Stochastic chance constraint with discrete probabilities of wind sources in economic dispatch

In this paper, wind power (WP) modelling is improved in Economic Dispatch (ED). These proposed models are more realistic, practical, and accurate models. Hence the proposed models minimize the risk due to uncertainty. The stochastic probability of stochastic WP based on the Weibull probability density function is included in the ED model as a stochastic chance constraint; the here-and-now strategy. This strategy avoids the probabilistic infeasibility of the Wait-and-See strategy. The correlated bivariate distribution including continuous and discrete probabilities has been derived to be used as stochastic chance constraint. As the correlated bivariate Weibull distribution is very complex and difficult mathematically and is limited to two random variables (RVs) only, the correlated Normal distribution has been proposed to model wind sources especially for more than two random variables. The Augmented Lagrangian Genetic Algorithm has been used to obtain the optimal solutions. Ten unit test system has been used to illustrate the effectiveness of the proposed models. Based on presented models, it is shown that, the results obtained provide direct guidelines for system operators to make correct decisions to schedule the power systems with wind power. It can be concluded that the proposed models provide valuable information and suggestions for safe, reliable, and economic power systems operation.