An Improved Analytical Methodology for Joint Distribution in Probabilistic Load Flow

Abstract

This paper presents a novel analytical method based on improved Gaussian mixture model (GMM) to solve the probabilistic load flow problem. The proposed method accounts for the uncertainty introduced due to increasing percentages of renewable generation. First, the joint probability density function of several wind farms outputs is derived by using the improved GMM with the estimated parameters obtained by genetic algorithm (GA) in this paper, which could improve the accuracy of the probabilistic model. Next, the analytical expressions between the output power of wind farms and line power of power system are deduced by linearizing load flow equations. And, the joint probability density function and joint cumulative distribution function of line power are obtained from linear load equation and joint probability density function of wind output power. Finally, the proposed method, Monte Carlo simulation (MCS) and traditional GMM based methods are all tested on a modified IEEE 39-bus system and a modified IEEE 118-bus system with multiple wind farms, which demonstrates the feasibility of the proposed method.

Keywords

• gaussian mixture model
• maximum likelihood estimation
• genetic algorithm
• density function
• distribution