Probability distributions of outputs of stochastic economic dispatch

•A method to carry the uncertainty of wind speed for optimal S-ED problem presented.•The algorithm provides estimates of PDFs of the outputs of the S-ED problem.•The outputs are optimal PDFs of fossil fuel outputs, losses, and total power cost.•The outputs are used to perform many useful statistical analyses for decision-making.

This paper introduces an approach to carry the uncertainty about the wind speed through the optimization for the economic dispatching. This approach uses simulated wind speed data points for inputs to economic dispatch models and produces data for estimating the probability distributions of optimal fossil fuel generation outputs, transmission loss, and total cost of power generation. Large samples of simulated data allow statistical analyses of the outputs such as the mean, median, percentiles, and confidence intervals for each output variable, plots of distributions of all output variables, and correlation measures for examining relationships between pairs of the output variables. Through the proposed algorithm, a generation expansion planner can perform useful analyses without executing the algorithm repeatedly. The algorithm and its results are illustrated through an example of an economic dispatch model and a model for the distribution of the wind speed based on a forecast for the planning target time.