A Bivariate Chance Constraint of Wind Sources for Multi-Objective Dispatching
- 1 Electrical Power and Machine Department, Faculty of Engineering, Cairo University, Cairo, Egypt.
- 2 Electrical Power and Machine Department, Faculty of Engineering, Cairo University, Cairo, Egypt.
- 3 Electrical Power and Machine Department, Faculty of Engineering, Cairo University, Cairo, Egypt.
Abstract
The economic emission dispatch (EED) problem minimizes two competing objective functions, fuel cost and emission, while satisfying several equality and inequality constraints. Since the availability of wind power (WP) is highly dependent on the weather conditions, the inclusion of a significant amount of WP into EED will result in additional constraints to accommodate the intermittent nature of the output. In this paper, a new correlated bivariate Weibull probability distribution model is proposed to analytically remove the assumption that the total WP is characterized by a single random variable. This probability distribution is used as chance constraint. The inclusion of the probability distribution of stochastic WP in the EED problem is defined as the here-and-now strategy. Non-dominated sorting genetic algorithm built in MATLAB is used to handle the EED problem as a multi-objective optimization problem. A 69-bus ten-unit test system with non-smooth cost function is used to test the effectiveness of the proposed model.
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- P. Zhang and S. T. Lee, “Probabilistic Load Flow Computation Using the Method of Combined Cumulants and Gram-Charlier Expansion,” IEEE Transactions on Power Systems, Vol. 19, No. 1, 2004, pp. 676-682. doi:10.1109/TPWRS.2003.818743
- A. Schellenberg, W. Rosehart and J. Aguado, “CumulantBased Probabilistic Optimal Power Flow (P-OPF) with Gaussian and Gamma Distributions,” IEEE Transactions on Power Systems, Vol. 20, No. 2, 2005, pp. 773-781. doi:10.1109/TPWRS.2005.846184
- A. Schellenberg, W. Rosehart and J. Aguado, “Introduction to Cumulant-Based Probabilistic Optimal Power Flow (P-OPF),” IEEE Transactions on Power Systems, Vol. 20, No. 2, 2005, pp. 1184-1186. doi:10.1109/TPWRS.2005.846188
- D. Villanueva, A. Feijóo and J. Luis Pazos, “Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power,” Smart Grid and Renewable Energy, Vol. 2, No. 1, 2011, pp. 12-20. doi:10.4236/sgre.2011.21002
- Q. Fu, D. C. Yu and J. Ghorai, “Probabilistic Load Flow Analysis for Power Systems with Multi-correlated Wind Source,” Power and Energy Society General Meeting, San Diego, 24-29 July 2011, pp. 1-6. doi:10.1109/PES.2011.6038992
- H. Yang and B. Zou, “The Point Estimate Method Using Third-Order Polynomial Normal Transformation Technique to Solve Probabilistic Power Flow With Correlated Wind Source and Load,” Asia-Pacific Power and Energy Engineering Conference (APPEEC), Shanghai, 27-29 March 2012, pp. 1-4. doi:10.1109/APPEEC.2012.6307479
- X. Liu, “Economic Load Dispatch Constrained by Wind Power Availability: A Wait-and-See Approach,” IEEE Transactions on Smart Grid, Vol. 1, No. 3, 2010, pp. 347355. dio:10.1109/TSG.2010.2057458
- X. Liu and W. Xu, “Economic Load Dispatch Constrained by WP Availability: A Here-and-Now Approach,” IEEE Transactions on Sustainable Energy, Vol. 1, No. 1, 2010, pp. 2-9. doi:10.1109/TSTE.2010.2044817
- J. Hetzer and D. C. Yu, “An Economic Dispatch Model Incorporating Wind Power,” IEEE Transactions on Energy Conversion, Vol. 23, No. 2, 2008, pp. 603-611. doi:10.1109/TEC.2007.914171
- D. Villanueva, A. Feijóo and J. Pazos, “Simulation of Correlated Wind Speed Data for Economic Dispatch Evaluation,” IEEE Transactions on Sustainable Energy, Vol. 3, No. 1, 2012, pp. 142-149. doi:10.1109/TSTE.2011.2165861
- Y. Fang, D. Zhao, M. Ke, X. Zhao, C. Herbert and K. Wong, “Quantum-Inspired Particle Swarm Optimization for Power System Operations Considering Wind Power Uncertainty and Carbon Tax in Australia,” IEEE Transactions on Industrial Informatics, Vol. 8, No. 4, 2012, pp. 880-888. doi:10.1109/TII.2012.2210431