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A Multiyear Dynamic Approach for Transmission Expansion Planning and Long-Term Marginal Costs Computation
Antnio Silvestre D. Braga and Joo Tom Saraiva, Member, IEEE
AbstractThis paper presents a multicriteria formulation for multiyear dynamic transmission expansion planning problems. This formulation considers three criteria: investment costs, operation costs, and the expected energy not supplied. The solution algorithm adopts an interactive decision-making approach that starts at a nondominated solution of the problem. This solution is identied transforming two of the three criteria in constraints specifying aspiration levels and using afterwards simulated annealing to deal with the integer nature of investment decisions. After obtaining this rst solution, the decision maker can alter the aspiration levels and run the application again to obtain a new solution. Once an expansion plan is accepted, the algorithm computes long-term marginal costs, reecting both investment and operation costs. These costs are more stable than short-term ones and inherently address the revenue reconciliation problem well known in short-term approaches. The developed algorithm is tested using a case study based on the Portuguese 400/220/150-kV transmission network. Index TermsLong-term marginal costs, simulated annealing, tariffs for use of networks, transmission expansion planning.

NOMENCLATURE The notation used throughout the paper is detailed as follows. STMC Short-Term Marginal Cost. LTMC Long-Term Marginal Cost. Short-term marginal price in bus . f Objective function of an optimization problem. Active load and generation in bus . i, p Index of load scenarios and periods in the planning horizon. nsc, np Number of load scenarios and number of periods. Duration of scenario . nbuses Number of buses. MBR Marginal-Based Remuneration. MC Marginal Cost. PNS Power Not Supplied. G Penalization of PNS. Generation variable cost in bus .
Manuscript received September 10, 2004; revised January 10, 2005. Paper no. TPWRS-00484-2004. A. S. D. Braga is with the Instituto Politcnico da Guarda, Escola Superior de Tecnologia e Gesto, 6300-559 Guarda, Portugal (e-mail: asdbraga@ipg.pt). J. T. Saraiva is with the Electrotenique and Computers Department, Faculdade de Engenharia da University do Porto and also with INESC Porto, Campus da FEUP, 4050 Porto, Portugal (e-mail: jsaraiva@fe.up.pt). Digital Object Identier 10.1109/TPWRS.2005.852121

DC sensitivity coefcient of the active ow in branch regarding the injected power in bus . Bounds on generation in bus . Bounds on the ow in branch . m and n Indices for buses. Active ow in branch . Estimate of active losses in branch . Loss Estimate of active losses in all branches. Conductance of branch . Phase difference across branch . Dual variables of an optimization problem. IC, OC, TC Investment, Operation, and Total Costs. EENS Expected Energy Not Supplied. Variation of the Investment and Operation costs. Variation of the load in bus . Solution of the Simulated Annealing Algorithm. ITC, WSC Iteration counter and worse solution counter. Temperature parameter and cooling rate parameter. K Boltzman constant. EF Evaluation function of the Simulated Annealing. Variation of the Evaluation Function. current Index of the current solution of the Simulated Annealing. new Index of a sampled solution of the Simulated Annealing. opt Index the optimal solution of the Simulated Annealing. rp Random number or probability. YSTMR Yearly Short-Term Marginal Remuneration. YLTMR Yearly Long-Term Marginal Remuneration. YOC, YIC, YTC Yearly Operation, Investment, and Total Costs. TSTMR Total Short-Term Marginal Remuneration. TLTMR Total Long-Term Margianal Remuneration. Return rate. I. INTRODUCTION OR THE LAST 25 years, the electric industry has been experimenting with a liberalization and restructuring process that started in Chile, spread to England and Wales in 1990, and then to other European countries, Australia, New Zealand,

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Latin American countries, and the United States. Initially, there was a strong accent on market mechanisms on the generation sector and on the liberalization of the access to the networks. As this movement developed, there was a new challenge in decoupling distribution network operation from retailing. This nally introduced competition at the extreme activities of the industrygeneration and retailingwhile keeping network transmission and distribution areas as natural monopolies. This unbundling process lead to a new organizational paradigm in which one can identify a number of activities with new actors and remuneration mechanisms: Generation activitiesincluding generation under normal competitive regime, generation under any special tariff regime (namely, including extra payments to renewables), and the supply of ancillary services; Network activitiescomprising both transmission and distribution wiring activities. In Europe, transmission providers are usually merged with system operators leading to transmission system operators. Regarding distribution, the July 2003 EU Directive requires decoupling distribution wiring activities from retailing and the creation of independent distribution system operators; Transactionsthe commercial relationship between generation and demand is performed by centralized pool markets or by bilateral contracts as well as by a number of nancial mechanisms aiming at reducing the risk inherent to short-term activities; Coordination activitiesincluding technical and regulatory aspects. Security of operation is ensured either by independent system operators (ISOs) or by transmission system operators (TSOs). At a regulatory level, network activities are typically not subjected to competition, thus requiring regulatory mechanisms designed and supervised by regulatory agencies. Electricity markets implemented in several countries suffered from a short-term drawback in the sense that they failed in transmitting long-term signals to induce investments in new generation and transmission capacity. These facts, together with the peculiarities of the product to be marketed and the difculties in licensing new transmission lines due to environmental constraints, lead to several well-known and discussed problems just illustrating the difculties in combining short-term approaches with long-term requirements. Regarding transmission, expansion plans must now be prepared in a decoupled way from generation and distribution. This means that in some way, transmission networks will now have to run after new users both at the generation and the demand side, introducing a new level of uncertainty regarding the location of connection points. The increasing number of wind parks together with their increasing installed capacity leads to power surplus in some distribution networks that now start to inject in transmission. As the installed capacity increases, connection points start to move from distribution to transmission, creating new challenges to transmission planners. This new environment still has to accommodate some characteristics typical of transmission expansion problems. They

are discrete problems due to the integer nature of investment decisions, and one can easily identify a number of criteria to meet leading to multicriteria formulations. Apart from that, expansion plans should display a multiyear dynamic nature. This means they should neither correspond to a set of yearly plans identied in a sequential and an independent way for each year in the horizon nor a set of individual investments selected to address particular problems in the network. In fact, an investment scheduled for a particular year can have a positive impact in years afterward and can also contribute to solve problems elsewhere in the system, given the interconnected nature of transmission networks. In view of the referred complexities and of the existing models and algorithms, this paper presents a multicriteria formulation for the transmission expansion planning problem considering investment costs, operation costs, and a reliability index, represented by the Expected Energy Not Supplied (EENS). This problem is solved in an interactive way with the decision maker. The algorithm starts by identifying a rst nondominated solution of the multicriteria problem. This solution is built by converting two criteria in constraints specifying aspiration levels. The decision maker has the chance to modify the initially used aspiration levels to improve some specic criteria or allow some other to get degraded in some sort of tradeoff analysis. The algorithm proceeds with subsequent changes of the aspiration levels until the decision maker is satised with the current nondominated solution. In each run, a nondominated solution corresponding to an expansion plan is built using simulated annealing, given its ability to preserve the discrete nature of the original problem. Once this phase nishes, one can compute long-term nodal marginal costs reecting both operation and investment costs. These values are more stable than short-term ones, given that they include a long-term trend based on investment costs, and they inherently address the revenue reconciliation problem that is usual in short-term applications. The paper includes overviews on transmission expansion planning and on simulated annealing in Sections II and III, Sections IV and V address regulatory issues and concepts about marginal costs, and Section VI details the transmission expansion planning formulation, the adopted algorithm, and the computation of long-term marginal costs. Section VII presents the results obtained with the application of this formulation to a case study based on the Portuguese transmission 400/220/150-kV grid, and Section VIII draws the most relevant conclusions. II. OVERVIEW OF TRANSMISSION EXPANSION PLANNING The literature on this topic includes a large number of publications that can be gathered in two large groups: formulations to analyze preprepared expansion plans. Most of these formulations correspond to software packages developed by utilities or in research centers closely related with them. As examples, they aim at characterizing expansion plans from the point of view of reliability, transient behavior, or stability. Packages such as TRELSS and CREAM developed by EPRI

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and several others implemented by CEPEL in Brazil, ENEL in Italy, and EDF in France are examples of these approaches; optimization models aiming at building expansion plans according to some criteria. In this case, it is important to mention that there is not a common transmission expansion formulation accepted by all researchers. Different publications describe different models as well as solution algorithms. Traditionally, the expansion formulations included continuous variables to represent the capacity of new branches, thus requiring approximations to obtain a nal technically feasible solution. For instance, [1][4] describe linear and nonlinear approaches to this problem. Such other papers as [5] and [6] adopt Branch and Bound and Benders Decomposition-based methods in a way to preserve the discrete nature of investments. Some others select investments according to a Merit Index or to a tradeoff relation between investment cost and the resulting benet [7][9]. More recently, several emergent techniques, such as simulated annealing, genetic algorithms, tabu search, and game theory, started to be applied to this problem [10][17]. References [10] and [12] describe the application of genetic algorithms to the transmission expansion problem. References [15] and [16] detail the use of tabu search, [11] adopts simulated annealing, and [14] uses grasp. All these models have in common the fact that each solution is evaluated by a cost function reecting investment costs plus a penalty on unserved energy. It comes clear that if this penalty is high, the plan tends to have larger investment costs displaying a tradeoff between investments and unserved energy. This also means that all these approaches combine in a single function two criteria related with investment costs and reliability requiring some prior knowledge of the maximum price that the consumers are willing to pay for electricity. Finally, [17] corresponds to an initial report on the current paper but not yet considering the full multicriteria approach nor the complete application to the Portuguese transmission system, as included in the present paper. III. SIMULATED ANNEALINGAN OVERVIEW Simulated annealing [18], [19] is a metaheuristic optimization procedure that, together with genetic algorithms and tabu search, is specially designed to address combinatorial problems. These approaches usually provide good solutions in the sense that they improve a performance index, but it is not usually possible to guarantee global optimality. Metaheuristic search procedures move away from one solution by sampling another one that is accepted if it improves the selected performance index. If it is worse, it can still be accepted, depending on a small acceptance probability. This is used to escape from local optima and to make a wider search on the solution space until a more promising area is located. This is an important advantage when compared with traditional gradient-based algorithms. The acceptance probability is progressively reduced to avoid oscillation and to make sure that

the search is more chaotic in the beginning and concentrated in a promising area as the algorithm proceeds. The simulated annealing algorithm is summarized below. 1) Select an initial solution in the solution space X and set the iteration counter ITC at 0. computing the evaluation function 2) Evaluate . to and to The index 3) Assign opt denotes the best solution identied so far. 4) Sample a new solution in the neighborhood of the at iteration ITC. current solution 5) Testing then assign to ; a) if , then assign to and b) if to ; c) else ; get a random number rp in compute the probability of accepting worse soluby (1) where is tions at iteration ITC the Boltzman constant

ITC d)

(1)

, assign to ; if End if a stopping rule is reached; and go back to step 4). otherwise, let Along the algorithm, the temperature is lowered in a slow pace so that the system can evolve to a low-energy state in a clear analogy with thermodynamic cooling problems. Usually, the temperature evolves by levels, meaning that each one is used during a xed number of iterations. After that, the temperature is lowered by a coefcient , which is inferior but usually close to 1.0. 6) IV. REGULATORY ASPECTS Regulation became a crucial activity in the electricity industry as a way to set targets, to induce improvements on technical and economic behaviors, to impose rules on activities still conducted on a monopoly basis, and to defend consumers. Transmission activities are most widely provided in a monopoly basis, and therefore, they require being regulated from a technical and an economic point of view. In several countries, as in Portugal, the transmission system provider must provide its service according to a number of indices specied by the regulatory agency for several security criteria. This ensures the adequate levels of quality of service while inducing expansion and reinforcement investments. TSOs are then usually obliged to prepare and submit expansion plans to the regulatory agency to guarantee those indices. If approved, those plans will be remunerated by tariffs for the use of transmission networks. This mechanism shows some interesting aspects. The link between technical issues and economic aspects becomes clear. Technical security or supply indices determine investments to be remunerated by tariffs.

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Once an expansion is approved, it represents a commitment of the regulatory agency to an evolution of those tariffs along the planning horizon. Given the impact of investments in tariffs, it becomes clear that expansion plans have to be built carefully, namely, to defend consumers. If available and ensuring the same technical results, a less costly investment plan will have to be selected. In Portugal, the TSO has to prepare a transmission expansion plan with a six-year horizon based on forecasts of new generation stations, of new demand from distribution systems, on indications about distributed generation either directly connected to transmission or to distribution, and on the specied security indices. This plan is submitted to the regulatory agency, and it is updated every two years to progressively accommodate more rened forecasts for several parameters affected by uncertainties. V. NODAL MARGINAL COSTS A. Denitions The marginal cost of electricity [20] can be dened as the impact on the objective function of an optimization problem due to a change in the demand (2) (2)

at the nodal cost at the bus to which they are connected. As an example, in (3), we assumed that MCs, short term or long term, were computed for a load scenario or system topology having duration and is the number of load scenarios along a year MBR MBR (3)

MBR based on STMC is usually reduced when compared with the regulated amount [25], [26] (percentages varying from 10%20% are reported for different systems) leading to the already referred revenue reconciliation problem. On the contrary, MBR based on LTMC inherently addresses this problem since LTMCs also reect investment costs. B. Computation of STMCs For a given topology and set of loads, STMCs can be obtained solving the problem in (4)(8). The model includes the following: a global balance generation/load (5); generation (6) and PNS (7) limit constraints; branch ow constraints (8) established with the dc sensitivity coefcients

(4) Electricity marginal costs display a geographical nature and can either be short or long term, depending on whether they reect only short-term operation costs or they include both longterm operation and investment costs. STMC or LTMC can then be used to set STMP or LTMP to be used in tariffs for use of networks. STMC can be obtained as subproducts of dispatch problems by adequately using dual variables in linearized problems [21], [22]. In this case, they are easily computed, but they are very volatile since they depend on the load level [23], on the conguration in operation, on transmission limits, on generation costs, and on component outages. This volatility leads to the concept of spot prices as time-dependent STMC. LTMCs reect operation and investment costs along a multiyear horizon. This means that they should be computed in the scope of transmission expansion planning problems, turning their calculation more complex. LTMCs are more stable than STMC since they include a long-term trend, and they are able to transmit economic signals to induce more efcient uses of the network. Given the complexity of their computation, there are not numerous examples of their use in real tariff systems. One of the rare examples is the ICRP, adopted in England and Wales and detailed in [24]. When STMC or LTMC are available, we can compute the marginal-based remuneration to assign to the transmission provider as a part of its regulated remuneration. This amount comes from the geographic dispersion of these costs and leads to a surplus coming from expression (3). In this case, we specied that each generator or load is paid or pays the electricity (5) (6) (7)

(8) In this formulation: is the generation level in bus , and is the cor responding variable cost; is the load in node and PNS represents Power Not Supplied penalized by G; and are the minimum and maximum generation levels in node ; and are the minimum and maximum active ow levels in branch ; is the dc model sensitivity coefcient relating the active ow in branch with the injected power in node . Once this problem is run, active losses can be estimated by is the branch conductance, and (9). In this expression, is the phase difference along branch (9) The results of the problem in (4)(8) can now be adjusted to include an estimate of active losses using the algorithm that follows.

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1) Solve problem (4)(8) and set iteration counter itr at 1. 2) Build the nodal injection vector and compute voltage phases using the inverse of the dc model bus admittance matrix. 3) Estimate branch losses using (9) and add half of the losses in branch m-n to the loads in nodes m and n. 4) Solve problem (4)(8) considering the new load vector and increase itr by 1. 5) Build the nodal injection vector and compute voltage phases using the inverse of the dc model bus admittance matrix. 6) Check convergence by comparing voltage phases in two consecutive iterations. If convergence was not yet reached, return to 3).

The investment cost of a plan IC is the sum of investment , along the np periods in the horizon, adequately adcosts justed using a return rate (11) IC (11)

Using the results obtained in the last iteration of this algorithm, the STMC in node is computed using (10). In this expression, is the STMC at node k, is the dual variable of is the active ow in branch m-n, is the constraint (5), is the dual dual variable of an active branch limit constraint, variable of the PNS constraint in node , and Loss represents active losses in all system branches Loss (10)

For each period in the horizon, operation costs are determined by solving the short-term dispatch problem in (4)(8), admitting that the elements in the plan under analysis are available in the selected commissioning years and in subsequent periods. This means solving as many short-term dispatch problems as the number np of periods. The total operation cost will be the addition of the yearly costs adjusted in a similar way to (11). The developed formulation also considers a reliability index since investments can also be driven by the degradation of reliability. In our case, we used the EENS, computed for each period using a pseudochronological simulation described in [27]. As a result, a plan is characterized by the OC, IC, and EENS, leading to a multicriteria problem. B. Dealing With the Multicriteria Problem The problem under analysis is very complex due to its integer nature and its size. This prevents using several methods to deal with multicriteria problems, namely, ones that build the nondominated frontier to be presented to the decision maker. In this case, the decision maker could conduct a tradeoff analysis to get more insight about the set of nondominated solutions and nally select one of them. In our case, we adopted an interactive approach that does not require the knowledge of the nondominated frontier and that is able to address a generic problem as (12)(16). In this formulation, is the vector of criteria, are short-term operation variables (generation, branch ows, etc.), represents the discrete list of reinforcements or expansions, (13) are operation constraints for every year of the horizon, and (14) represents limits on the number of reinforcements or expansions per period or limits related with the available amount of money to invest per year. Finally, (15) represent operation and technical limit constraints, and (16) enumerate the available transmission capacities related with possible investment decisions OC IC EENS (12) (13) (14) (15) (16)

VI. TRANSMISSION EXPANSION PLANNING ALGORITHM A. General Aspects Transmission expansion planning problems have some peculiarities that should be stressed. In the rst place, they have to accommodate two time scales. A shorter one within which available components are xed and one wants to evaluate operation costs, namely, related with congestion and active losses, and alonger one where one has to deal with investment decisions. These two time scales are interrelated in the sense that operation costs can be reduced by new investments. Apart from this, investments should be seen in a global way since a new component especially selected to address some local problem on a specic year can, in fact, have a positive impact in other years and in other locations given the meshed nature of transmission networks. Investment decision variables are discrete, leading to a discrete optimization problem. One should keep in mind that load will change along the horizon and that, in most cases, there are several and most usually contradictory criteria. This turns the problem into a multicriteria discrete one. In the developed formulation, the discrete nature of this problem is preserved since the user species a list of possible components to reinforce or build. Each possible reinforcement or new component is characterized by its investment cost, and the algorithm will eventually select it as whole, that is, not as in continuous problems in which one can obtain a value between 0 and 1 for a decision variable. This has the drawback of leading to a technically infeasible solution that, once rounded to the closest integer, would not be, in general, the optimal one.

limits on

The interactive approach starts by building a rst nondominated solution using the -constrained method detailed in [28]. This method requires converting all objectives but one in constraints using aspiration levels. This leads to an integer single objective problem. In our implementation, the decision maker species aspiration levels for the investment cost and for EENS, and the identied nondominated solution is then presented to the decision maker. If he is not satised, he can change the aspiration levels, imposing an improvement of some criteria or

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admitting a degradation of another one. This is iterated until the decision maker is satised with the solution. This solution approach is conceptually different from the one described in several references, for instance, in the ones referred to in the last paragraph of Section II. In these cases, two criteriainvestment costs and unserved energywere combined in a single objective function requiring a priori the specication of the penalty on load curtailment. The approach adopted in this paper does not require this a priori value. Instead, it gives the planner a more intervening role in appreciating a plan and eventually changing aspiration levels to build a new solution more in accordance with his requirements.

6) a) b)

If

, then do the following. . Get a random number Compute the probability of accepting worse soluby (17) tions

(17) c) d) 7) 8) , then assign to and to . Increase the WSC by 1. If WSC is larger than a specied maximum number of iterations without improvements, then go to 9). If the ITC is larger than the maximum number of iterations per temperature level, then do the following. Decrease the current temperature level T by a rate . If the new temperature level is smaller then the minimum allowed temperature, then go to 9). Set the ITC to 1. Else, increase the ITC by 1; go back to 3). End. If

C. Identication of Nondominated Solutions The single objective problem resulting from the application of the -constrained method still has an integer nature. To preserve this characteristic and to ensure that the solutions to be obtained are technically feasible and implementable, we adopted simulated annealing. This algorithm uses a list of expansions and reinforcements from which it samples components to build and the corresponding year. According to the ideas in Section III, the algorithm organizes elements of the list of expansions and reinforcements in a structured multiyear dynamic plan as detailed below. 1) 2) a) b) c) Consider the current transmission/generation system as the initial topology and denote it as . Analyze the current solution: Compute the IC and the EENS. Solve problem (4)(8) to evaluate the short-term OC for the current topology. as the sum of OC Build the evaluation function and penalizations for IC and EENS, in case they are out of the ranges specied by the decision maker. to and to . Assign to and to . Assign Set the iteration counter (ITC) to 1. Set the worse solution counter (WSC) at 0. , in the neighborhood of the Identify a new plan current onesample one of the periods in the planning horizon, and then sample a new installation to build, among the ones in the list of possible additions, or to decommission, among the existing ones. A new installation will then be available in subsequent periods. Analyze the new plan: Check if the limit for the number of installations to build per period is exceeded, if the limit for yearly investments is exceeded, or if the global investment limit is exceeded. If it does, discard this solution and return to 3). , and and obtain Compute . the new value for the evaluation function, If , then do the following. to and to . Assign to and to . Assign Set the WSC at 0.

a) b) c)

9)

D. Computation of LTMCs Given the integer nature of investments, it is not correct to use a differential-based expression like (2) to compute LTMC. Therefore, using the ideas in [29], we compute an approximation of LTMC using (18). For node , load is increased by , and the expansion-planning algorithm is run to identify the most adequate plan and to evaluate the impacts on operation and investment costs, OC and IC, regarding the initial solution, and that is, to evaluate

(18)

d) e) f) g) 3)

VII. C

4) a)

b) 5) a) b) c)

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northsouth and westeast 400-kV lines with two 400-kV links with the Spanish grid (in the north and center). In 2004, a third 400-kV link with the Spanish grid located in the south was commissioned; 220-kV lines in the central and northeast parts of the country. There were three 220-kV links in the northeast; 150-kV lines in the south and northwest.

TABLE I PART OF THE LIST OF POSSIBLE INVESTMENTS

As required by Portuguese regulations, the expansion planning exercise aimed at building a six-year plan20022007. We used data in [30], a demand increase of 3.5% per year, a maximum number of 36 new additions per year, to simulate nancial constraints and a 10% return rate. We also admitted that the generation system was going to evolve as indicated in [30] from 2002 to 2007: a new natural gas station (4 292 MW starting at 2002, 2004, 2005, and 2006) and new hydro stations (2 118 to start in 2002 and 178 MW to start in 2004). B. List of Possible Lines and Substations to Build Due to the new generation stations and to the evolution of the distribution system along the six-year horizon, it will be necessary to connect 59 new nodes. It is also important to stress that there are plans to increase the installed capacity in wind parks up to 3500 MW by 2010. Some of these wind parks will have a direct impact on the transmission system because they will be directly connected to transmission substations. The remaining ones will have a indirect impact either because the demand of some distribution networks seen by the transmission system will be reduced while some other distribution networks will become self-sufcient or the ows will, in fact, be reversed toward the transmission grid. The expansion exercise used a list with 180 possible investments that are partially enumerated in Table I. For each of them, Table I indicates the extreme buses, the type of investment, the transmission capacity, and the investment cost. To enlarge the solution space, that is, to increase the combinatorial level of the problem, we admitted that each element in this list can be used twice, that is, lines or transformers can be installed in parallel. C. Transmission Expansion Plan for 20022007 The most adequate plan identied by the algorithm described in Section VI includes 100 investments distributed as follows: 36 in 2002, 12 in 2003, 27 in 2004, 14 in 2005, seven in 2006, and four in 2007. Table II shows part of this plan, indicating for each investment the corresponding commissioning year. The investments in Table II correspond to the ones in Table I that were incorporated in the nal plan. D. LTMCs As indicated in Section VI-D, the LTMCs can be computed as soon as an expansion plan is selected by evaluating the impact in operation and investment costs of varying the demand. These marginal costs can then be used to set LTMP. Table III indicates the values of LTMCs (in kilowatthours) along the six-year horizon for several buses of the 400/220/150-kV grid.

TABLE II SELECTED INVESTMENTS AND THEIR TEMPORAL LOCATION

TABLE III LTMCS (IN kW.h)

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TABLE IV GLOBAL RESULTS FOR PNS, COSTS, AND REMUNERATIONS

systems and to set the corresponding appropriate levels of tariffs for use of networks.

REFERENCES
[1] R. Villasana, L. L. Garver, and S. J. Salon, Transmission network planning using linear programming, IEEE Trans. Power App. Syst., vol. PAS-104, no. 2, pp. 349355, Feb. 1985. [2] M. V. Pereira, L. M. V. G. Pinto, S. H. Cunha, and G. C. Oliveira, A decomposition approach to automated generation/transmission expansion planning, IEEE Trans. Power App. Syst., vol. PAS-104, no. 11, pp. 30743083, Nov. 1985. [3] H. K. Youssef and R. Hackam, New transmission planning model, IEEE Trans. Power Syst., vol. 4, no. 1, pp. 918, Feb. 1989. [4] A. P. Meliopoulos, R. P. Webb, R. J. Bennon, and J. A. Juves, Optimal long range transmission planning with AC load ow, IEEE Trans. Power App. Syst., vol. PAS-101, no. 10, pp. 41564163, Oct. 1982. [5] S. T. Y. Lee, K. L Hicks, and E. Hnyilicza, Transmission expansion by branch-and-bound integer programming with optimal costCapacity curves, IEEE Trans. Power App. Syst., vol. PAS-93, no. 5, pp. 13901400, Sep.-Oct. 1974. [6] A. Seifu, S. Salon, and G. List, Optimization of transmission line planning including security constraints, IEEE Trans. Power Syst., vol. 4, no. 4, pp. 15071513, Nov. 1989. [7] A. Monticelli, M. V. Pereira, S. H. Cunha, B. J. Parker, and J. C. G. Praa, Interactive transmission network planning using a least-effort criterion, IEEE Trans. Power App. Syst., vol. PAS-101, no. 10, pp. 39193925, Oct. 1982. [8] M. Morozowski, A. G. C. Melo, M. V. Pereira, and L. M. V. G. Pinto, Priority evaluation and ranking of transmission system projectsComputer models and results, IEEE Trans. Power Syst., vol. 5, no. 3, pp. 10171023, Aug. 1990. [9] J. R. Barros, A. C. G. Melo, and A. L. da Silva, Optimization of transmission expansion planning and impact in the reliability tariffMethodology and case study, in Proc. Symp. Specialists Elect. Oper. Expansion Planning, Braslia, Brazil, May 2002. [10] H. Rudnick, R. Palma, E. Cura, and C. Silva, Economically adapted transmission systems in open access schemesApplication of genetic algorithms, IEEE Trans. Power Syst., vol. 11, no. 3, pp. 14271440, Aug. 1996. [11] R. A. Gallego, A. B. Alves, A. Monticelli, and R. Romero, Parallel simulated annealing applied to long term transmission network expansion planning, IEEE Trans. Power Syst., vol. 12, no. 1, pp. 181188, Feb. 1997. [12] E. L. Silva, H. A. Gil, and J. M. Areiza, Transmission network expansion planning under an improved genetic algorithm, IEEE Trans. Power Syst., vol. 15, no. 3, pp. 11681174, Aug. 2000. [13] J. Contreras and F. F. Wu, A kernel-oriented algorithm for transmission expansion planning, IEEE Trans. Power Syst., vol. 15, no. 4, pp. 14341440, Nov. 2000. [14] S. Binato, G. C. Oliveira, and J. L. Arajo, A greedy randomized adaptive search procedure for transmission expansion planning, IEEE Trans. Power Syst., vol. 16, no. 2, pp. 247253, May 2001. [15] E. L. Silva, J. M. A. Ortiz, G. C. Oliveira, and S. Binato, Transmission network expansion planning under a tabu search approach, IEEE Trans. Power Syst., vol. 16, no. 1, pp. 6268, Feb. 2001. [16] H. Mori and Y. Sone, A parallel tabu search approach to transmission network expansion Planning, in Proc. IEEE Porto Power Tech. Conf., Porto, Portugal, Sep. 2001. [17] A. S. D. Braga and J. T. Saraiva, Transmission expansion planning and long term marginal prices calculation using simulated annealing, in Proc. Bologna Power Tech., Bologna, Italy, Jun. 2003. [18] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by simulated annealing, Science, vol. 220, no. 4598, pp. 671680, May 1983. [19] E. Aarts and J. Korst, Simulated Annealing and Boltzman Machines. New York: Wiley, 1990. [20] F. Schweppe, M. Caramanis, R. Tabors, and R. Bohn, Spot Pricing of Electricity. London, U.K.: Kluwer, 1988. [21] M. Rivier and I. J. Prez-Arriaga, Computation and decomposition of spot prices for transmission pricing, in Proc. 11th Power Syst. Comput. Conf., Avignon, France, Aug. 1993, pp. 371378. [22] H. Rudnick, R. Palma, and H. Lira, Penalty factor calculations for marginal pricing of transmission systems in a hydroelectrical system, in Proc. Stockholm Power Tech., Stockholm, Sweden, Jun. 1995, pp. 704709.

E. Cost Recovery Analysis Finally, using the LTMP, the LTMR was computed, and a cost recovery analysis was conducted. Table IV displays the nal aggregated values. This table includes the following information: the yearly EENS and its percentage regarding the demand. This percentage is quite reduced, although it increases as the planning horizon develops; the YSTMRs and YLTMRs obtained using (3) with STMP and with LTMP; the YOC, YIC, and YTC; the TC and the TSTMRs and TLTMRs as sums of the yearly amounts. All costs and remunerations are referred to the initial year using the referred 10% rate; the percentage of TC recovered by TSTMR (41.04%) and by TLTMR (99.45%). VIII. CONCLUSION In this paper, we described an integrated approach to identify adequate transmission expansion plans together with setting the tariffs for use of transmission networks based on LTMCs. These two issues have a close relation because in several countries, transmission companies are remunerated according to their costs. This means that investments should be adequately selected as they have a direct impact in consumer tariffs. The described approach identies expansion plans in the scope of a multicriteria formulation that builds nondominated solutions using the -constrained method and simulated annealing. The use of this metaheuristic enabled us to address the integer nature of investment decisions and to build realistic and technically feasible solutions corresponding to sets of equipments to build organized in a multiyear dynamic expansion plan. The results obtained with this model indicate that LTMPs can almost completely cover the incurred operational and investment costs. This means this approach inherently addresses the revenue reconciliation problem that is usual when short-term approaches are used. This kind of approach is useful both for transmission companies and regulatory agencies given the link between plans and tariffs referred to above. In this sense, it can be very useful as a way to ensure or increase the quality of service in modern power

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[23] J. T. Saraiva, Evaluation of the impact of load uncertainties in spot prices using fuzzy set models, in Proc. 13th Power Syst. Comput. Conf., Trondheim, Norway, Jul. 1999, pp. 265275. [24] M. C. Calviou, R. M. Dunnett, and P. H. Plumptre, Charging for use of a transmission system by marginal cost methods, in Proc. 11th Power Syst. Computat. Conf., Avignon, France, Aug. 1993, pp. 385391. [25] I. J. Prez-Arriaga, F. Rubio, J. Puerta, J. Arceluz, and J. Marin, Marginal pricing of transmission services: An analysis of cost recovery, IEEE Trans. Power Syst., vol. 10, no. 1, pp. 546553, Feb. 1995. [26] J. T. Saraiva, J. P. Silva, and M. T. P. de Leo, Evaluation of the marginal based remunerationA case study using the portuguese transmission network, in Proc. IEEE Porto Power Tech., Porto, Portugal, Sep. 2001. [27] A. L. da Silva, L. A. Manso, J. C. Mello, and R. Billinton, Pseudochronological simulation for composite reliability analysis with time varying loads, IEEE Trans. Power Syst., vol. 15, no. 1, pp. 7380, Feb. 2000. [28] C.-L. Hwang and A. S. Masud, Multiple Objective Decision MakingMethods and ApplicationsA State of the Art Survey. Berlin, Germany: Springer-Verlag, 1979. Lecture Notes in Economics and Mathematical Systems. [29] E. Khan, Electric Utility Planning and Regulation. Washington, DC: American Council for an Energy-Efciency Economy, 1988. [30] Characterization of the National Transmission Grid in December 31st 2001, Rede Electrica Nacional (REN). [Online]. Available: http://www.ren.pt

Antnio Silvestre D. Braga was born in Seia, Portugal, in 1964. He received the licentiate, M.Sc., and Ph.D. degrees from Faculdade de Engenharia da Univ. do Porto (FEUP), Porto, Portugal, in 1991, 1997, and 2004, respectively, all in electrical and computer engineering. In 1991, he joined the Polytechnic Institute of Guarda (IPG), Guarda, Portugal.

Joo Tom Saraiva (M00) was born in Porto, Portugal, in 1962. He received the M.Sc., Ph.D., and Agregado degrees in electrical and computer engineering from the Faculdade de Engenharia da Universidade do Porto (FEUP), Porto, Portugal, in 1987, 1993, and 2002, respectively. He is currently a Professor with FEUP. In 1985, he joined INESC Portoa private research institutewhere he was Head Researcher and collaborated in several projects related with the development of DMS systems, quality in power systems, and tariffs due for the use of transmission and distribution networks. Several of these projects were developed under consultancy contracts with the Portuguese Electricity Regulatory Agency.