An Application of the Aumann-Shapley Approach to the Calculation of Inter TSO Compensations in the UCTE System Kristin Dietrich1, Luis Olmos1, Ignacio Pérez-Arriaga1 1
University Comillas, Madrid, Spain Institute of Research in Technology C/ Alberto Aguilera 23 28015 Madrid, Spain Phone: + 34 91 542-2800 E-mail:
[email protected] [email protected] [email protected]
Keywords—Inter TSO Compensations, Cooperative Games, Network Cost Allocation Abstract--Calculating Inter TSO Compensations (ITC) has turned out to be a highly critical issue in facilitating the formation of a competitive Internal Electricity Market in Europe. Plenty of methods have been proposed to calculate ITCs, but few of them have the features that are required, namely fairness, transparency and reasonability of their results. This article presents the Aumann-Shapley approach to calculate the compensations for the use of networks by cross-border flows. Using the fundamentals of game theory, the Aumann-Shapley approach lets agents themselves choose the most appropiate generation-load counterpart and thus minimizes at the same time individual and global network usage. A numerical example involving a large fractione of the UCTE grid (17 countries) demonstrates the functioning of the proposed method and its suitability for its implementation in the European context.
I
I. INTRODUCTION TO INTER TSO COMPENSATIONS
N the recently liberalized EU electricity market, commercial transactions do not take place only within countries but also between agents from different nations, since consumers aim to buy their energy at the lowest possible price. 978-1-4244-1744-5/08/$25.00 ©2008 IEEE
International transactions produce power flows in at least two different national networks (those where the buyer and the seller are located). As a result agents from a country may end up using the grid of other countries. Consequently, the latter must be compensated for the external use the former agents are making of their grids. This compensation takes the form of Inter-TSO-Compensations (ITC). This first chapter provides an overview of the current state of the ITC discussion in Europe. Subsequently, a short literature review of the ITC mechanisms that have been proposed, with a focus on the Aumann-Shapley method (AS), is provided. An in detail description of the latter method is given in Chapter II. Its mathematical formulation and implementation are presented in section II.B. These are followed by a critical evaluation of the method in II.C. Chapter III includes ea numerical example of application of the AS method based on real data of the European grid. Finally, chapter IV concludes. A. The need for ITCs The European Directive 96/92/EG concerning common rules for an internal electricity market (IEM) confirms ethe need for an efficient internal electricity market in Europe where competition among agents takes place. Agents in the IEM should behave as if they belonged to one single area, thus being able to buy and sell electricity freely. Free electricity
trade would result in an increase in the social benefit. However, agents would make a significant use of the grids of other countries in this situation, i.e. agents would benefit from lines built in other countries. Using a system of unique panEuropean cost-reflective tariffs would tackle this problem. However, decision makers in Europe have decided to leave the computation of transmission tariffs within each country in the hands of the competent national authorities. A system of compensations among countries (ITCs) has been implemented whereby TSOs shall be compensated for hosting cross-border flows whose origin or end is located in other countries. Compensations should be paid by the TSOs of the areas where these flows originate and the TSOs of the areas where these flows end [1]. A transitory method shall be applied to compute ITCs corresponding to years 2008 and 2009. However, this mechanism lacks some required basic features. The adopted ITC mechanism should be fair, which means that agents should be treated on a non-discriminatory basis, i.e. as if all of them belonged to the same area. This is tantamount to assuming that ITCs cannot depend on political borders. Apart from that, the method should be cost reflective and send appropriate economic signals for new network investments (especially for new cross border interconnections). This requires that the compensation that each country receives from another one must correspond to the actual network usage that the agents from the latter make of the grid of the former. Compatibility of the ITC method with existing regulation is necessary. Regulation 1228/2003 implies that compensations have to be calculated on the basis of physical flows of electricity. It also states that the extra cost incurred by each TSO shall be computed as the forward looking long-run average incremental cost corresponding to external flows. Finally, according to regulation, not only the costs caused by cross-border flows but also the benefits brought about by them shall be taken into account when calculating ITCs. Other desirable features of the ITC method include the following: access to the input data should be easy, the method should be simple to be understood by all parties, and verification of results should be possible. B. Literature Review Authors in [2] and [3] discuss and analyze some of the most representative ITC mechanisms that have already been proposed within the EU context. They conclude that the Average Participation method (AP) is the preferred approach for the computation of ITCs based on its compliance with the main requirements outlined in section I.A. AP tracks power flows from the nodes where they originate to the ones where this power is consumed using the actual snapshot of flows. However, the association of European Transmission System Operators (ETSO) and others decided not to back the adoption of AP as the long term ITC method. Thus, authors in [4] propose other two methods, the so called Marginal Participation method (MP) and the With-and-Without-Transits method (WWT), for its implementation in the IEM. MP computes the participation of an agent located in node N in the use of each line according to the marginal impact on the corresponding line flow of a transaction between node N and a
reference node R. The same reference node R is employed to compute the participation of every agent in the system. WWT computes the compensation to a country based on the change in the line flows of the country resulting from the removal of the transit crossing the country. The contribution of each country to the total compensation fund is proportional to the total amount of imports into and exports from the country. Both the MP and the WWT methods lack some basic properties that any ITC method should have. Thus, a search for an efficient method has been recently launched within ETSO. This article puts forward another method for its consideration in the EU context: the Aumann-Shapley method (AS). As explained latter, AS is deeply rooted in economics theory mechanism and has already been proposed for the allocation of the cost of losses to agents, see [5], for the allocation of transmission-costs in power systems, see [6], and for the allocation of the cost of network upgrades, see [7]. II. AUMANN-SHAPLEY MECHANISM The Aumann-Shapley mechanism (AS) aims to allocate the cost of transmission lines to their users. It is based on the fundamentals of cooperative game theory. The allocation of transmission costs can be seen as a cooperative game. Players in the game correspond to the agents in the electrical system: generators and loads. Each player aims to maximize his personal benefit, which means he seeks to minimize the cost of the lines he is deemed to be using. The solution of the game is the fraction of the total transmission cost to be paid by each player. Rationality of players leads to the formation of coalitions. Coalitions are subsets of agents. The transmission cost to be born by each of them equals the cost of the grid used by generators in the coalition to supply the coalition loads. Each coalition is mathematically seen a subset of the great coalition in which all agents take part. The sum of all individual cost assignments equals the total transmission cost of the system. A. Description of the algorithm The application of the AS method involves deciding from the outset how total costs are shared between the two types of agents in the system: generators and loads. Once the allocation of transmission costs between generators and loads has been determined, charges to be paid by individual generators are computed separately from those to be paid by loads. However, the process to be followed in order to compute the responsibility of each generator in the grid costs is analogous to the one followed for loads. According to AS, each agent, either generator or demand, must choose the demand nodes to which to send its production or from which to obtain the power it consumes. When computing the charges to be paid by generators, for instance, they are considered sequentially and included into a large coalition that ends up containing all the generators in the system. Each new generator G that becomes part of the coalition must choose the loads to supply among the ones that have not been chosen yet by those generators that joined the coalition before G.
The flows, and the resulting network usage which in the end will determine how much each generator will have to pay, are computed with a load flow of the entire regional network. In this load flow, power injections by all those generators that are already part of the coalition are modeled. The network cost that is allocated to each generator is that corresponding to the increase in the total network usage resulting from the inclusion in the coalition of the power injection by the generator and the power withdrawals by the loads it supplies. Therefore, at any time during the application of the AS algorithm, the term coalition refers to the group of all those generators whose incremental network usage has already been computed and those loads that these generators have chosen to supply. Changes in the line flows produced by the power transaction between the generator and the loads it has chosen must be taken into account with their sign. This means that the generator would be charged for the change in the usage of those lines whose flow increases as a result of the inclusion of the aforementioned transaction, while it would be credited for the change in the total usage made of those lines whose flow decreases because of the inclusion of the generator in the coalition. The process is continued until all generators have been included in the coalition and have therefore chosen the nodes where to send its production in the cheapest possible way. This exercise allows to obtain how much of the total network cost should be charged to each one of the generators in the system, for the considered snapshot. The same method can be applied for each one of the snapshots that are considered to represent the entire year. Then some average is taken and the final charges are obtained for each generator. As explained, the method is clearly unfair, since the generators that are listed in the first place have more choices to select the demand nodes than the last ones in the list. In order to fix this problem, the order of the list has to be changed and the entire exercise has to be repeated as many times as the total number of different permutations of the set of generators. The final grid charge to be paid by each generator is computed as the average of the charges obtained for the generator over all these permutations. The total number of permutations is huge, but this is not a problem, since one does not need to run all these cases. There is an interesting mathematical property that makes it possible to obtain the average charge for each generator exactly and in a very efficient way, see [8]. A brief description of the implementation algorithm proposed by authors in [8] is provided in the next subsection (B). The same process can be repeated starting now from the demand nodes. Each demand node will be given the choice to select the generation nodes from which it wants to be supplied, so that the charge for the use of the network is minimal. Again, this has to be run for all possible permutations in the list of demand nodes and for all considered snapshots. Studying the results from the application of the basic algorithm, it can be easily realized that the unit charge to be paid by each generator or load clearly depends on the size of this agent. In order to avoid discriminating agents based on
their size, the power injection or withdrawal by every generator and load is divided into elementary parts of the same size (e.g. 1 MW) that are considered as separate agents in the allocation process. The total charge faced by each agent is then computed by adding up the network charges allocated to all the elementary power injections and withdrawals that the agent is responsible for. B. Mathematical Formulation and Implementation of the AS method. In order to determine the average incremental use that each power unit produced or consumed in a node, in a certain scenario, is making of the transmission grid, all the possible permutations of the whole set of elementary power units produced or consumed in the system in this snapshot must be considered. For each ordering, the incremental contribution of the power unit located in the nth position of the list to the use made of the grid is computed as the difference between the aggregate use that the previous n-1 power units make of the grid, when they choose the loads they supply or the generators they receive power from, and the total use made of the network when the nth unit is considered jointly with the previous ones. According to the law of large numbers, when the number of power units considered before a certain one is very large, it can be reasonably assumed that, for most orderings, these power units will be located following the same pattern as that of the total generation (if we are allocating the network use to generators) or load (if we are allocating it to consumers) operating in the system during the considered hour. Thus, when computing the incremental contribution of a power unit located in the nth position of the list to the total grid use, one can reasonably assume that the fraction of previous n-1 power units located in each node of the system is proportional to the total amount of generation produced or load consumed in this node for the considered scenario. Given that all possible orderings of power units must be considered, the network use attributed to each unit ‘U’ must be computed as the average of the incremental network use corresponding to this unit when it is considered in the 1st, 2nd, 3rd,…, ‘n’th, …, ‘K-1’th and ‘K’th place, being ‘K’ the total number of power units produced or consumed in the system during each scenario. If ‘K’ is very large, the total number of permutations of power units turns out to be very high. Thus, we may take a subset of them as representative of all the orderings that exist. If we choose ‘k’ situations, these should be the ones where 0, K/k, 2*K/k, 3*K/k,.. and (k-1)*K/k power units have been given the opportunity to choose supplier or consumer before the considered power unit ‘U’. If elementary power units are sufficiently small, the number of power units considered before unit ‘U’ in any of these ‘k’ orderings, but the first one, should be very high. Any of the previously chosen ‘k’ orderings should be as representative as possible of all those orderings where the same number of power units choose their counterpart before unit ‘U’. Thus we can suppose that the distribution of these power units follows the same pattern as that of the generation (when computing the
network use by generators) or load (when computing the network use by loads) in the system. Assuming that the agents behave rationally, and according to the way that the incremental network usage attributable to each agent is computed, the first n-1 units of power produced (respectively consumed) that are considered in each of these ‘k’ orderings will choose the loads (respectively generators) they serve (respectively receive power from) so that the aggregate network use they make is as small as possible. Therefore, the aggregated use they make of the network will result from the optimization problem where this use is minimized. Consider, for example, that we want to compute the incremental network use corresponding to a power unit ‘U’ produced in node ‘N’ when ‘n-1’ power units have chosen the load they serve before ‘U’. Then, mathematically speaking, the incremental contribution of ‘U’ to the network use can be computed as the shadow price of the power balance equation, for node ‘N’, in the above mentioned optimization problem. Finally, the network use that an elementary power unit ‘U’ is held responsible for results from averaging the incremental contribution of ‘U’ to the network use over the ‘k’ different orderings of the list of power units that are considered. In other words, the average network incremental use for a power unit ‘U’ that is produced or consumed in node ‘N’ is computed as the average, over the ‘k’ optimization problems where the total electrical usage made of the network is minimized for different load levels, of the shadow prices obtained for the power balance equation for node ‘N’. Equations (1) to (6) provide the formulation of the optimization problem to be solved in order to optimize the use made of the network by a certain group of agents (either generators or loads). L
min
∑ LEN
i, j
⋅ φi , j
(1)
i =1
subject to :
φi , j = f i , j ,1 + fi , j ,2 fi , j ,1 ≥ fi , j ,2 ≥
θi − θ j xi , j
θ j − θi
Di + ∑ j
xi , j
θi − θ j xi , j
fi , j ,1 , Di ≥ 0
−∑ k
θk − θi xk ,i
∀i, j
(2)
∀i, j
(3)
∀i , j
(4)
= gi ∀i, j
∀i
(5) (6)
where i is the set of nodes in the system and j is an alias for it; LEN i , j is the length of the line between nodes i and j ;
φi , j is the flow between both nodes; f i , j ,1 and f i , j ,2 are two
auxiliary variables that are used to represent the absolute value of the flow φi , j ; Di is the demand in node i , which is a variable in the problem where we are determining the use that generators make of the grid and gi is the generation in this node, which is an input parameter in this problem. The problem where the use of transmission lines is allocated to loads has the same format as the previous one. However, in the latter problem Di should be an input parameter to the problem whereas gi should be a variable of the problem. Line losses have been neglected for the sake of simplicity. It would be perfectly possible to take them into account in our formulation, though we would have to resort to a linear representation of them, since parametric programming theory can only be applied to linear problems. C. Critical evaluation of the Aumann - Shapley concept AS exhibits some remarkable good features. It is based on a sound economic criterion. Given that transmission charges should not depend on commercial transactions, the method lets each agent choose where its injected (retrieved) energy goes to (comes from) so that its network charges are minimized. The method applied to doing this is well known and is economically sound: the Aumann-Shapley value. This approach is deeply rooted in economics theory. Each agent is charged for its average incremental contribution to the usage made of the network. Since all possible orderings of generators and loads are considered when the great coalition is formed, and network users are not discriminated based on their size, this method can be considered to be fair. Due to the scheme developed in [8] and presented in the previous section, we do not need to run a separate simulation for each ordering of the generators or loads in the system. This trick results in computing times that are very reasonable. Besides, all loop flows and network effects are taken into account. No assumptions are made here. The use of electricity laws is unquestionable. The flows that result from injecting and retrieving power at the nodes are computed using the usual laws for electricity circuits. Finally, the method ignores commercial transactions and political borders, except when, at the end, it has to aggregate results for each agent to obtain the net network charges at country level. III. A NUMERICAL EXAMPLE A. Description of case example We have applied the AS method to a scenario representing the actual operation of part of the UCTE system during the winter peak load hour in 2001. The case study comprises 17 countries, 3383 nodes and 4956 lines. Countries considered are Austria, Switzerland, the Czech Republic, Slovakia, Poland, Germany, the Netherlands, Belgium, France, Bosnia, Croatia, Slovenia, Hungary, Italy, Portugal, Spain and Ukraine. Table 1 shows the main characteristics of the countries considered in the scenario.
SK
UA
H
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BIH
A
CZ
SLO
B
NL
D
I
CH
F
Fig. 1. Use that each country is making of the whole regional grid
As it can be seen in Fig.1, France is the major user of the regional grid. The use of the grid by other big countries, like Germany, Italy or Spain, is less than half of that made by France. The use of the regional grid by other countries is significantly smaller. Fig. 2 shows the cost of the used fraction of the grid of each country. The French grid is used more than any other in the region. The cost of the used fraction of the national grids in Germany, Spain, Italy and Poland is also high, which is normal taking into account the size of these countries.
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500 450 400 350 300 250 200 150 100 50 0 I
B. Numerical Results In a first step, we have computed the total use each country is making of the whole regional grid (i.e. the grid of the 17 considered countries). This is called regional grid use. Grid charges for individual agents in each country are aggregated to compute the use of the regional grid by this country. Afterwards, we have computed the total use made of the grid of each country, called national grid use. This includes the use the own country is making of its grid. Actual line flows and line capacities have been taken into account. Finally, net compensations to be received or paid by each country are calculated as the difference between each national grid size and the use of the regional grid made by the corresponding country. If the net compensation for a country is positive, the external use made of the grid of this country is larger than the use that this country makes of others’ grids. Thus, in total this country would receive a net compensation. If this compensation is negative, the use made by this country of others’ grids is larger than the external use made of its grid. Thus, this country would face a net payment. The sum of the net compensations for all countries must be equal to zero, since the countries that get a positive net compensation are paid by those countries which turn out to have a negative one.
Countries
F
The optimization problems to be solved have been modeled using GAMS. Standard construction, operation and maintenance costs have been assumed for grid assets. These were obtained from [2]. Only one snapshot has been considered. Therefore, results are not representative of the operation during the whole year 2001. Calculating representative values of annual compensations would require considering an adequate number of scenarios (snapshots) and averaging the results obtained from them.
500 450 400 350 300 250 200 150 100 50 0 E
1852 361 193 5321 2604 5042 1752 3923 764 577 791 235 146 683 725 567 29
P
Imports
P
Exports
E
Generation
Regional Grid Use (Mio. Euro)
Demand
E Spain 29095 28289 554 P Portugal 6359 6891 755 F France 64804 74126 8486 I Italy 31480 26509 0 CH Switzerland 5720 5876 2686 D Germany 50260 49648 3887 B Belgium 7060 6405 1053 NL Netherlands 10651 7134 325 SLO Slovenia 870 928.8 814 A Austria 2867 4295 1961 CZ Czech Rep. 8361 9706 2099 PL Poland 15179 16005 843 BIH Bosnia 427 438 146 HR Croatia 1057 1122 733 H Hungary 3972 3655 373 SK Slovak Rep. 2700 2723 569 UA Ukraine 0 250 279 Table 1: Aggregated data for the considered UCTE scenario
National Grid Use (Mio. Euro)
Code Name
Countries Fig. 2. Cost of the used fraction of the different national grids
Net compensations to be received by countries are shown in Fig.3. Switzerland turns out to be the major recipient of compensations. Generation and demand in Switzerland are very similar. Due to its geographical situation (Switzerland is surrounded both by large importers and by those countries exporting power to the former ones), line flows from other countries use the Swiss grid more than it might be the case for peripheral countries, such as Slovakia or Hungary, thus resulting in a positive net compensation for Switzerland. France has to pay the highest net compensation (around 42% of all compensations to be paid). This is due to the fact that this country is the largest exporter in the region. Other main recipients are Spain, whose grid is used by Portugal and France, Germany and Austria, probably due to their geographical location. The major importer in this scenario, Italy, faces the second largest net payment. Despite being a large importer, The Netherlands faces a small net
[3]
[4]
10 [5]
5 0
[6]
-5 -10
[7] UA
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-15 Countries
Fig. 3. Net payments for each country
Despite being one of the smallest countries in the region, Bosnia is credited with a large positive net compensation. This is related to the fact that exports from the country equal imports into the country (thus, the country is neither a net exporter nor an importer) and the transit crossing the country is comparable in size with the local generation or demand. As it was expected, net compensations are mainly driven by the geographical location of countries and their national energy balances. Therefore, the numerical results that have been computed seem to be in line with basic intuition. In any case, computing compensations and charges for a system comprising all UCTE countries would be advisable. IV. CONCLUSIONS A well known method, based on cooperative games theory, has been applied to compute ITCs in the IEM . According to this mechanism, agents in an electrical system, namely demand and generators, are free to choose the generation or load they receive energy from or supply energy to, respectively. Taking into account all possible permutation of agents the average incremental cost due to each agent is determined. It has been shown that AS satisfies economic, engineering and regulatory requirements and provides a fair allocation of transmission costs within a regional market. Results obtained from a representative case example reinforce the authors view that AS is a suitable option to calculate compensations for cross-border flows in Europe. V. REFERENCES [1]
[2]
15
E
Net compensation (Mio. Euro)
payment probably because it is importing power from power stations in other countries that are close to the Dutch border, like those located in the north-western part of Germany. On the other hand, Belgium, which is importing far less power than The Netherlands, faces a significant net payment because it is importing power mainly from generators located deep into the French grid.
EC, Regulation (EC) No 1228/2003 of the European Parliament and of the Council of 26 June 2003 on conditions for access to the network for cross-border exchanges in electricity, (OJ L 176, 15.7.2003, p. 1).
[8]
FSR, “A study on the inter-TSO compensation mechanism,” 2005, Florence School of Regulation. Available: http://www.iue.it/RSCAS/ Professional Development/FSR/. L. Olmos and I. J. Pérez-Arriaga, “Evaluation of three methods proposed for the computation of inter-TSO payments in the Internal Electricity Market of the European Union”. Transactions on Power Systems, Volume: 22, Issue: 4, 2007. pp: 1507-15422. Consentec/Frontier (2005). “Study on the further issues relating to the inter-TSO compensation mechanism”, European Commission. Directorate-General Energy and Transport. Available: http://europa.eu.int/comm/energy/index_en.html. Report prepared by Consentec and Frontier Economics. P. A. Kattuman, J. W. Bialek, N. Abi-Samra, “Electricity Tracing and Cooperative Game Theory,” 13th Power Systems Computing conference (PSCC) , Trondheim, 1999. G. C. Stamtsis, I. Erlich, “Use of cooperative game theory in power system fixed -cost allocation,” IEEE Proceedings Generation, Transmission and Distribution, 2004, Vol.151 (No.3). F. Evans, J. M. Zolezzi, H. Rudnick, “Cost Assignment Model for Electrical Transmission System Expansion: An Approach through the Kernel Theory,” in IEEE Transactions on Power Systems, 2003, Vol. 18 (No.2), pp.625-32. M. Junqueira, L.C.Costa Jr, L.A. Barroso, G.C. Oliveira, L.M. Thomé and M.V. Pereira, “An Aumann-Shapley Approach to Allocate Transmission Service Cost among Network Users in Electricity Markets”, IEEE Transactions on Power Systems, Volume: 22, Issue: 4, 2007. pp: 1532-1546.
VI. BIOGRAPHIES Kristin Dietrich (b.1982) received an Industrial Engineering and Management degree from the University of Technology, Dresden, Germany in 2007. She has worked on matters of regulation and economy of electrical systems as well as electricity modeling. From March to June 2007 she was visiting student at the Instituto de Investigación Tecnológica (IIT), since July 2007 she is Research Assistant at the IIT and concentrates her work on topics related to transport of electricity. Luis Olmos (b.1976) received an Electrical Engineering degree and a Ph.D. degree from the Universidad Pontificia Comillas (UPCO) in 2000 and 2006, respectively. Currently, he is a researcher at the Instituto de Investigación Tecnológica. His interests include areas such as the regulation of electricity markets and planning of power systems. He has worked on several aspects of the operation of power systems, such as the provision of ancillary services (load-frequency regulation). Currently, he is working on transmission pricing issues in the context of regional markets with a special focus on the problems of congestion management, sunk costs recovery, tariff design and grid expansion.. Ignacio J. Pérez-Arriaga (b. 1948) obtained the PhD, and Master of Science in Electrical Engineering from the Massachusetts Institute of Technology (USA) and the Electrical Engineer degree from the Universidad Pontificia Comillas, Madrid, Spain. He is full Professor of Electrical Engineering and has been the founder and Director for 11 years of the Instituto de Investigación Tecnológica in the Universidad Pontificia Comillas, where he has also been Vicerector for Research and is presently Director of the BP Chair on Sustainable Development. He has served for 5 years as Commissioner at the Spanish Electricity Regulatory Commission. He is a Member of the Spanish National Academy of Engineering. He is the Director of Training at the Florence School of Regulation, within the European University Institute in Florence. He has worked in power system dynamic analysis, monitoring and diagnosis of power system devices and systems, intelligent computer design of industrial systems, planning and operation of electric generation and networks, sustainability of energy models and regulation and restructuring of the power industry. In this later topic he has been consultant for governmental agencies or electric utilities in more than 30 countries. He has published more that 150 papers on the aforementioned topics.
