An Enhanced Markov Chain Monte Carlo-Integrated Cross-Entropy Method with a Partially Collapsed Gibbs Sampler for Probabilistic Spinning Reserve Adequacy Evaluation of Generating Systems

Abstract

Probabilistic adequacy evaluation of allocated spinning reserve is beneficial to economically regulating this foremost auxiliary service to counterbalance unforeseen generation-demand mismatches. As the time horizon for a probabilistic spinning reserve adequacy investigation task may vary from several to dozens of minutes, adaptive importance sampling methods, such as the classical cross-entropy method and its variants, are appealing instead of the classical non-sequential Monte Carlo to estimate desired reliability indices due to the rareness of demand-not-supplied contingencies. In this article, a new adaptive cross-entropy method is proposed, particularly, nesting a specially optimized partially collapsed Gibbs sampler to help in avoidance of locally trapped Markov chain samples which may be encountered by traditional cross-entropy methods. RTS-79 is utilized for illustrating the superiority of the proposed method, termed E-MICEM, against its parent method, i.e., the Markov chain Monte Carlo-integrated cross-entropy method. Two traditional indices including loss of load probability and expected demand not supplied are comparatively evaluated and the simulation results suggest that the E-MICEM is superior in the efficiency of estimating the two indices. Some advices are also given on the build-in-parameter regulation for the E-MICEM applicable to the systems of different dimensions.

Keywords::

• spinning reserve
• cross-entropy
• Markov chain Monte Carlo
• partially collapsed Gibbs
• generating systems

Acknowledgments

The author would like to thank the support in part by National Natural Science Foundation of China (Project No. 51507177), and by Chinese Universities Scientific Fund (Project No. 1081-15055173), and by Visiting Scholarship of State Key Laboratory of Power Transmission Equipment & System Security and New Technology (Chongqing University) (2007DA10512716419).

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Yue Wang

Yue Wang received the B.S. degree in automation form the School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, China in 2005, the M.S degree in electrical engineering from the Huazhong University of Sience and Technology, Wuhan, China in 2007 and the Ph.D. degree in electrical engineering from the College of Electrical Engineering, Zhejiang University, Hangzhou, China in 2014. His industrial experience is with Jinhua Electric Power Transmission and Transformation Ltd. from 2007 to 2010. He is now a faculty with the College of Information and Electrical Engineering, China Agricultural University, Beijing, China. His research interests include power system risk assessment and power system operation security and reliability.