Objective PDF-Shaping-Based Economic Dispatch for Power Systems with Intermittent Generation Sources via Simultaneous Mean and Variance Minimization∗

With the ever increased penetration of renewables in power grid, economic power dispatch faces a challenge in terms of minimizing the generation cost which is increasingly affected by random factors and constraints subjected to random inputs. In this context, the cost functions are random for which the widely used mean value based minimization can only achieve limited profit gain. Indeed, as the probability density function (PDF) is a comprehensive measure of characteristics of any random variables, the desired optimization should address the shaping of the PDF of the generation cost function rather just its mean value. Through a simple case study, this paper firstly reveals the long tail PDF shape of the cost function when the traditional mean-value based optimization is used. This is then followed by the development of a novel PDF-shaping-based method that optimizes both the mean and variance of the PDF of the cost function. It has been shown that the proposed approach can reshape the PDF of the generation cost function so as to make it as left and as narrow as possible, leading to a significant low risk for high generation cost. Generic PDF shaping based optimization in [22] has also been described. Simulation tests have been included to show the effectiveness of the proposed approach and encouraging results have been obtained.