Transaction Security Cost Analysis By Take-risk Strategy

Transcription

1 Transaction Security Cost Analysis By Take-risk Strategy Hong Chen, Claudio A. Cañizares, Ajit Singh University of Waterloo Waterloo, Canada Abstract - Transaction Security Cost (TSC) analysis is important for managing and pricing transmission congestion in competitive electricity markets. This paper presents a novel TSC analysis method based on a take-risk strategy that relies on on-line Available Transfer Capability (ATC) and transaction impact computations, using voltage stability criteria and related tools. A sample system is used to illustrate some of the basic concepts introduced in this paper. Keywords - Electricity markets, Locational Marginal Prices (LMP), risk, Available Transfer Capability (ATC), voltage stability 1 Introduction N the current electricity markets, system security considerations are becoming more critical for healthy and efficient market operation. Because of security constraints, the transfer capabilities of transmission systems are limited; thus, transactions in electricity markets need to be evaluated and analyzed based on system security to ensure their operational feasibility. The cost associated with ensuring transaction operational feasibility is referred to as Transaction Security Cost (TSC), which is an important component of an unbundled transaction cost [1]. From an economic point of view, accurate costs provide the correct price signals to foster comparable service and fair competition, creating a stable market environment where profits can be generated. Hence, correct TSC information will help market operators determine fair locational prices and co-ordinate and manage transactions. The costs can be used as proper feedback signals from market operators to encourage market participants to make adequate decisions, which in turn can help maintain system security [2, 3]. Market participants could also take advantage of these signals to make competitive and profitable market decisions. Determining the costs associated with system security has been of great interest in power systems, especially under the framework of competitive electricity markets [4,, 6, 7]. In most of these references, Lagrange multipliers generated during optimization procedures are used to analyze the different cost components of power system operation and define Locational Marginal Prices (LMP) []. The idea of pricing security was first advanced in [9] by considering line flow constraints; contingency pricing was studied in [3], and the costs related to outages were analysed in reference [2]. However, in all these papers, rather conservative limits on the transmission system power flows and bus voltage magnitudes are typically used to somewhat represent system security. These limits are typically determined through off-line studies and by making fairly conservative assumptions to account for operating uncertainties. When some of these limits are reached, the system is considered to have a transmission congestion problem, and hence operating and price signals are generated to ensure the operational feasibility of potential transactions. Representing system security through the use of these limits may lead to incorrect price signals and may even compromise system security, as these limits most likely do not reflect the security margins for the actual operating conditions. Hence, in the present paper, an on-line technique based on voltage stability criteria is used to compute the actual system Available Transfer Capability (ATC), and thus better evaluate transmission congestion. Based on the assumption that ATC has been already maximized by properly changing system topology and the control settings of generators, FACTS devices, etc., the present paper proposes a probability-based technique to handle operational infeasible transactions, i.e., transactions that exceed the system s ATC. The probabilistic view proposed here consists on relaxing the operating limits considering that the system feasibility region is usually set conservatively [2, 3], and it is referred here as take-risk. This paper is structured as follows: In Section 2, ATC computational issues are briefly discussed from the point of view of voltage stability; transactions impact on ATC is also defined, so that total security costs can be distributed among these transactions. Section 3 describes in detail the basic ideas of the proposed take-risk TSC analysis method. In Section 4, a six-bus system example is used for illustration purpose. Finally, the main contributions are highlighted in Section, and possible future research directions are discussed. 2 ATC and Transaction Impact 2.1 ATC Computations ATC, as defined by NERC, is a measure of the transfer capability remaining in the physical transmission network for further commercial activity over and above already committed uses [10]. This is an important market signal indicating the capability of a transmission system to securely and reliably deliver energy. The value of ATC is determined by system security constraints, i.e., thermal limits, voltage limits and stability limits, taking into ac-

2 count possible system contingencies; as the system operating conditions change over time, the limiting factor can be either one of these limits. For large systems, stability limits tend to be the main limiting factor. In heavily loaded systems, voltage stability limits usually become dominant. The latter is typically the case in current market environments, as transmission systems are operating under more stressed conditions because of increased transaction levels associated with open access. In order to ensure secure system operation while making the most out of the existing transmission networks, the ATC computation must be accurately and quickly updated as system conditions change. In most of the current implementations of electricity markets, the ATC is determined in off-line studies, and represented in the bidding process as rather conservative limits on the power flowing though the transmission lines or main transmission corridors. This could easily lead to either fictitious congestion problems, or unsecured operating conditions. However, the proper computation of the ATC is a problem, as the actual determination of the stability limits requires costly time domain simulations. Hence, in this paper, the stability limits are approximately represented using voltage stability margins, which can be readily computed, giving a good idea of the relative stability of the network [11]. In this case, a bifurcation-based Continuation Power Flow (CPF) method is used for adequate and fast ATC computations [12], using the loading margin as an approximation of the ATC [13, 14, 1]. Thus, assume that the system can be represented using the set of non-linear equations (1) where represents the vector of system variables; stands for the loading margin, which is the amount of additional load increase the system can withstand before collapse; and represents the vector of transactions [16], which are controllable system parameters (all other controllable parameters are assumed to be already defined to maximize the system ATC). The ATC is then defined here as (2) which is readily computed using a CPF, considering a set of contingencies. 2.2 Transaction Impact on ATC Since voltage stability criteria is used to determine the ATC value, the sensitivities of the ATC with respect to various system parameters can then be readily determined [16]. Thus, transaction impact on ATC is defined here as the sensitivities of the ATC with respect to the given transactions, i.e.,, which show how the ATC is affected by transaction changes. At a system stable equilibrium point!", if there is a small transaction change, the system will move to another stable equilibrium point $ % & % %, where '(% & %!% )* (3) Using Taylor series expansion on (3), and neglecting higher order terms to simplify the problem, it follows that +-, ). -% +0/. 1% where +0, )., +0/. and +2 ). are the Jacobians of with respect to, and, respectively, at the equilibrium point $! 4!". The transactions impact on ATC can then be reasonably approximated as (4) () Based on ATC and voltage stability concepts, is either associated with a saddle-node bifurcation or system limits, if oscillatory stability problems are neglected [11]. Hence, the sensitivities of with respect to must be defined for each one of these cases Saddle-Node Bifurcations Saddle-Node Bifurcations (SNB) are characterized by a pair of equilibrium points coalescing and disappearing as the bifurcation parameter slowly changes [11]. At a SNB point, transaction changes can be analyzed using (4) as follows [16]: 67 +,. -% 67 + /. 1% 6) where 6 is the left eigenvector corresponding to the zero eigenvalue of the Jacobian +,. at the SNB point. Since 6 7 +, ). *, it follows from (6) that Limits 9 (6) ) / ). (7) The value of can also be affected by voltage/thermal limits or Limit-induced Bifurcations (LIB). LIBs are equilibrium points where a system control limit is reached, which in some cases may lead to a system collapse, and it is characterized by a jump on the eigenvalue of the steady-state Jacobian +, ). [11]. As opposed to a SNB, +,. is not singular at a limit or LIB; hence, equation (7) does not apply at this point. In general, a system reaches a limit can be characterized by two different set of nonlinear equations, i.e., :4 '4 ;4 '"* 4< '4 ;4 '"* () : >=? where, the first set of equations corresponds to the < =@ original system, whereas corresponds to a modified set of equations where the limit is active. Assuming that for a small transaction change, one has +, :. +0,4<C. A% A% + / :. +0/4<C. 1% + 2 :. 1% +24<D. B* B* (9)

3 : : Eliminating from (9) leads to 7 +-,4<D. +-, :. +2:. +24<D. " 7 (10) ψ 1 where +-/4<D. +0,4<D. +-, :. +-/:. (11) Observe that the sensitivity formula (10) applies to any limit condition, independent of whether it corresponds to a LIB or voltage/thermal limit. Thus, equation (7) and equation (10) are used to determine transaction impact on ATC, which can be used for rescheduling transactions when transmission congestion happens [17]; and is also used here to distribute total security cost among transactions. 3 Take-risk Strategy TSC is determined here by taking a probabilistic view of the ATC, since this value is usually calculated based on an (N-1) contingency criterion. Thus, by considering that there is a certain probability for contingencies to occur, one can take a risk by assuming that the contingencies may not actually occur and then determine a security cost associated with this risk. Under this strategy, the system may be loaded beyond its ATC value, which is referred here to as, up to the maximum loading value for the system without contingencies, which is referred to as. Hence, if transactions obtained from the bid-matching process fall within, they are feasible and accepted with no security cost. If transactions fall out of, they will be rejected. If transactions fall between and, they may be accepted and charged a security cost, with the operator taking a risk of losing the system due to a possible contingency. The total security cost,, is mainly quantified as the expected system collapse cost [2], i.e., 2 2 = (12) where is the system collapse cost, and represents the probability of system collapse. The higher the probability of collapse, the higher the total security cost. 2 To find out the corresponding security cost, can be estimated at using statistical data. The key part is then determining the probability of collapse, which is associated with the probability distribution of system collapse and the loading margins, i.e., and ; as the total transaction level approaches, the risk increases. Thus, the probability of system collapse can be expressed as (13) The function will vary for different markets. The approximate shape of is shown in Figure 1. 0 Ln Lc (ATC) (loading margin under normal conditions) Figure 1: Probability of system collapse for security cost analysis. The probability distribution function of system collapse is assumed here to be 7 / /! / " " $ % with the corresponding probability density function '& (*) %,+ 7 /.-0/ /! / - / " " T (14) (1) where 76 is a constant that is used to represent the probabilistic distribution of system collapse. For example, for the test system described in Section 4, ψ a= T MW Figure 2: Probability distribution of system collapse. When a=2 $, the probability of system collapse is : uniformly distributed on 9 (solid curves in Figure 2 and Figure 3). When <;, the probability : of system collapse is linearly distributed on 9 (dashed curves in Figure 2 and Figure 3). When <=, the probability of system collapse : is quadratically distributed on 9 (dot-dashed curves in Figure 2 and Figure 3). As becomes larger, the rate of change of probability of system collapse with respect to a small transaction in- a=3

4 crease gets larger as the transaction level hard limit. approaches the Bus 2 (GENCO 2) Bus 3 (GENCO 3) f Bus 6 (ESCO 3) 0.01 a=3 Bus 1 (GENCO 1) 0.01 a=1 a= Bus (ESCO 2) T MW Figure 3: Probabilistic density of system collapse. According to the transaction impact on ATC, the total security cost is then distributed to each transaction which has a negative impact on the ATC. Hence, one may define a Transaction Contribution Factor as = = (16) Bus 4 (ESCO 1) Figure 4: A six bus test system. Participants Quantity (MW) Bid price ($/MWh) GENCO GENCO 2 2. GENCO ESCO ESCO ESCO Table 1: Price-quantity bids where corresponds to the MW level of transaction. The parameter value is included in this normalization process to account for the level of the corresponding transaction in the security cost. Transactions that have positive impacts are given a zero TCF value, so that transactions that do not create the security problem are not charged for the cost of keeping the system secure. Then, the Transaction Security Cost for each transaction,, is defined as = (17) $/MWh ESCO 1 ESCO 2 GENCO 2 ESCO 3 GENCO 1 From (17), a LMP that accounts only for security costs based on the take-risk strategy proposed can be defined as 7 GENCO 3 where % for generators for loads represents the Market Clearing Price. 4 Example (1) The six bus system shown in Figure 4 [1], with three generation companies (GENCOs) that provide supply bids and three energy supply companies (ESCOs) that provide demand bids shown in Table 1, is used here to illustrate the proposed take-risk TSC analysis method. UWPFLOW is used for all the loading margin calculations [19] ATC 4 6 Figure : High-low bid matching with demand-side bidding. The simple auction method that consists of matching the highest buying bids with the lowest selling offers, as shown in Figure, is employed here to determine the MCP. The market is cleared at an. The potential transactions in this case are: GENCO 2 sells 2 MW, GENCO 3 sells 20 MW, ESCO 1 buys 2 MW, ESCO 2 buys 10 MW and ESCO 3 buys 10 MW. These potential transactions define the load and generation increase direction for the computations. In this case, =; =*=, - $, while, thus, security costs must be considered. By using the transaction impact analysis described in MW

5 7 7 9 Section 2, the generation impacts are determined to be : < and load impacts are / / : 9 7 (19) $ : 7 (20) The corresponding TCFs are shown in Table 2. Transaction (i) GENCO 2 (2) GENCO 3 (3) 0 ESCO 1 (4) 0.4 ESCO 2 () ESCO 3 (6) Table 2: Transaction Contribution Factors Based on the assumption that the average direct interruption cost of system load is $10/kWh [2, 4, 20], 2 is then assumed to be $ =; $ h for the total system load of =*; MW. The total security costs for different probability distribution functions are shown in Table 3. The larger the value of, the lower the assumed risk of ; ) to facilitate more transactions. The corresponding TSCs and LMPs are shown in Table '; 4 for two risk levels; observe that for a low risk level ( ), the LMP differences are large, as expected, these reflect the rather conservative security margins associated with low values of. Transaction ( ) ($/h) ($/MWh) ($/h) ($/MWh) GENCO 2 (2) GENCO 3 (3) ESCO 1 (4) ESCO 2 () ESCO 3 (6) Table 4: Transaction Security Costs system collapse for a given transaction level, and hence the lower the security cost associated with the transactions. ($/h) $ $ ; = $ $ ; $ $ ; $ $ Table 3: Total Security cost for different probabilistic distribution functions In this example, if is chosen to be less than 4, the TSC will be very high due to high collapse costs and high assumed risks of collapse. One would expect that in competitive electricity markets with reliable transmission systems, a large value of could be chosen (e.g., Conclusions This paper presents a new TSC analysis method based on a take-risk strategy that relies on a probabilistic point of view of the ATC. Adequate on-line ATC and transaction impact computation techniques are proposed to better evaluate transmission congestion, and to generate proper operational and price signals for the market participants. Test results indicate that the proposed take-risk TSC analysis method is efficient and transparent, and can be easily integrated in simple auction market structures. However, the method still needs to be tested in more realistic applications. Furthermore, a more detailed probabilistic analysis could be used to determine the actual values of the risk level, based on the history of system contingencies. Nevertheless, an operator may be able to use the proposed probability distribution functions with a risk level consistent with the operational knowledge of the system. REFERENCES [1] L. Willis, J. Finney and G. Ramon, Computing the Cost of Unbundled Services, IEEE Computer Applications in Power, Vol. 9, No. 4, pp , October [2] F. Alvarado, Y. Hu, D. Ray, R. Stevenson and E. Cashman, Engineering Foundations for the Determination of Security Costs, IEEE Transactions on Power Systems, Vol. 6, No. 3, pp , August [3] R. J. Kaye, F. F. Wu and P. Varaiya, Pricing for System Security, IEEE Transactions on Power Systems, Vol. 10, No. 2, pp. 7 3, May 199. [4] G. Strbac, S. Ahmed, D. Kirschen and R. Allan, A Method for Computing the Value of Corrective Security, IEEE Trans. on Power Systems, Vol. 13, No. 3, pp , August 199. [] O. Moya, Model for Security of Service Costing in Electric Transmission Systems, IEE Proc.- Generation, Transmission, and Distribution, Vol. 144, No. 6, pp , November [6] A. Jayantilal and G. Strbac, Load Control Services in the Management of Power System Security Costs, IEE Proc.- Generation, Transmission and Distribution, Vol. 146, No. 3, pp , May [7] T. J. Overbye, D. R. Hale, T. Leckey and J. D. Weber, Assessment of Transmission Constraint Costs: Northeast U.S. Case Study, Proceeding of IEEE Winter Meeting, Singapore, January [] K. Xie, Y. H. Song, J. Stonham, E. Yu, and G. Liu, Decomposition Model and Interior Point Methods for Optimal Spot Pricing of Electricity in Deregulation Environments, IEEE Transactions on Power Systems, Vol. 1, No. 1, pp. 39 0, February [9] F. C. Schweppe, W. C. Caramanis, R. D. Tabors, and R. E. Bohn, Spot Pricing of Electricity, Kluwer Academic Publisher, 19. [10] NERC, Available Transfer Capability Definitions and Determination. NERC, USA, 1996.

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