Improved Gaussian Mixture Model Based Probabilistic Power Flow of Wind Integrated Power System

This paper presents a novel analytical method based on an 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, which the deterministic load flow calculation method does not consider. First, the joint probabilistic density function of correlated wind power sources is derived by using the improved GMM. Because the expectation maximization (EM) algorithm tends to converge to the local optimum in the modeling process, the parameter to be estimated is obtained by genetic algorithm (GA) in this paper, which improves overall accuracy of the model. Next, the linear expressions between injected power and line power are deduced by linearizing load flow equations. Finally, the joint probability density function and joint distribution function of line power is obtained from joint probability density function of injected power. The results obtained using the proposed method and Monte Carlo simulation (MCS) on the modified IEEE 9-bus system demonstrate that the proposed method gives better accuracy with less time than MCS.