A New Solution for Stochastic Optimal Power Flow: Combining Limit Relaxation with Iterative Learning Control

- Journal title : Journal of Electrical Engineering and Technology
- Volume 9, Issue 1, 2014, pp.80-89
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/JEET.2014.9.1.080

Title & Authors

A New Solution for Stochastic Optimal Power Flow: Combining Limit Relaxation with Iterative Learning Control

Gong, Jinxia; Xie, Da; Jiang, Chuanwen; Zhang, Yanchi;

Gong, Jinxia; Xie, Da; Jiang, Chuanwen; Zhang, Yanchi;

Abstract

A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

Keywords

Chance constrained programming;Iterative learning control;Stochastic optimal power flow;Wind power;

Language

English

References

1.

Shoults, R.R.; Sun, D.T., "Optimal Power Flow Based Upon P-Q Decomposition," IEEE Trans. Power App. Syst., vol. PAS-101, no. 2, pp. 397-405, Feb., 1982.

2.

Yu-chi Wu; Debs, A.S.; Marsten, R.E., "A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows," IEEE Trans. Power Syst., vol. 9, no. 2, pp. 876-883, May, 1994.

3.

Taiyou Yong, and Lasseter, R.H. "Stochastic optimal power flow: formulation and solution," in Proc. 2000 IEEE Power Engineering Society Summer Meeting., pp. 237-242, July, 2000.

4.

SCHELL ENBERG A. "Probabilistic and stochastic optimal power flow," Ph.D. dissertation, Dept. of Electrical and Computer Engineering, Alberta, Canada: University of Calgary, 2006.

5.

H. Zhang, and P. Li, "Probabilistic analysis for optimal power flow under uncertainty," IET Gen., Transm., Distrib., vol. 4, no. 5, pp. 553-561, May 2010.

6.

Schellenberg, A., Rosehart, W., and Aguado, J. "Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions," IEEE Trans. Power Syst., vol. 20, no.2, pp. 773-781, May, 2005.

7.

G. Verbic and C. A. Canizares, "Probabilistic optimal power flow in electricity markets based on a two-point estimate method," IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1883-1893, Nov. 2006.

8.

KIMBALL L M, CL EMENTS K A, PAJ IC S, et al. "Stochastic OPF by constraint relaxation," in Proc. 2002 IEEE Power Technology Conference, Vol. 4, Jun 23-26, 2003, Bologna, Italy.

9.

A. Charnes and W.W. Cooper, "Chance-constrained programming," Manage. Sci., vol. 6, no. 1, pp.73-79, Oct.1959.

10.

H. Yu, C. Y. Chung, K. P. Wong, and J. H. Zhang, "A chance constrained transmission network expansion planning method with consideration of load and wind farm uncertainties," IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1568-1576, Aug. 2009.

11.

U. A. Ozturk, M. Mazumdar, and B. A. Norman, "A solution to the stochastic unit commitment problem using chance constrained programming," IEEE Trans. Power Syst., vol. 19, no. 3, pp. 1589-1598, Aug.2004.

12.

Y. Xiao, Y. H. Song, and Y. Z. Sun, "A hybrid stochastic approach to available transfer capability evaluation," Proc. Inst. Elect. Eng., Gen., Transm, Distrib, vol. 148, no. 5, pp. 420-426, Sep. 2001.

13.

Hui Zhang, and Pu Li, "Chance Constrained Programming for Optimal Power Flow under Uncertainty," IEEE Trans. Power Syst., vol. 26, no.4, pp. 2417-2424, Nov., 2011.

14.

Wang, Shuang, Yang, Hongming, and Zuo, Shuang; "Optimal Dispatch of Power System with Stochastic Wind Generation," advances in engineering design and optimization, vol. 37-38, pp. 783-786, Nov., 2011.

15.

Qianfan Wang, Yongpei Guan, and Jianhui Wang; "A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment with Uncertain Wind Power Output," IEEE Trans. Power Syst., vol. 27, no. 1, pp. 206-215, Feb., 2012.

16.

Zhipeng Liu, Fushuan Wen, and Ledwich, G. "Optimal Siting and Sizing of Distributed Generators in Distribution Systems Considering Uncertainties," IEEE Trans. Power Delivery, vol. 26, no.4, pp. 2541-2551, Oct., 2011.

17.

Z. Hu and X. Wang. "Stochastic Optimal Power Flow Approach Considering Load Probabilistic Distributions", Automation of Electric Power Systems, 2007, 31,(16), pp. 14-17 & 44, 2007.

18.

Bukkems, B.; Kostic, D.; de Jager, B.; Steinbuch, M., "Learning-based identification and iterative learning control of direct-drive robots," IEEE T CONTR SYST T, vol. 13 , no. 4, pp.537-549, July, 2005.

19.

Amjady, N., Keynia, F., and Zareipour, H. "Wind Power Prediction by a New Forecast Engine Composed of Modified Hybrid Neural Network and Enhanced Particle Swarm Optimization," IEEE Transactions on Sustainable Energy, vol. 2, no. 3, pp. 265-276, July, 2011.

20.

MA Lei, LUAN Shiyan, and JIANG Chuanwen. "A review on the forecasting of wind speed and generated power," Renewable and Sustainable Energy Reviews, vol. 13, no. 4, pp. 915-920, May, 2009.

21.

Bludszuweit, H., Dominguez-Navarro, J.A., and Llombart, A. "Statistical Analysis of Wind Power Forecast Error," IEEE Trans. Power Syst., vol. 23, no. 3, pp. 983-991, Aug., 2008.

22.

Fabbri, A., GomezSanRoman, T., RivierAbbad, J., et al, "Assessment of the Cost Associated with Wind Generation Prediction Errors in a Liberalized Electricity Market," IEEE Trans. Power Syst., vol. 20, no. 3, pp. 1440-1446, Aug., 2005.

23.

Tewari, S.; Geyer, C.J.; Mohan, N. "A Statistical Model for Wind Power Forecast Error and its Application to the Estimation of Penalties in Liberalized Markets," IEEE Trans. Power Syst., vol. 26, no.4, pp. 2031-2039, Nov., 2011.

24.

X. Li, Y. Li, and S. Zhang, "Analysis of probabilistic optimal power flow taking account of the variation of load power," IEEE Trans. Power Syst., vol. 23, no. 3, pp. 992-999, Aug. 2008.

25.

The advanced theory of statistics, vol.1 2ed 1945 Kendall M.G. 466s

26.

Ruiz-Rodriguez, F. J.; Hernandez, J. C.; Jurado, F., "Probabilistic load flow for photovoltaic distributed generation using the Cornish-Fisher expansion," ELECTRIC POWER SYSTEMS RESEARCH, vol.89, pp. 129-138, Aug., 2012.

27.

Tan, Kok-Kiong Kiong ; Zhao, Shao ; Xu, Jian-Xin Xin, "Online automatic tuning of a proportional integral derivative controller based on an iterative learning control approach," Control Theory & Applications, IET, 2007, 1 , (1) , pp. 90-96.

28.

Shen, D. ; Mu, Y., and Xiong, G., "Iterative learning control for non-linear systems with deadzone input and time delay in presence of measurement noise," Control Theory & Applications, IET, 2011, 5 (12), pp. 1418-1425.

29.

An Luo, Xianyong Xu, Lu Fang, et al; "Feedback-Feedforward PI-Type Iterative Learning Control Strategy for Hybrid Active Power Filter With Injection Circuit," IEEE Transactions on Industrial Electronics, 2010, 57, (11), pp. 3767-3779.