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Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties

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  • Chen, J.J.
  • Wu, Q.H.
  • Zhang, L.L.
  • Wu, P.Z.

Abstract

This paper presents a multi-objective mean–variance–skewness (MVS) model for reliably assessing the problem of nonconvex and stochastic optimal power flow (NSOPF), considering valve-point effect, stochastic load and uncertain integrated wind power. The MVS model aims to maximize both the expected return and skewness while simultaneously minimizing the risk, which is formulated as a competing and conflicting three-objective optimization problem. Based on such a model, we propose a multi-objective optimization algorithm, multiple preys based evolutionary predator and prey strategy (MPEPPS), to provide Pareto solutions, which show the trade-off relationship among the expected return, the skewness and the risk of the dispatching objective. Subsequently, a multi-criteria decision making method, the technique for order preference by similarity to an ideal solution (TOPSIS), is applied for determining the final dispatch solution. The objective of this paper is to develop a reliable model to assess the NSOPF from the perspective of economics and reliability of power system operation, and propose an efficient algorithm to obtain a solution that considers all of the possible load and wind power simultaneously. Simulation results based on a modified IEEE 30-bus power system demonstrate the reliability and effectiveness of the MVS and MPEPPS in solving NSOPF.

Suggested Citation

  • Chen, J.J. & Wu, Q.H. & Zhang, L.L. & Wu, P.Z., 2017. "Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties," European Journal of Operational Research, Elsevier, vol. 263(2), pages 719-732.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:719-732
    DOI: 10.1016/j.ejor.2017.06.018
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    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Zhao, Zhiwei & Yang, Jingming & Hu, Ziyu & Che, Haijun, 2016. "A differential evolution algorithm with self-adaptive strategy and control parameters based on symmetric Latin hypercube design for unconstrained optimization problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 30-45.
    3. Anthony Papavasiliou & Shmuel S. Oren, 2013. "Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network," Operations Research, INFORMS, vol. 61(3), pages 578-592, June.
    4. Wang, Ligang & Yang, Yongping & Dong, Changqing & Morosuk, Tatiana & Tsatsaronis, George, 2014. "Multi-objective optimization of coal-fired power plants using differential evolution," Applied Energy, Elsevier, vol. 115(C), pages 254-264.
    5. Gotoh, Jun-ya & Takano, Yuichi, 2007. "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Elsevier, vol. 179(1), pages 80-96, May.
    6. Elberg, Christina & Hagspiel, Simeon, 2015. "Spatial dependencies of wind power and interrelations with spot price dynamics," European Journal of Operational Research, Elsevier, vol. 241(1), pages 260-272.
    7. Lin, Yashen & Johnson, Jeremiah X. & Mathieu, Johanna L., 2016. "Emissions impacts of using energy storage for power system reserves," Applied Energy, Elsevier, vol. 168(C), pages 444-456.
    8. Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
    9. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    10. Joshi, Deepa & Kumar, Sanjay, 2016. "Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(1), pages 183-191.
    11. Ruiz, C. & Conejo, A.J., 2015. "Robust transmission expansion planning," European Journal of Operational Research, Elsevier, vol. 242(2), pages 390-401.
    12. Zhao, M. & Chen, Z. & Blaabjerg, F., 2006. "Probabilistic capacity of a grid connected wind farm based on optimization method," Renewable Energy, Elsevier, vol. 31(13), pages 2171-2187.
    13. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    14. Bahmani-Firouzi, Bahman & Farjah, Ebrahim & Azizipanah-Abarghooee, Rasoul, 2013. "An efficient scenario-based and fuzzy self-adaptive learning particle swarm optimization approach for dynamic economic emission dispatch considering load and wind power uncertainties," Energy, Elsevier, vol. 50(C), pages 232-244.
    15. Li, Y.Z. & Wu, Q.H. & Li, M.S. & Zhan, J.P., 2014. "Mean-variance model for power system economic dispatch with wind power integrated," Energy, Elsevier, vol. 72(C), pages 510-520.
    16. Mohandes, M. & Rehman, S. & Rahman, S.M., 2011. "Estimation of wind speed profile using adaptive neuro-fuzzy inference system (ANFIS)," Applied Energy, Elsevier, vol. 88(11), pages 4024-4032.
    17. Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    18. Yang, Jian-Bo, 2001. "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties," European Journal of Operational Research, Elsevier, vol. 131(1), pages 31-61, May.
    19. Chen, Kuilin & Yu, Jie, 2014. "Short-term wind speed prediction using an unscented Kalman filter based state-space support vector regression approach," Applied Energy, Elsevier, vol. 113(C), pages 690-705.
    20. Ji, Bin & Yuan, Xiaohui & Chen, Zhihuan & Tian, Hao, 2014. "Improved gravitational search algorithm for unit commitment considering uncertainty of wind power," Energy, Elsevier, vol. 67(C), pages 52-62.
    21. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    22. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    23. Zhang, Junlong & Lam, William H.K. & Chen, Bi Yu, 2016. "On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows," European Journal of Operational Research, Elsevier, vol. 249(1), pages 144-154.
    24. Chronopoulos, Michail & Lumbreras, Sara, 2017. "Optimal regime switching under risk aversion and uncertainty," European Journal of Operational Research, Elsevier, vol. 256(2), pages 543-555.
    25. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    26. Joro, Tarja & Na, Paul, 2006. "Portfolio performance evaluation in a mean-variance-skewness framework," European Journal of Operational Research, Elsevier, vol. 175(1), pages 446-461, November.
    27. Zheng, J.H. & Chen, J.J. & Wu, Q.H. & Jing, Z.X., 2015. "Multi-objective optimization and decision making for power dispatch of a large-scale integrated energy system with distributed DHCs embedded," Applied Energy, Elsevier, vol. 154(C), pages 369-379.
    28. PAPAVASILIOU, Anthony & OREN, Schmuel S., 2013. "Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network," LIDAM Reprints CORE 2500, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. Bruno, Sergio & Ahmed, Shabbir & Shapiro, Alexander & Street, Alexandre, 2016. "Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 250(3), pages 979-989.
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