inter-TSOpayments. However, conict may arise if the compensation that acountry must pay another one is not in accordance with the elec-trical usage that the former is making of the grid of the latter. Forinstance, Inter TSO Compensation methods (ITC methods) im-plicitly allocate the cost of any existing or new transmission line.Therefore, theadoption of an inefcient method may be an obstaclefor building some needed regional grid investments. Consequently,one should give careful consideration to the selection of the ITCmethod.

This paper analyzes, both qualitatively and quantitatively, theimplementation of the most relevant ITC methods that have beenconsidered so far in the European debate. When assessing eachmethod from a conceptual point of view, considerable attention isdevoted to the critical examination of its main underlying assump-tions.

Index Terms Cross-border tariffs, European electricitymarket, game theory, interconnected power systems, powertransmission economics, power transmission planning, regionalmarkets, transmission lines, transmission pricing.

I. INTRODUCTION

T HERE is wide agreement both within the academic com-munity and industry that nodal energy prices are optimalshort-term economic signals for agents participating in a com-petitive electricity market [1]. Application of nodal prices togenerators andconsumers results in a net surplus. If investmentsin transmission lines were continuous, economies of scale werenot present in the transmission activity and those engineeringreliability constraints that were taken into account in networkplanning were also considered in system operation, this net sur-plus would sufce to recover the complete construction, op-eration and maintenance costs of the transmission grid. How-

Manuscript received October 9, 2006; revised July 24, 2007. This work isbased on others that were supported by the European Commision and Red Elc-trica de Espaa. Paper no. TPWRS-00684-2006.

The authors are with the Instituto de Investigacin Tecnolgica, UniversidadPonticia Comillas, 28015 Madrid, Spain (e-mail: [email protected]).

Color versions of one or more of the gures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identier 10.1109/TPWRS.2007.907118

ever, these ideal conditions do not hold in actual transmissionetworks. Hence, the surplus resulting from the application onodal prices falls short of the amount needed to completelcover the total costs of the grid [2], [3].

What is more, nodal prices are only used in a few electricitmarkets, since most of them use a single energy price, plusome simplied mechanisms to account for the effect of losseandnetwork constraints. Therefore, some mechanism for the recovery of network costs must be put in place in order to ensurthat the owners of the network receive adequate remuneration

In the new competitive regulatory framework, investment in anew transmission line is justied whenever the expected presenvalue of the aggregated economic benet that the line brings tall network users (generators and consumers) is larger than thexpected present value of the cost of the line [4]. In other wordthe economic benets that new lines provide to generators anconsumers should be the driver behind any transmission invesment. Therefore, conceptually speaking, the fraction of the coof a line that is not recovered through nodal prices should be alocated to network users in proportion to the benet they obtai

from the line. Unfortunately, allocation of the cost of a transmission facility to its economic beneciaries is difcult in pratice. Consequently, some measure of electrical use is frequentladopted as a reasonable approximation to benets [3][5].

Transmission tariffs corresponding to the infrastructure costof the grid do not have any purpose in the operation, i.e., shorterm, timeframe, since network infrastructure costs are the result of the expansion of the grid and they are deemed not tbe affected by the decisions by agents on how much power tproduce or consume in the short term. The objective of thestariffs is twofold. First, they allow grid owners to recover theregulated costs. Second, they provide locational signals to newgenerators and loads, or those considering retirement. In othewords, these tariffs should make agents realize the transmissionetwork costs incurred by the system because they locate in onpart of the network or another.

The European Commission set up the Florence RegulatorForum as an institutional framework within which parties involved in the creation of the IEM could meet and discuss mesures to achieve a workable and efcient electricity market ithe European Union [6]. As a result of the Florence procesparties have reached a preliminary consensus on a set of fundamental issues concerning the scheme of cross-border tarication (CBT) to be adopted for the IEM. By cross-border tarication we refer to the complete scheme of charges to the net

work users because of their utilization of the EU transmissio0885-8950/$25.00 2007 IEEE


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1508 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 4, NOVEMBER 2007

network. Economic ef ciency criteria should be used when de-signing these signals. The EU Directive 2003/54/CE and its as-sociated Regulation 1228/2003 represent the current state andoutcome of the Florence process.

Instead of creating a system of pan-European transmissiontariffs, it has been decided that any generator or demand in

any EU country must only pay the transmission tariff that ap-plies in that country. Payment of the transmission tariff pro-vides access to the entire EU grid (this stems from the so calledsingle system paradigm as a mental framework that has in-spired the deliberations of the Florence Forum). However, thissimple scheme in principle ignores the fact that agents fromother countries use the network of the considered country, andvice versa. Thus, the parties have decided to create a system of compensations and charges resulting from a) the external uti-lization of the infrastructure of networks and b) the transmis-sion losses incurred because of cross-border transactions andloop ows. This paper does not intend to cover the vast litera-ture that exists on transmission network pricing. The paper onlyfocuses on the small set of approaches that have been consid-ered so far by the European regulators and the stakeholders of the IEM in the debate over the adoption of a sound method tocompute these compensations and charges.

The idea behind the method of inter-TSO payments is simple.Countries must receive a compensation because of the use thatexternal agents make of their networks. But countries have alsoto be charged because of their utilization of the networks of others. The net outcome of the compensation and charges forone country is its net payment , either positive or negative. Thisannual net payment must be used to modify the annual regu-lated transmission cost from which the transmission tariffs of

this country are computed. The result of all this is a systemof entry/exit tariffs whereby an agent who pays the modi edlocal access tariff gains access to the entire European grid. Thisscheme, using a crude provisional algorithm to compute theinter-TSO payments, has been in place since March 2002.

Before presenting the different inter-TSO payment methodsand assessing their application in the IEM market, we shallbrie y outline the main characteristics of the EU transmissionsystem. According to a report by the European Commission [7],the total estimated electricity generation of the 25 countries be-longing to the EU plus Norway, Switzerland and the three can-didate countries (Bulgaria, Romania, and Turkey), was about3500 TWh in the year 2005, while the total electricity con-sumption was about 3000 TWh (the aggregate net exports of the 30 countries were positive). The total amount of power ex-changes among these countries was about 350 TWh in the year2003, which represents approximately 10% of the electricityproduced. According to another report, see [8], the total lengthof 400 and 220 KV transmission lines in the region (30 coun-tries) is close to 300 000 km. The transmission grid within mostEuropean countries is developed enough for the local generationto supply the local load. However, this grid is not prepared tohost large power transfers between the different European coun-tries. Thus, the European Commission has given priority to thereinforcement of some corridors that are central to the energy

trade in the region and whose capacity is well below what is re-quired to achieve the integration of national markets [7].

After this introduction, Section II of the paper describes themain methods for computation of inter-TSO payments that havebeen actually considered. Section III provides numerical resultsfrom the application of these methods to a stylized simpleregional system. Section IV analyzes each one of the threemethods according to a set of evaluation criteria previously

dened. Finally, Section V concludes.

II. DESCRIPTION OF THE CONSIDERED INTER -TSOCOMPENSATION METHODS

The purpose of this paper is to contribute to the ongoing dis-cussion among the main parties and institutions of the Europeanelectricity industry on the selection of a permanent method forthe computation of inter-TSO payments in this region. This iswhy the paper only considers those ITC methods actually pro-posed for implementation in the IEM, see [9]. Apart from pro-viding a description of these methods, this section assesses theperformance of each with respect to the aforementioned criteria,except for the sensitivity analysis of the results they produce,which is examined in Section III.

ITC methods that have been formally proposed in the IEMfall into one of two families.

Family 1: This set comprises methods that allocate the uti-lization of each transmission facility to individual network users. The results so obtained are aggregated at countrylevel in order to calculate inter-TSO compensations andcharges. These methods take into account the complete setof actual cross-border ows.

Family 2: Here, a country must only be compensated forthe use of its grid by those cross-border ows that have

their source and sink outside of this country. In otherwords, family 2 methods compute how much use of thenetwork of a country corresponds to transit ows. Thesemethods avoid computing individual network charges forgenerators and consumers. Instead, they just compute theglobal compensation due to each country.

We shall only analyze the main representatives of these twofamilies since the rest of the considered ITC methods only in-troduce minor variations. Within family 1 we shall study theMarginal Participation (MP) and the Average Participation(AP) methods, and within family 2 only the With and WithoutTransits method (WWT). Gathering the information requiredto apply these methods should not be a problem, since the Eu-ropean TSOs agreed to provide the information that is requiredto assess the performance of each one of them. In any case, theinput data requirements of each method will be also brie y dis-cussed.

In all the considered methods, the property of tie lines, andthus the associated compensation, is established according tothe location of the reference meters for the measurement of electricity ows at the cross-border points. The cost of mer-chant cross-border lines is excluded from the inter-TSO pay-ment mechanism, although their ows are accounted for as anyother ow. A few merchant lines have been built within theEU-30 system. There are at least two of them within the Nordic

region (the SwePol link and the BalticCable). Others have beenproposed for construction in Italy.


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OLMOS AND P REZ-ARRIAGA: THREE METHODS PROPOSED FOR THE COMPUTATION OF INTER-TSO PAYMENTS 1509

The main body of this section provides a detailed descriptionof the three methods that have been chosen. Finally, Section II-Drefers to other methods that have been proposed in the Europeancontext and the technical literature.

A. Marginal Participation (MP)

The MP method tries to identify how much of the power thatows through each one of the lines in the system is due to theexistence of each network user . In order to do so, this methodanalyzes how the ows in the grid change when minor modi -cations are introduced in the production (or consumption) of anagent . An in-depth description of the MP method can be foundin [5].

It is a fundamental technical characteristic of power systemsthat generation and demand must always be balanced. There-fore, if generation at node is increased by 1 MW, then someother nodes in the grid must increment their demand or reducetheir generation in order to keep the system in balance. Thus,when computing the use that agent makes of the grid, we needto choose a node or set of nodes that balances the increase or de-crease in the production considered for this agent. MP assumesthat the same slack node balances the increases or decreases inthe power production by all the agents in the system.

The following paragraphs describe the procedure followed tocompute the participation of each agent in the use of transmis-sion lines (see [5] also).

1) Obtain marginal sensitivities of the ow through linewith respect to the injection at bus .

2) Given an agent located at node , agent s responsibilityin the ow over line amounts to the marginal sensitivity

times agent s power output. The power output ispositive for generators and negative for demands. Thus, thetotal participation of a generic agent in line is

.3) The cost of each line is allocated pro rata to the different

agents according to their total participation in the ow overthe line.

As can be seen, MP assumes that the relationship between theow through a line and the behavior of agent is linear.

Given that the power output at the slack bus balances the in-crease or decrease in the power production by each agent, thesensitivity actually expresses how much the ow throughline increases when the generation at bus increases by 1 MWand the demand at the slack bus increases by 1 MW as well (ig-noring losses). Equation (1) provides the mathematical expres-sion of sensitivity . In this equation is the ow over line

, is the net power injection at bus , is the slack bus, and is a unit transaction between bus and the slack bus

(1)

Once we have computed the electrical usage that each agentin the system makes of each individual line, and in order to com-pute compensations among countries, we would rst have toadd up the ows through each line that the agents within eachcountry are responsible for in order to determine the fraction of the cost of this line that this country must pay. Finally, we would

Fig. 1. Tracing rule applied in AP.

have to add up the compensations each country should pay eachother one for the use the former is making of all the lines in thegrid of the latter.

B. Average Participation Method (AP)

The Average Participation method determines the sources of the supply to loads and the destination of the power injectedby generators. In doing so, it establishes to what extent eachagent is responsible for causing the ow over each line. Themethod employs simple heuristic rules that only make use of the actual pattern of network ows. An in depth description of the AP method can be found in [5].

The AP method tracks the ows over the lines, either up-stream, or downstream by following the actual ow of electro-magnetic energy as given by the actual measures and splittingit at the junctions (nodes) in the same proportion as the actualows do. Based on this single assumption, AP establishes a cor-respondence between incoming ows to each node and out ows

from the node.Causality, or attribution of responsibility, directlyows from this assumption.Fig. 1 depicts in ows to and out ows from a node . In ows

have been represented on the left of node whereas out owsare represented on the right. Notice that the power production atnode N is an in ow to this node while the power consumption isan out ow from the node. Equation (2) provides the contributionof inow in Fig. 1 to out ow , according to AP. Asexplained above, the fraction of in ow that is deemed to bepart of out ow is computed as the ratio of the size of thelatter to the total amount of power owing through node

(2)

Using (2), the ow in any line of the system can beexpressed as a linear function of the generation located at thesending end node of the line and the incoming ows to thatnode. Thus, using matrix notation, the vector of system lineows could be expressed as

(3)

where is the vector of line ows, is the matrix of unitcontributions of the in ows to the nodes of the system to theoutows from these nodes, is the matrix of unit contribu-tions of the power injections at the nodes of the system, i.e., the


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amounts of power produced at the different nodes of the system,to the out ows from these nodes and is the vector of amountsof power generated at the nodes of the system. Rearranging (3)we obtain

(4)

where is the identity matrix and is the matrix of unit con-tributions of the amounts of power generated at the nodes of the system to the line ows in the system. Thus, the element

of matrix represents the unit contribution of genera-tion at node to the ow in line . A similar expression can beobtained when computing the contributions of nodal power con-sumptions to line ows

(5)

where is the matrix of unit contributions of the out owsfrom the nodes of the system to the in ows to these nodes,is the matrix of unit contributions of the loads at the nodes of thesystem to the in ows to these nodes, is the vector of powerconsumptions at the nodes of the system and is the matrixof unit contributions of the loads at the nodes of the system tothe line ows in the system.

Once we have decided which fraction of the total costof the grid should be recovered from loads and which fraction

should be recovered from generators, line ows can be ex-pressed as

(6)

The compensation that country must pay each country in theregion (including country itself), for the use that generatorsand loads within country are making of the grid of these coun-tries, is computed according to (7)

(7)

where is the vector of payments assigned to countryfor the use that it is making of the grid of each country in theregion, is the line ownership matrix, whose element is1 if line number belongs to country number and 0 otherwise,

is the line cost matrix, which is a diagonal matrix whereelement is equal to the ratio of the cost of line to the sizeof the power ow for this line, and is the node ownershipmatrix, which is again a diagonal matrix whose elementis 1 if node belongs to country and 0 otherwise. Finally, thenet compensation to be received by each country resultsfrom deducting the total amount that country must pay for theusage it is making of the regional grid from the total regulatedcost of its grid, which country must recover from the gridpayments made by countries in the region including itself

(8)

where is the total annual regulated cost of the grid of country and is a row vector of ones with dimensionsbeing p the number of countries in the region.

Fig. 2. Example of application of the AP method.

Fig. 2 illustrates the application of the AP method to computethe use that generator G makes of the grid in a simpli ed power

system with four countries. The upper part of Fig. 2 depicts theactual ows, as well as the loads and generation in the system.The lower part of the gure describes the use of the grid by gen-erator G. The line ows allocated to this generator are repre-sented using bold lines and numbers. The numerical value of the contribution of generator G to the power consumed at eachnode is shown within small squares. Using the same notationpresented above, (9) provides the mathematical expression of the contribution of generator to load

(9)

where is the th column of matrix , is theth column of matrix , is the power output of generator, is the power consumption by load , and

is the transpose of the element wise division of vectorsand .

Once all the ows in the system have been examined, the useof each line is allocated pro rata of how much of the line owhasbeen tracked down either upstream or downstream to eachagent. This implies that 50% of the use of every line is assignedto loads and 50% to generators.

Then inter-TSO payments among countries are obtained byaggregation of the individual contributions of agents in the sameway that was explained for MP. Authors in [5], [10], and [11]provide a more detailed description of the AP method. This


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method was rst developed and used in New Zealand in the late1980s and elsewhere later.

C. With and Without Transits Method (WWT)

WWT computes the external use of the grid of a country asthe use that corresponds to transit ows through the country.

Hence, the concept of transit is critical in WWT. The compen-sation to be received by a country is obtained from a compensa-tion fund. Countries must contribute to the total compensationfund according to the net amount of power they inject into orwithdraw from the grid. A description of the WWT method canbe found in [12].

1) Concept of Transit: The transit through a country can bebroadly de ned asthat partof the ows in the grid of this countrythat is unrelated to the activity of the agents inside the country.It seems reasonable to charge those agents responsible for thetransit through a country with the costs born by this countrybecause of the existence of the transit. These costs are assumedto correspond to the fraction of the network of country thatis actually used by the transit. However, the intuitive but im-precise de nition of transit given above does not translate into aclear mathematical expression. Therefore, several mathematicalformulations of the transit through a country are possible. Thedif culty stems from the fact which we have also encounteredwhen dealing with methods of Family 1 that we do not havean indisputable method to ascertain which ows at the borderof a country cross the country and which ones are associated tothe internal agents.

This paper has adopted the same de nition of transit that hasbeen routinely used by ETSO. Other stakeholders have objectedto the concept and utilization of transits, but no other practical

denition has been offered. Given a country with multiple in-terconnections with other countries, resulting in several importor export ows, the volume of the transit through the country iscomputed as the minimum value between the sum of all importows and the sum of all export ows. The volume of the transitthrough a country, as de ned here, is simple to compute. Oncethevolumeof the transit hasbeen determined, it remains the task of distributing it among the several interconnection lines. Thisinvolves determining the fraction of the ow over each borderline that is part of the transit. Following the procedure that isalso proposed by ETSO in order to identify transit ows, wehave distributed the total transit among cross-border ows in

proportion to the volume of these ows.2) Description of the Method: WWT compares the network ows in the considered country in two different situations. Theactual network ows are compared to the ows ina ctitious sit-uation where the transit through the country has been removed.

The ctional without transit situation is completely deter-mined once we accept the de nition of transit and the allocationrule for this transit explained above. Fig. 3 shows the two situ-ations that must be compared when applying the WWT methodto determine the external use made of the grid of a country A.The transit through this country is

MW. Once the transit has been eliminated in the systemof Fig. 3, ows in the cross-border lines result from deducting,from the original ow over each of these lines, the fraction of the transit through the country that has been assigned to the line.

Fig. 3. Application of the WWT method.

This transit is distributed among imports and exports propor-tionally to the size of each cross border ow. Thus, the owover line L3 in the without transit situation must be zero, sinceall the imports must be considered to be part of the transit. Thefraction of export ows that are part of the transit is equal to

. Therefore, two sevenths of

every export ow is considered to be part of the transit andmust be deducted from the original ow to obtain the ow inthe without transit situation.

Once the situations to compare are completely de ned,we need to quantify the impact of the transit on the net-work use. There are several ways of doing this. The mostpopular one which we have used here to obtain numericalresults consists of computing a global measure of network usage the total volume of MW in the entire network inthe two with and without transit situations and comparingboth amounts. Notice here that the ctional ows correspondingto the without transit situation must be solved for using a loadow model.

Consider the example of Fig. 3, if we note by the lengthof line , the network usage in the real situation would be

whereas that in the without transit, situation would be

Hence, the transit T through the country would be found respon-sible for

Note that the use made of line L2 increases when we re-move the transit: the real ow over this line is 300 MW whereasthat when the transit is removed turns out to be

. Transit T must be credited for this reduction of theow in line L2. If transit T did not exist, a larger line would beneeded. This is why the use made of this line by the transit hap-pens to be negative.

The WWT algorithm does not provide any indication of howto allocate the compensation due to a country among the re-maining ones. Here, we have followed the rule that has been pro-posed and applied by ETSO. First the total compensation fundis computed by adding the compensations due to all countries.Responsibility for contributing to this fund is then allocated to


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the different countries on the basis of their responsibility in gen-erating cross-border/transit ows. The net import or export owof each country has been used as a proxy to quantify this respon-sibility.

Next, a mathematical statement of the WWT method is pro-vided. First, the increase in the line ows within a country that

are deemed to be caused by the transit through the country inscenario can be expressed as

(10)

where is the vector of incremental line ows withincountry deemed to be caused by the transit through thecountry in scenario , is the matrix of PowerTransfer Distribution Factors of the line ows in country withrespect to the net power imports at the cross-border nodes of this country in that scenario and is the vector of incre-mental net power imports at the cross border nodes of country

that are due to the transit through this country in scenario(the fraction of the cross-border ows that is deemed to be partof the transit).

Therefore, the increase in the global annual usage of the gridwithin country that is caused by the existence of a transitthrough this country can be expressed as

(11)

where is the increase in the total usage of the grid of country due tothetransitand istherowvectorof the lengthsof the lines within country . The compensation that countryis entitled to is computed according to the expression in (12)

(12)

where is the compensation that country is entitledto, is the total regulated annual cost of the grid of thiscountry and is the total usage made of the grid of thiscountry throughout the year. Once the compensation that eachcountry is entitled to has been computed, the total size of theglobal compensation fund can be obtained as

(13)

Then, the contribution of each country to the global compen-sation fund can be obtained as

(14)

where isthe contribution ofcountry tothe global com-pensation fund, is a unit vector with dimensions withthe number of cross-border nodes in the corresponding countryand is the vector of net power imports at the cross-bordernodes of country . Finally, the net compensation to be receivedby country is computed according to the expression in (15)

(15)

D. Other Inter-TSO Compensation Methods of Interest

This section has described and conceptually analyzed theapplication of three of the most representative methods that havebeen proposed for the computation of inter-TSO compensationsin Europe. It has been only since early 2006 that other ITC

methods have been proposed in the European context asalternatives to the three ones that are discussed in this paper.Methods recently developed and being considered include thefollowing.

Improved Modelling for Infrastructure Cost Allocation (IMICA), which determines the impact that power ex-changes de ned between the net exporters and importersin a region have on the electrical use made of the trans-mission grid of third countries. This method was proposedby ETSO in May 2006.

A recent application of the Aumann-Shapley value concept(AS method) to the problem of allocating the cost of thetransmission grid to its users (generators and loads). Aninteresting algorithm has been proposed for implementingthis method and it has been successfully applied to theBrazilian transmission network, although it has not beenof cially adopted [13].

Despite exhibiting some interesting features, the analysis of these two methods falls out of the scope of our paper. A succinctdescription and analysis of both of them can be found in [14].

For brevity, other interesting methods that have been pro-posed in the technical literature are not analyzed here. Most of these methods fall within family 1 and they differ from eachother in the choice of the destination or source of the power injected or withdrawn by each agent. Thus, for example, authors

in [15] and [16] propose a principle (the Equivalent BilateralExchanges or EBE principle) whereby loads (respectively, im-porting countries) are deemed to be served by all the genera-tors (respectively, exporting countries) in the system in propor-tion to the size of the latter (respectively, the net export fromeach country). In [16], authors allocate the cost of each na-tional transmission grid to local generators, demands, importsand exports according to the EBE principle. Then, the fractionof the cost of each national grid that imports and exports aredeemed to be responsible for is allocated to the net import orexport in other countries using an equivalent multinational net-work where the grid within each country is represented by a

single node. The EBE principle is applied to do this. Authorsin [16] claim that the method proposed in their article may behelpful in a multinational context because it does not requirecountries to provide information that may be considered con-dential by market agents, such as the power output of eachplant. However, this is not a concern in Europe, since coun-tries have agreed to provide a central institution with detailedinformation on their national networks. This central or coordi-nating role is currently played by ETSO, the European Asso-ciation of System Operators. Cost allocation to agents (respec-tively, countries) in [15] and [16] results from assigning the costof each line (respectively, the equivalent cost attributable to theow though each cross-border line) proportionately to the owproduced on this line by the bilateral transactions taking placebetween each generator or load (respectively, each exporting or


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Fig. 4. Stylized system used to show the properties of the results produced by the three considered methods.

importing country) and the loads or generators (respectively, theimporting or exporting countries) the former is deemed to serve(or receive power from). Methods based on the EBE principle,and other methods that are similar to them, may be well suited tosmall, highly integrated systems of a national dimension. How-ever, they do not provide meaningful results when applied to theEuropean system as a whole (note that the participation of eachcountry in the use of the grid of others resulting from [16] wouldbe much dispersed). The method in [15] results in every agentof the system participating in the use of lines that are located faraway from him, which seems counter-intuitive when the systemconsidered is large. Analogously, the method in [16] results ineach country participating in the use made of the grid of othersthat are located far away from the former. Finally, similarly towhat happens in the MP method, the participation of agents inthe use of lines may not be compatible with the grid restrictionsexisting in a system likethe European one. The example in Fig. 7shows that results produced by MP may be at odds with limitsimposed by the transmission grid.

III. A PPLICATION OF THE CONSIDEREDMETHODS TO A CASE EXAMPLE

Numerical studies comparing the three considered ap-proaches and their variations have been performed by theauthors of this paper and also by others [9], [12], [17], [18].Here, a stylized model of a multinational power system is usedto reinforce the qualitative conclusions presented above with

some numerical results.The case example is presented in Fig. 4. This system consists

of six areas (countries): P, E, F, D, I, and H. Load and generationwithin each country have been represented using a pair of equiv-alent agents: one generator and one load. The system includes13 lines, whose electrical parameters and ows are provided inthe gure, and 12 nodes (two per country) where either an equiv-alent generator or an equivalent load is located. It has been as-sumed that half of each cross-border line is owned by each oneof the countries sharing the border. Broad similarities betweenthis system and Western Europe are obvious. However, we donot claim that the numerical values obtained here are represen-tative of the ones that would be obtained if the correspondingmethod were actually applied in this region. The results for eachmethod and the comparison among them are presented next.

A. Results for the Marginal Participation Method

The numerical results corresponding to the application of theMP method for two possible choices of the slack bus are shownhere: in case 1, node 8 has been chosen as the responding nodewhereas, in case 2, node 2 is the responding node. For cases 1and2, respectively, Tables I andIII provide the individual contri-butions (in MW) of agents to the ow over lines; while Tables IIand IV give the same results aggregated at country level. Finally,Tables V and VI provide the compensations and charges amongcountries in the two cases. In these two last tables, the rows la-beled with the name of a country show the use that the corre-sponding country makes of the grid of all the countries in thesystem. The row labeled Use by others provides the use of thegrid of each country by others. The row labeled Use of others provides the use that each country makes of others grids. Fi-nally, the row labeled Net use provides, for each country, thedifference between the two previous results. Numbers in thesetwo tables are expressed in thousands of MW .

Finally, Fig. 5 shows the path followed by the ow injected bythe generator in node 2 when the slack node is located in node8.

B. Results for the Average Participation Method

Tables VII IX show the results obtained when applying theAP method to the system in Fig. 4. The interpretation of thesetables is the same already explained for the corresponding tables

obtained with MP.In order to compare the results provided by AP and MP, Fig. 6represents the path followed by the ow injected by the gener-ator in node 2 according to AP.

C. Results for the With and Without Transits Method

Compensations and charges resulting from the WWT methodare shown in Table X, which has the same structure and meaningas previous similar tables. Due to the fact that only countries P,E, and D are crossed by transits, the remaining countries (F, I,and H) do not receive compensation.

If country P is split into two new systems P1 and P2, the transitthrough P1 and P2 is zero and none of these two countries is en-titled to any compensation. In addition, the total net ow pro-duced by P1 and P2 is different from that produced by P. Conse-


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TABLE ICONTRIBUTIONS OF AGENTS TO THE FLOW OVER LINES , R ESULTING FROM THE MP M ETHOD , W HEN NODE 8 IS THE SLACK BUS

TABLE IICONTRIBUTIONS OF COUNTRIES TO THE FLOW OVER LINES , R ESULTING FROM THE MP M ETHOD , W HEN NODE 8 IS THE SLACK BUS

TABLE IIICONTRIBUTIONS OF AGENTS TO THE FLOWS OVER ELECTRICAL LINES , RESULTING FROM THE MP M ETHOD , W HEN NODE 2 IS THE SLACK BUS

TABLE IVCONTRIBUTIONS OF COUNTRIES TO THE FLOWS OVER LINES , R ESULTING FROM THE MP M ETHOD , W HEN NODE 2 IS THE SLACK BUS


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TABLE VCOMPENSATIONS AMONG COUNTRIES PRODUCED BY THE MP M ETHOD

CORRESPONDING TO THE USAGE OF TRANSMISSION FACILITIESWHEN NODE 8 IS THE SLACK BUS

TABLE VICOMPENSATIONS AMONG COUNTRIES PRODUCED BY THE MP M ETHOD

CORRESPONDING TO THE USAGE OF TRANSMISSION FACILITIESWHEN NODE 2 IS THE SLACK BUS

Fig. 5. Path followed by the ow injected by the generator in node 2, accordingto the MP method, when the slack node is in node 8.

quently, the contributions of countries to the total compensationfund changeas well. As a resultof this, compensations among allcountries change substantially, as Table XI shows.

D. Comparison of the Results

Table XII shows the net compensation or charge that corre-sponds to each country, with each one of the three methods, afterall intermediate computations have been carried out. The differ-ences in the numerical values clearly indicate that the choice of

one method or another would have a signi cant impact on thecompensation to be received by each country.

IV. A NALYSIS OF THE CONSIDERED METHODS

As discussed in the introduction, all the methods discussed

in the paper are based on the principle that the level of utiliza-tion of a network by external agents is an acceptable measureof the costs of infrastructure born by the corresponding systembecause of cross-border transactions and loop ows [9], [18],[19]. An unambiguous de nition of electrical use does notexist, since electricity ows cannot be tracked down as a uid ina pipe. However, the method nally adopted to compute com-pensations among countries should, at least, comply with someminimum requirements.

a) The main underlying assumptions behind the methodshould be compatible with sound engineering and eco-nomic principles. The principles that any ef cient methodshould comply with are the following: Principle 1: Additivity: The network charges obtained

for a set of agents, or set of groups of agents, whenconsidered separately should sum to the total network charge obtained for the set of agents when consideredas a whole.

Principle 2: The network ows attributed to each agentshould be compatible with the limits imposed by thenetwork, namely the limit on the amount of power thatcan ow over each transmission line. This is due to thefact that congestion in the grid linking two areas effec-tively isolates the operation of the system in one areafrom that in the other. Hence, the impact of the power

produced or consumed by an agent in one area on theuse of the network in the other area must necessarily belimited by the capacity of the interconnection betweenboth areas.

Principle 3: In those cases, like the European one,where generation and load are scattered all over thesystem, the electrical use of transmission lines by anagent or country should normally decrease with thedistance from the latter.

b) The method should be able to separately allocate the costof individual network investments, so that each countrycontributes to the cost of each new line proportionally

to the bene ts it gets from that investment. This may benecessary for the involved countries to support or at leastnot to oppose the construction of new lines of a regionalscope.

c) Results provided by the method should make economicand engineering sense and should be reasonable under allcircumstances.

d) Preferably, it should be simple to understand and apply.The amount of data required to apply the method shouldnot be large or dif cult to obtain.

e) Previous experience with its utilization would be consid-ered a positive trait, since it increases the con dence inthe method.

Other possible assessment criteria that may be critical inother applications, such as the computing effort required by


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TABLE VIICONTRIBUTIONS OF COUNTRIES TO THE FLOWS OVER LINES RESULTING FROM THE AP M ETHOD

TABLE VIIICONTRIBUTIONS OF AGENTS TO THE FLOWS OVER ELECTRICAL LINES RESULTING FROM THE AP M ETHOD

each method, are not a differentiating factor in this case, sinceinter-TSO payments will only have to be computed once a year.

The following subsections provide a comprehensive assess-ment of the considered methods.

A. Marginal Participation Method

a) Compatibility of Assumptions With Engineering/Eco-nomic Principles: Both MP and AP separately compute thefraction of the network that is used by each agent. Then, theparticipation by a country or group of agents in the use of theregional grid results from adding up the individual contribu-tions of the agents within the group or country to the total usemade of the grid. Consequently, both the Marginal and AverageParticipation methods comply with the principle of additivity

(principle 1).The critical assumption of the MP method is that the sameslack node (or combination of nodes) is used to compute theutilization of the network by all agents, regardless of where theyare located or their size . Using the same slack node for everyagent in the system results in very elegant mathematical prop-erties [5], [20]. However, as explained below, it is unacceptablewhen allocating the cost of a large multinational network, likethe European one, where many countries are weakly intercon-nected.

Next, an example is provided that illustrates the dependenceof the results produced by MP on the choice of the slack node. Italso explains why these results may be nonsensical. The systemin Fig. 7 comprises three systems 1, 2, and 3. Systems 1and 3 are interconnected by link K. This link may represent

a large grid comprising several systems and its capacityis the net transfer capacity between areas 1 and 3. We shallassume that the capacity of link K is close to zero .This may correspond to a situation where systems 1 and 2are located at one end of a large region while system 3 is lo-cated at the other end and some of the interconnections betweencountries in the region are weak.

Consider rst the situation where the slack node s is thelower right hand node that is located within system 3. Then,generators and loads in areas 1 and 2 will be deemed to sig-nicantly contribute to the ows through lines in area 3. Thisis hardly compatible with the fact that the amount of generationor load in the former areas will certainly have a negligible im-pact on the use made of the grid of the latter (the operation in

areas 1 and 2 can be considered to be independent of thatin area 3). Thus, for example, assuming that all the lines in3 are of the same impedance and applying Kirchhoff s laws,MP would determine that load D1 is using 3333.3 MW of thecapacity of line L, which is not compatible with the capacity of the inter-connector between areas 1 and 3. Since the network usage attributed to agents may not be compatible with the ca-pacity of transmission lines, MP does not comply with principle2. Generators and loads in area 3 will be deemed not to usetransmission lines in areas 1 and 2.

On the other hand, if the slack node is assumed to be locatedin system 2 then generators and loads in system 3 would bedeemed to be using the lines in areas 1and 2 to a large extentwhereas the use made by market agents in areas 1 and 2 of the grid in 3 would probably be deemed to be negligible. In


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TABLE IXCOMPENSATIONS AMONG COUNTRIES FOR THE AP M ETHOD CORRESPONDING TO THE USAGE OF TRANSMISSION FACILITIES

Fig. 6. Path followed by the ow injected by the generator in node 2 according to AP.

other words, the allocation to the agents in the different systemsor countries of the use made of the lines signi cantly dependson the arbitrary choice of location of the slack node.

Since the cost allocation factors critically depend on the se-lection of the slack node (e.g., Oslo, Athens, Lyon, or any com-bination of them), the results of the algorithm are fatally in-uenced by this arbitrary decision. For instance, if the slack node is placed in Madrid, the network users in Portugal willnot pay for the use of lines outside the Iberian Peninsula. How-ever, if Warsaw is chosen instead, the Portuguese agents willhave to pay a fraction of the cost of lines in France, Germany orPoland. Therefore, this method does not comply with principle3, since the participation of an agent or country in the use of a line does not necessarily decrease with the distance between

one and the other. Some authors have claimed that changing theslack node simply shifts all the allocation factors by the sameamount, which is true, see [5]. But the obvious implication isthat nonsensical results, when modi ed by a constant additiveamount, must remain nonsensical.

b) Ability to Allocate the Cost of Individual Network Invest-ments: The MP method directly allocates the cost of any lineto grid users both external to the country and also internal. Thismethod automatically determines which countries are using anew line and to what extent. MP may yield both positive andnegative contributions of agents and countries to the ow overnew lines. This implies that the MP allocation of the cost of theselines may result in a counter-intuitive outcome. For instance, thenetwork users within a country may haveto pay more than 100%of the cost of a new line being built in the country.

c) Assessment of the Numerical Results Provided by the Method: The numerical results corroborate our previous quali-

tative conclusions. Speci cally, the results critically depend onthe choice of the slack bus. For instance, when 8 is the slack node country P happens to be using lines in F and D, which isnot the case when 2 is the slack node. Comparison of Tables IIand IV is self-explanatory.

Note also that, since MP is a marginal approach, it does ignorethe capacity of the interconnections. Therefore, a country suchas P may be using lines in countries such as F or D to an extentthat exceeds the interconnection capacity at the border betweenE and F.

Table II shows that when node 2 is the slack bus countries Fand I have a negative use of lines L8-9 and L6-8, respectively.

This would imply that, if L8-9, for instance, is a new linebeing built, countries D and H, who build the line, will have topay country F for it. This does not seem helpful for the futurereinforcement of interconnections in Europe. What is more,ETSO has argued repeatedly that these negative utilizations of a transmission corridor caused by external agents do notreduce the size of the investment that is actually needed. TheWWT method may result in negative utilization of lines aswell.

Power ows produced by agents according to the MP methodmay not make any sense. Thus, for example, ows attributed tothe generator in node 2 when the slack node is located at node 8are incompatible with the fact that countries E and P as a wholeare importing from F in the case example, see Fig. 5. Besides,the interconnection E-F (among others) may not have enough


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TABLE XINTER -TSO C OMPENSATIONS PRODUCED BY THE WWT M ETHOD WHEN APPLIED TO THE STYLIZED REPRESENTATION OF THE IEM S YSTEM

TABLE XIINTER -TSO C OMPENSATIONS PRODUCED BY THE WWT M ETHOD WHEN APPLIED TO THE STYLIZED REPRESENTATION OF THE IEM S YSTEM

AND P IS SPLIT INTO TWO NEW SYSTEMS P1 AND P2

TABLE XIICOMPARISON OF THE NET COMPENSATION TO BE RECEIVED BY COUNTRIES INTHE STYLIZED EXAMPLE ACCORDING TO MP, C ONSIDERING TWO DIFFERENT

CHOICES OF THE SLACK BUS , AP, AND WWT

Fig. 7. Dependence of the MP results on the location of the slack bus.

capacity to withstand the large ows originating in node 2 andending in node 8.

d) Simplicity and Data Requirements: The basic idea behindthe MP method is easy to understand. However, applying theMP method requires having available a detailed load ow modelcomprising all the countries in the region, as well as informa-tion on the annual regulated cost of lines and other transmissionassets. Load ows are well known by power system engineers.However, they are more dif cult to understand by nontechni-cally trained people.

e) Experience. Suitability to Europe: The MP method canprovide useful results when used for a single system, where allgenerators are under a central market-based dispatch and there

is at all times some physical generator responding to smallchanges in production or demand in any node in the country.Under these circumstances, when the marginal generator isadopted as the slack one, the results may be disputed, but theyare meaningful. Chile and Argentina use MP, although theyhave adopted the main load center (Santiago or Buenos Aires,respectively) as the single slack node. The situation in the IEM,with 25 countries and so many overlapping and independentmarkets, is totally different.

The large size of the European system, the fact that signi cantcongestion exists at several bottlenecks within it and the largenumber of independent markets that are in place result in theoperation of some parts of this system being mostly independentfrom that in others. Hence, considering the same slack node forthe whole system does not seem to make any sense.


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Fig. 8. Rationale for the AP method, Part 1.

B. Average Participation Method

a) Compatibility of Assumptions With Engineering/Eco-nomic Principles: The ow of electromagnetic energy in thespace surrounding transmission lines is due to the contributionof individual loads and generators and it is established at thespeed of light. According to electromagnetic theory, the owsof energy are the result of the joint and inseparable contributionof all sources and sinks acting together. Hence, indisputablyassigning the ow over a line to speci c agents is impossible.The actually metered power ows that are guided by the linesare the only ones that exist and cannot be disputed.

AP simply assumes that each one of these individual con-tributions, when the ow in the line reaches an intersection,branches exactly in the same proportion as the actual ows of energy . Despite the fact that this is an arbitrary assumption, it

seems reasonable and leads to intuitive and robust results, as weshall see later. Once this single assumption is accepted, AP canbe easily used to track the ows upstream and downstream togenerators and loads, respectively.

For example, in the system represented in Fig. 8, in ows intonode are the ow of 200 MW and the local generationof 600 MW. From the map of ows depicted in the gure, weknow that the total in ow of 800 MW into node branches as300, 250, and 250 MW. Then, it seems reasonable to assumethat any in ow into this node, as for instance a 50 MW owproduced by some agent , should be branched pro-rata to 300,250, and 250. Thus, would result in ows of 18.75, 16.25

and 16.25 MW, respectively; seeFig. 9. Branching the line owsproduced by each agent according to this rule is the single basicassumption that lies behind the application of the AP method.

Economics provides a justi cation for the proportionalitybranching rule used in the AP method. Authors in [19] and [21]show that the solution provided by the branching rule of the APalgorithm when computing the path followed by the in owsinto a node is the Aumann-Shapley value of the cooperativegame where incoming MWs into this node are allocated to theoutgoing ones. [19] points out that this proof is only valid if it is assumed that all the contributions by the different agentsto the ow in a line have the same direction as the actual owin the line. This is due to the fact that the contributions of inows to each node to the out ows from this node that wouldresult from the application of the AP method, if line ows were

Fig. 9. Rationale for the AP method, Part 2.

considered as the sum of opposing ows, would be differentfrom the contributions computed when only the net line owsare considered. A more detailed discussion on this topic can befound in [19].

Other methods could be developed that make use of decom-position schemes using counter ows. AP makes the simplestchoice of just using the net owover each line to track the powerinjected or withdrawn by the agents, since it is the only one thatcan be metered (and therefore be certain of).

The contribution of each agent or group of agents to the owover a line cannot be negative according to AP, since any powerow produced by an agent is deemed to branch in the sameproportion as the net line ows. That is to say, the power injectedor withdrawn by each agent is deemed to follow the same paths

as the net line ows. Taking into account this, and the fact thatthe contributions of all the countries in a system to the owover each line add up to the net ow over the line, one mustconclude that the participation of any agent or country in the useof each line, according to the AP method, cannot be larger thanthe capacity of the line. Therefore, AP complies with principlenumber 2.

The AP method has been criticized because it does not makeuse of any advanced network analysis tool, such as a load owalgorithm, nor does it exhibit the nice mathematical propertiesfeatured by MP. The reason that no such tool is needed is simple:AP does not need to make use of ctitious power system condi-

tions that have to be computed, such as the ow patterns fromeach agent to the slack node that are computed in MP or thewithout transits conguration of ows computed in WWT.AP only uses the actual pattern of the ows that is provided bythe system operator and the basic underlying assumption ex-plained before. There is therefore no need to compute anythingthat is not provided by the existing ows themselves. It is not thecomplexity of the computation algorithm what makes a methodbetter, but the soundness of its underlying assumptions.

Finally, due to the fact that the ows that are tracked to aparticular generator, or load, branch into smaller ones until theyreach the loads where they die, or the generators where theycome from, the contributions of agents to the use of lines inmost real systems tend to decrease with the distance from theseagents. Therefore, the AP method complies with principle 3.


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b) Ability to Allocate the Cost of Individual Network Invest-ments: Similarly to what happens with MP, the method directlyallocates the cost of any line to market agents, both generatorsand loads. Hence, it automatically determines which countriesare using a new line and to what extent. Contrary to what hap-pens in MP, agents cannot have a negative contribution to the

ow over a line according to AP. Therefore, AP is, in principle,well suited to the task of assigning the cost of new lines in a re-gional market.

c) Assessment of the Numerical Results Provided by the Method: The conclusions that can be drawn from the numer-ical results are in line with the previous qualitative assessmentof the AP method. The values appear to be in line with basicintuition: Table VII Table IX show that agents and countriesmostly use the grid in their vicinity. Only in the presence of large ows (like those produced by agents in F, which is, by far,the largest exporter in the region) are market agents deemed tobe using transmission facilities that are located far away fromthem. Additionally, and as mentioned before, contributions of agents and countries to the line ows are consistent with thecapacity of the inter-connectors.

Contrary to what happens in the MP method, each agent onlyparticipates in the use of the immediately neighboring lines,which is quite reasonable taking into account the topology of the grid and the pattern of ows in the system; see Fig. 6.

d) Simplicity and Data Requirements: AP makes use of asimple rule in order to track the ows in the system, which canbe understood by nontechnically trained people. Computationof compensations among countries directly follows from this rule.

Applying the AP method requires having available the mapof line ows, the detailed generation and demand pattern within

all the countries in the region and information on the cost of transmission assets.

e) Experience. Suitability to Europe: Experience with its uti-lization exists since it has been applied in several countries. Itwas rst proposed for its application in New Zealand. Presently,it is being used in the Central American regional market for apurpose similar to the EU inter-TSO payments. Besides, it wasseriously considered in Poland or South Africa, among othercountries.

AP only takes into account the existing power ows, whichvary according to the characteristics of the regional grid. There-fore, its implementation in Europe should not be problematic.

C. With and Without Transits Method

a) Compatibility of Assumptions With Engineering/Eco-nomic Principles: WWT relies on two major assumptions:1) it is possible to de ne and identify a transit ow that fullycaptures the responsibility of external agents in the use of thenetwork of a given country and b) the responsibilities of thedifferent countries in the external use of the networks of otherscan be assigned pro rata of the volume of net imports or exportsof each country, regardless of any geographical or electricalconsiderations.

The rst assumption is challenged by manycounter-examplesthat show the inconsistencies of any de nition of transit that has

been attempted; see [18] and [19]. A list of the most salient ones(acknowledged by ETSO) follows.

The concept of Transit is ambiguous. The transit througha country, as it has been de ned, may include ows withorigin and end in external countries, which are the onlyones that should be considered part of the transit. How-

ever, this transit may also include ows that appear notto cross the country. Additionally, the de nition of transitdoes not distinguish loop ows, which originate and endin a given country and cross its borders, from other crossborder ows.

According to the de nition of transit, purely importing orexporting countries do not have a transit ow and do notdeserve any compensation. However, it may be argued thatthe networks of purely exporting countries are used by theimporters to withdraw the power and, analogously, the net-works of importing countries are used by those agents thatexport to them.

The without transit situation is an arti cial one: How canone subtract a transit if it is not clear what a transit is? How can one subtract the loop ows that are naturallyoccurring among systems in the absence of net power ex-changes? As a consequence, the resulting without tran-sits ow pattern is an arti cial construct that may not evenbe physically possible. Besides, subtracting a ow patternthat may not make sense from the actual ow pattern mayresult in nonsensical results (and it frequently does). Forinstance, the subtraction of the with and without con-ditions may lead to counter-intuitive results for individuallines, with serious implications in the allocation of the cost

of new lines. According to the WWT method, a countrymay have to pay more than 100% of the cost of a bene -cial line that this country has built in its territory, i.e., it mayhave to compensate other countries for the construction of this line. This would happen whenever the ow over theline in the real situation is larger than that in the withouttransit situation. Thus, one must conclude that the WWTmethod does not comply with principle 2.

The results obtained with WWT do not have the basic addi-tivity property. If a country (e.g., Germany) consists of sev-eral TSOs, WWT will result in different net ITC paymentsfor thecountry, as well as forother external countries, when

the German TSOs are considered individually or aggre-gated. Therefore, WWT does not comply with principle 1.

The secondmajor assumption of WWT is crude. For instance,if Portugal, Norway, and The Netherlands have the same netvolume of imports or exports, they will be charged an equalshare of the compensation that may be due to Belgium, thusignoring the topology of the networks and the actual pattern of ows. Therefore, WWT does not comply either with principle 3.It also ignores the EU Regulation 1228/2003, which states thatthe compensation to a country shall be paid by the operators of national transmission systems from which cross-border owsoriginate and the systems where those ows end.

b) Ability to Allocate the Cost of Individual Network Invest-ments: When de ning the without transit situation, the WWT


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method forces changes in the ows over many lines within eachcountry. Many times, these ows are not much related to im-port and export ows in the country. The WWT method mayresult in negative compensations for the external usage of thegrid of a country. Thus, for example, Spain, the Czech Republicand Portugal would have received negative annual compensa-

tions for the external use of their grids in the year 2005 if theWWT method had been applied to compute ITCs in Europe, asauthors show in [18]. The fact that a country receives a negativecompensation for the use of its grid by transits implies that thiscountry would have to compensate others for building a line inits territory, which seems dif cult to be accepted by the country.Additionally, after having determined the fraction of the cost of a new line within a country to be paid by external agents, WWTresorts to an arbitrary rule to allocate this cost among the re-maining countries.

c) Assessment of the Numerical Results Provided by the Method: A salient feature of WWT is the fact that it spreadsthe charges among all countries with non zero net imports orexports, as shown in Table X. Thus, for instance, according toTable X, H must pay some compensation to P, E, and D, whichdoes not make much sense.

Table X also shows that three of the countries in the system (F,I, and H) do not receive compensation because they are purelyexporting or importing countries. However, one could convinc-ingly argue that some demands that are external to these coun-tries make use of the grid of the exporting countries to obtainthe power they consume. Analogously, some generators that areexternal to these countries make use of the grid of the importingcountries to deliver the power they produce. Therefore, the gridof purely importing or exporting countries is also partially usedby external agents and these countries should also be entitled tocompensation.

Finally, Tables X and XI show that net compensations amongall countries change signi cantly when one country is split intotwo. Therefore, WWT does not have the basic property of addi-tivity, which does not talk favorably about its consistency.

Taken together, these results indicate that the WWT methodis not well suited to compute inter-TSO compensations amongcountries within the IEM.

d) Simplicity and Data Requirements: Applying the WWTmethod requires the ability to compute a detailed load ow forevery single country in the region. One may use either a singleload ow model comprising all the countries or a separate loadow model for each country. Information on the annual regu-lated cost of transmission assets is also necessary.

The concept behind the application of the WWT method issimple and intuitive. We only need to compare the system owsin twodifferent situations: thesituation that really occursand theone that results from removing the transit through the country.However, the WWT method employs a load ow model to com-pute the electrical usage of each system grid in the withouttransit situation. As explained above, most people involved inthe decision making process leading to the adoption of a longterm ITC mechanism are not familiar with load ow models.

e) Experience. Suitability to Europe: A variant of the WWTmethod has been applied in the NORDEL region to compute

TABLE XIIIASSESSMENT OF THE ITC M ETHODS ACCORDING TO THE DIFFERENT CRITERIA

compensations among countries for the network losses withineach country that are the responsibility of others.

V. C ONCLUSIONS

This paper has evaluated the network cost allocation methodsthat have been seriously considered so far by the stakeholdersof the Internal Electricity Market (IEM) in their search for apermanent and satisfactory approach.

Several aspects of the implementation of each method have

been discussed. Table XIII summarizes how each method faresagainst them using a score from 0 (least desirable) to 2 (most de-sirable). The scores re ect the subjective opinion of the authorsof this paper, but they are based on the previous discussion.

Among the several evaluation criteria that have been con-sidered, assessing the soundness of the basic underlying as-sumptions behind each method must play a central role in ouranalysis. If the basic assumption behind a method is criticallyawed, it is worthless to spend more time examining additionalfeatures of the method, since its results cannot be satisfactory.

The paper concludes that, among the three consideredapproaches the Marginal Participation method (MP), theAverage Participation method (AP), and the With and WithoutTransits method only AP is based on a reasonable set of assumptions and therefore is the only one capable of producing,under any circumstances, meaningful results that cannot beeasily challenged. This qualitative conclusion has been con-rmed and illustrated by the numerical results that have beenobtained from a stylized simple model of the IEM.

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[18] J. I. P rez-Arriaga and L. Olmos, 2003, Extension of the Project onCost Components of Cross Border Exchanges of Electricity, 2003,European Commission. Directorate-General for Energy and Transport.[Online]. Available: http://www.europa.eu.int/comm/energy/elec-tricity/publications/index_en.htm.

[19] L. Olmos, Regulatory design of the transmission activity in regionalelectricity markets, in Institute of Technological Research (Institutode Investigaci n Tecnol gica in Spanish). School of Engineering .

Madrid, Spain: Ponti cia Comillas Univ., 2006, p. 470.[20] M. Rivier and J. I. P rez-Arriaga, Computation and decomposition of spot prices for transmission pricing, in Proc. 11th PSCC Conf. , Avi-gnon, France, 1993.

[21] J. W. Bialek and P. A. Kattuman, Proportional sharing assumptionin tracing methodology, Proc. Inst. Elect. Eng. , vol. 151, no. 4, pp.526 532, 2004.

Luis Olmos was born in Madrid, Spain, in 1976. He received the Electrical En-gineering degree and the Ph.D. degree from the Universidad Ponti cia Comillas(UPCO) in 2000 and 2006, respectively.

Currently, he is a Researcher at the Instituto de Investigaci n Tecnol gica,

Madrid. His interests include areas such as the regulation of electricity marketsand planning of power systems. He has worked on several aspects of the op-eration of power systems, such as the provision of ancillary services (load-fre-quency regulation). Currently, he is working on transmission pricing issues inthe context of regional markets with a special focus on the problems of conges-tion management, sunk costs recovery, tariff design, and grid expansion.

Ignacio J. P rez-Arriaga was born in Madrid, Spain, in 1948. He received theElectrical Engineer degree from the Universidad Ponti cia Comillas, Madrid,Spain, and the Ph.D. and M.S.E.E. degrees from the Massachusetts Institute of Technology, Cambridge.

He is a full Professor of electrical engineering and has been the Founder andDirector for 11 years of the Instituto de Investigaci n Tecnol gica in the Univer-sidadPonti ciaComillas, where he hasalsobeen ViceDirectorfor Research andis presentlyDirectorof theBP Chair on Sustainable Development.He hasservedfor ve years as Commissioner at the Spanish Electricity Regulatory Commis-sion. He is the Director of Training at the Florence School of Regulation, withinthe European University Institute in Florence. He has worked in power systemdynamic analysis, monitoring and diagnosis of power system devices and sys-tems, intelligent computer design of industrial systems, planning and operationof electric generation and networks, sustainability of energy models, and reg-ulation and restructuring of the power industry. In this last topic, he has beenconsultant for governmental agencies or electric utilities in more than 30 coun-tries. He has published more that 150 papers on the aforementioned topics.

Dr. P rez-Arriaga is a Member of the Spanish National Academy of Engineering.

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