A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach

A power system with large integration of renewable energy based generations is inherently associated with different types of uncertainties. In such cases, probabilistic load flow is a vital tool for delivering comprehensive information for power system planning and operation. Efforts have been made in this paper to perform a critical review on different probabilistic load flow models, uncertainty characterization and uncertainty handling methods, since from its inspection in 1974. An efficient analytical method named multivariate-Gaussian mixture approximation is proposed for precise estimation of probabilistic load flow results. The proposed method considers the uncertainties pertaining to photovoltaic generations and load demands. At the same time, it effectively incorporates multiple input correlations. In order to examine the performance of the proposed method, modified IEEE 118-bus test system is taken into consideration and results are compared with univariate-Gaussian mixture approximation, series expansion based cumulant methods and Monte Carlo simulation. Effect of various correlation cases on distribution of result variables is also studied. The effectiveness of the proposed method is justified in terms of accuracy and execution time.