A Bivariate Chance Constraint of Wind Sources for Multi-Objective Dispatching

Copyright © 2013 Mostafa Elshahed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 de-pendent on the weather conditions, the inclusion of a significant amount of WP into EED will result in additional con-straints to accommodate the intermittent nature of the output. In this paper, a new correlated bivariate Weibull probabil-ity 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