Spinning reserve plays an important role in balancing generation and demand mismatch within a short time interval. Probabilistic spinning reserve adequacy evaluation (PSRAE) is useful to aid operators in monitoring the adequacy of system upward spinning reserve exposed to unforeseen disturbances and making risk-adverse decisions for unit dispatching. As a short time period, for example, 30 s–15 min, is usually considered in PSRAE, the generating system in question is commonly of high reliability, which renders naive non-sequential Monte Carlo methods inefficient. In this study, the high reliability phenomenon of generating systems is explained through a toy case study, thereafter, aiming to develop an efficient method for PSRAE, a simulation method based on the cross-entropy which has been widely applied in many areas to improve naive Monte Carlo methods for tackling rare-event simulation issues, integrated with Markov chain Monte Carlo is proposed. The indices of loss of load probability and expected demand not supplied are used to quantify the spinning reserve inadequacy risk. Through case studies conducted on the RTS-79, usefulness of the PSRAE is discussed and the proposed method is proven to be superior to the classical cross-entropy method and thus could be taken as a candidate tool for the PSRAE to practical systems.

References

1. 1)
  - 11. Khatir, A.A., Cherkaoui, R., Zima, M.: ‘Literature survey on fundamental issues of frequency control reserve (FCR) provision’. Swiss Electric Research, 2010.
2. 2)
  - 12. Rubinstein, R.Y., Kroese, D.P.: ‘The cross-entropy method. A unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning’ (Springer, New York, NY, USA, 2004).
3. 3)
  - R. Billinton , R. Karki . Capacity reserve assessment using system well-being analysis. IEEE Trans. Power Syst. , 2 , 433 - 439
4. 4)
  - 10. Abiri-Jahromi, A., Fotuhi-Firuzabad, M., Abbasi, E.: ‘Optimal scheduling of spinning reserve based on well-being model’, IEEE Trans. Power Syst., 2007, 22, (4), pp. 2048–2057 (doi: 10.1109/TPWRS.2007.907378).
5. 5)
  - 2. Billinton, R., Wangdee, W.: ‘Aleatory uncertainty in power system reliability index assessment’. Advances in Risk and Reliability Technology Symp., 2013, pp. 356.
6. 6)
  - 19. Rubinstein, R.Y., Glynn, P.W.: ‘How to deal with the curse of dimensionality of likelihood ratios in Monte Carlo simulation’, Stochastic Models, 2009, 25, (4), pp. 547–568 (doi: 10.1080/15326340903291248).
7. 7)
  - 8. Khan, M.E., Billinton, R.: ‘Composite system spinning reserve assessment in interconnected systems’, IEE Proc., Gener. Transm. Distrib., 1995, 142, (3), pp. 305–309 (doi: 10.1049/ip-gtd:19951716).
8. 8)
  - 23. Stadlin, W.O.: ‘Economic allocation of regulating margin’. IEEE Paper 71 TP99-PWR, Nov. 1970.
9. 9)
  - 26. Robert, C.P., Casella, G.: ‘Monte Carlo statistical methods: Citeseer’ (Springer, New York, 2004).
10. 10)
  - 1. McDonald, J.D.F.: ‘Reliability of future distribution networks: Handling variability and uncertainty’. Power and Energy Society General Meeting, 2012, pp. 1–5.
11. 11)
  - 22. Chan, J.C.C., Kroese, D.P.: ‘Improved cross-entropy method for estimation’, Stat. Comput., 2012, 22, (5), pp. 1031–1040 (doi: 10.1007/s11222-011-9275-7).
12. 12)
  - 6. Billinton, R., Fotuhi-Firuzabad, M.: ‘Reserve capacity assessment in small isolated electric power generating systems’, Power Eng. J., 1996, 10, (2), pp. 73–80 (doi: 10.1049/pe:19960206).
13. 13)
  - 25. Li, Y.F., Zio, E., Lin, Y.H.: ‘Methods of solutions of inhomogeneous continuous time Markov chains for degradation process modeling’, Appl. Reliab. Eng. Risk Anal., Probab. Models Stat. Inference, 2013, pp. 3–16 (doi: 10.1002/9781118701881.ch1).
14. 14)
  - 15. Carvalho, L., González-Fernández, R.A., Leite da Silva, A., et al: ‘Simplified cross-entropy based approach for generating capacity reliability assessment’, IEEE Trans. Power Syst., 2012, 28, (2), pp. 1609–1616 (doi: 10.1109/TPWRS.2012.2213618).
15. 15)
  - 18. Wang, Y., Guo, C.X., Wu, Q.H., Dong, S.F.: ‘Adaptive sequential importance sampling technique for short-term composite power system adequacy evaluation’, IET Gener. Transm. Distrib., 2014, 8, (4), pp. 730–741 (doi: 10.1049/iet-gtd.2013.0279).
16. 16)
  - L.T. Anstine , R.E. Burke , J.E. Casey , R. Holgate , R.S. John , H.G. Stewart . Application of probability methods to the determination of spinning reserve requirements for the Pennsylvania – New Jersey-Maryland interconnection. IEEE Trans. Power Appl. Syst. , 68 , 726 - 735
17. 17)
  - 21. Dai, H.Z., Zhang, H., Wang, W.: ‘A support vector density-based importance sampling for reliability assessment’, Reliab. Eng. Syst. Safety, 2012, 106, pp. 86–93 (doi: 10.1016/j.ress.2012.04.011).
18. 18)
  - 16. González-Fernández, R.A., Leite da Silva, A.M., Resende, L.C., Schilling, M.T.: ‘Composite systems reliability evaluation based on Monte Carlo simulation and cross-entropy methods’, IEEE Trans. Power Syst., 2013, 28, (4), pp. 4598–4606 (doi: 10.1109/TPWRS.2013.2267154).
19. 19)
  - 13. da Silva, A.M.L., Fernandez, R.A.G., Singh, C.: ‘Generating capacity reliability evaluation based on Monte Carlo simulation and cross-entropy methods’, IEEE Trans. Power Syst., 2010, 25, (1), pp. 129–137 (doi: 10.1109/TPWRS.2009.2036710).
20. 20)
  - 17. Gonzalez-Fernandez, R.A., Leite da Silva, A.M.: ‘Reliability assessment of time-dependent systems via sequential cross-entropy Monte Carlo simulation’, IEEE Trans. Power Syst., 2011, 26, (4), pp. 2381–2389 (doi: 10.1109/TPWRS.2011.2112785).
21. 21)
  - 27. Rubinstein, R.Y.: ‘Simulation and Monte Carlo method’ (John Wiley & Sons, New York, 1981).
22. 22)
  - 4. Billinton, R., Allan, R.N.: ‘Reliability evaluation of power systems’ (Plenum, New York, 1996).
23. 23)
  - 24. Billinton, R., Allan, R.N.: ‘Reliability evaluation of engineering systems: concepts and techniques’ (Plenum, New York, 1992).
24. 24)
  - 17. Wang, Y., Guo, C.X., Wu, Q.H.: ‘A cross-entropy-based three-stage sequential importance sampling for composite power system short-term reliability evaluation’, IEEE Trans. Power Syst., 2013, 28, (4), pp. 4254–4263 (doi: 10.1109/TPWRS.2013.2276001).
25. 25)
  - 5. Thapar, O.D., Chauhan, R.C.: ‘Optimum evaluation of spinning reserve in a power system’, Irrigation Power, 1977, 34, (4), pp. 441–446.
26. 26)
  - 28. Frunt, J., Kling, W.L., van den Bosch, P.P.J.: ‘Classification and quantification of reserve requirements for balancing’, Electr. Power Syst. Res., 2010, 80, (12), pp. 1528–1534 (doi: 10.1016/j.epsr.2010.06.018).
27. 27)
  - 20. Kurtz, N., Song, J.: ‘Cross-entropy-based adaptive importance sampling using Gaussian mixture’, Struct. Safety, 2013, 42, pp. 35–44 (doi: 10.1016/j.strusafe.2013.01.006).
28. 28)
  - M. Fotuhi-Firuzabad , R. Billinton , S. Aboreshaid . Spinning reserve allocation using response healthy analysis. IEE Proc., Gener. Transm. Distrib. , 4 , 337 - 343

Probabilistic spinning reserve adequacy evaluation for generating systems using an Markov chain Monte Carlo-integrated cross-entropy method

References

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