# Voltage stability constrained OPF market models considering N 1 contingency criteria

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6 32 F. Milano et al. / Electric Power Systems Research 74 (2005) Table 1 6-Bus test system: OPF with off-line power flow limits Participant V (p.u.) LMP (\$/MW h) NCP (\$/MW h) P BID (MW) P 0 (MW) Pay (\$/h) GENCO GENCO GENCO ESCO ESCO ESCO Total T = 243.5MW Pay IMO = 464 \$/h Losses = 6.2 MW SATC = 0.3 MW Table 2 6-Bus test system: VSC-OPF without contingencies (λ cmin = 0.1) Participant V (p.u.) LMP (\$/MW h) NCP (\$/MW h) P BID (MW) P 0 (MW) Pay (\$/h) GENCO GENCO GENCO ESCO ESCO ESCO Total T = 274.4MW Pay IMO = 43.9 \$/h Losses = 8.25 MW SATC = 19.1 MW Table 3 shows the coefficients p ij used for the sensitivity analysis as well as the SATCs computed by means of the continuation power flows technique for the two steps required by the iterative method described in Section 3.1 when applying an N 1 contingency criterion. Observe that both methods lead to similar conclusions, i.e. the sensitivity analysis indicates that the line 2 4 has the highest impact in the system power flows, while the N 1 contingency criteria show that the outage of line 2 4 leads to the lowest SATC values. Table 4 depicts the final VSC-OPF results for the critical line 2 4 outage. This solution presents practically the same total transaction level as provided by the solution without contingencies in Table 3, but with different demand side bidding, and a higher SATC, as expected, since the system is now optimized for the given critical contingency. Observe that the rescheduling of demand bids results also in slightly lower LMPs and NCPs, as a consequence of including more Table 3 6-Bus test system: sensitivity coefficients p ij and SATC determined applying an N 1 contingency criterion for two iterations (λ cmin = 0.1) Line i j P ij (p.u.) p ij SATC 1 (MW) SATC 2 (MW) precise security constraints, which in turn results in a lower Pay IMO value with respect to the one obtained with the standard OPF problem (1) in Table 1 (the higher losses are due the transaction level being higher). The SATC in Table 4 corresponds to a λ cmin = 0.1, i.e. 10% of the total transaction level T, indicating that the current solution has the minimum required security level (λ c = λ cmin = 0.1). For the sake of comparison, Table 5 depicts the final solution obtained with a different inferior limit for the loading parameter, i.e. λ cmin = In this case, the line outage that creates the worst congestion problem is determined to be line 1 4. As expected, the higher minimum security margin leads to a lower T and, with respect to results reported in Table 4, also LMPs and NCPs are generally lower, which is due to the lower level of congestion of the current solution. Observe that a more secure solution leads to lower costs, because the demand model is assumed to be elastic; hence, higher stability margins lead to less congested, i.e. lower T, and cheaper optimal solutions. In this example, the OPF technique does not reach a solution for λ cmin > 0.15, which means that a solution with at least 15% of security margin is not feasible when taking in account an N 1 contingency criterion. Notice that it is not reasonable to set high values for λ cmin, since the resulting security margin already takes into account the most severe contingency, and is thus a conservative estimation of the system stability level Bus Italian HV transmission system Fig. 3 depicts the complete 129-bus 400 kv Italian transmission grid which is used here in order to discuss a more

7 F. Milano et al. / Electric Power Systems Research 74 (2005) Table 4 6-Bus test system: VSC-OPF with contingency on line 2 4 (λ cmin = 0.1) Participant V (p.u.) LMP (\$/MW h) NCP (\$/MW h) P BID (MW) P 0 (MW) Pay (\$/h) GENCO GENCO GENCO ESCO ESCO ESCO Total T = 274.3MW Pay IMO = 43.4 \$/h Losses = 8.31 MW SATC = 27.4 MW Fig Bus Italian 400 kv transmission system (most of this information is publicly available at the GRTN web site

8 34 F. Milano et al. / Electric Power Systems Research 74 (2005) Table 5 6-Bus test system: VSC-OPF with contingency on line 1 4 (λ cmin = 0.125) Participant V (p.u.) LMP (\$/MW h) NCP (\$/MW h) P BID (MW) P 0 (MW) Pay (\$/h) GENCO GENCO GENCO ESCO ESCO ESCO Total T = MW Pay IMO = 38.9 \$/h Losses = 4.52 MW SATC = 33.6 MW Table 6 Comparison of different OPF-based methods for the Italian system example OPF method Critical contingency T (GW) SATC (GW) Losses (MW) Pay GRTN (\$/MW h) OPF (1) Off-line power flows VSC-OPF (2) None Iterative VSC-OPF Turbigo-Bovisio VSC-OPF with sensitivity analysis Turbigo-Baggio realistic test case and to better test the proposed techniques. It has been assumed that 32 generators and 82 consumers participate in the market auction. Usually, Italy imports about the 10% of its power demand from France and Switzerland, hence power supply bids were assumed at the interties. All bids were based on prices around US\$/MW h, which are the average prices over the last few years in other European countries where electricity markets are currently in operation, and it also considers actual operating costs of thermal plants (55% of the electrical energy produced in Italy is thermal). Power bid levels were chosen to be about 30% of the average consumption in order to force system congestion. All system data and security constraints, i.e. voltage limits, generation reactive power limits and transmission line thermal limits, were provided by CESI, the Italian electrical research center. Table 6 depicts the total results for different OPF problem solutions, i.e. the standard OPF with off-line power transfer limits, the VSC-OPF without contingencies and the final results obtained with the proposed techniques for including the worst contingency, which was determined to be the outage of lines in the Milano area (buses Turbigo, Bovisio and Baggio) by both the N 1 contingency criterion and the sensitivity analysis. Conclusions similar to what is observed for the 6- bus example can be drawn, i.e. the proposed techniques yield a higher total transmission level T and a better SATC value, while reducing the payment to the Italian independent market operator GRTN (Gestore Rete Trasmissione Nazionale). Observe that the iterative method and the sensitivity-based technique yield two different critical lines, but provide practically identical results, as the two lines are in the same critical area, i.e. Milano. (The security constrained OPF solutions of (2) show a total loss increase, since the transaction level also increases.) Fig. 4 depicts the comparison of LMPs and NCPs obtained with the standard and the VSC-OPF for an outage of the Turbigo-Baggio line, confirming that a proper representation of voltage stability constraints and worst-case contingency result in a better distribution of costs (LMPs) and in a reduced impact of system congestion on electricity prices (NCPs). 5. Conclusions Fig. 4. Comparison between LMPs and NCPs obtained with the standard and the VSC-OPF with contingency on the Turbigo-Baggio line for the Italian system example. In this paper, two methods for including contingencies in a VSC-OPF-based market are proposed and tested on a simple test system as well as on a realistic network. Comparisons between the results obtained with the proposed techniques and those obtained by means of a standard OPF-based market

10 36 F. Milano et al. / Electric Power Systems Research 74 (2005) [16] C.A. Cañizares, H. Chen, W. Rosehart, Pricing system security in electricity markets, Proceedings of the Bulk Power Systems Dynamics and Control-V, Onomichi, Japan, [17] H. Chen, Security cost analysis in electricity markets based on voltage security criteria and web-based implementation, Ph.D. thesis, University of Waterloo, Waterloo, ON, Canada, [18] K. Xie, Y.-H. Song, J. Stonham, E. Yu, G. Liu, Decomposition model and interior point methods for optimal spot pricing of electricity in deregulation environments, IEEE Trans. Power Syst. 15 (1) (2000) [19] B.S. Gisin, M.V. Obessis, J.V. Mitsche, Practical methods for transfer limit analysis in the power industry deregulated environment, Proceedings of the PICA IEEE International Conference, 1999, pp [20] C.A. Cañizares (Ed.), Voltage Stability Assessment: Concepts, Practices and Tools, Technical Report, IEEE/PES Power System Stability Subcommittee, SP101PSS, August [21] W. Rosehart, C.A. Cañizares, V.H. Quintana, Multi-objective optimal power flows to evaluate voltage security costs, IEEE Trans. Power Syst. 18 (2) (2003) [22] Available transfer capability definition and determination, Technical Report, NERC, USA, [23] C.A. Cañizares, Z.T. Faur, Analysis of SVC and TCSC controllers in voltage collapse, IEEE Trans. Power Syst. 14 (1) (1999) [24] C. A. Cañizares, M. Pozzi, FACTS controllers performance and influence on voltage control in the presence of secondary voltage regulation, Technical Report, CESI, RETE-A0/021456, Milan, Italy, June 2000, 66 pp. [25] V.H. Quintana, G.L. Torres, Introduction to interior-point methods, IEEE PICA, Santa Clara, CA, [26] G.B. Sheblé, Computational Auction Mechanism for Restructured Power Industry Operation, Kluwer Academic Publishers, Boston, 1998.

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