The Generalized Cross-Entropy Method in Probabilistic Optimal Power Flow

This paper presents a new powerful density estimator and the application of the generalized cross-entropy method. A framework for probability density function estimation of the probabilistic optimal power flow problem results is presented. Large-scale probabilistic problems have a lot of uncertain parameters, some of which are correlated. Most of the existing methods for probabilistic power system analysis have a large computational burden or rely on asymptotic approximation to mitigate the computational burden, which reduces the precision level. Others that depend on the uncertainties are not applicable in large-scale problems and do not provide precise results in small cases. Compared to conventional methods, the proposed method has several advantages in probabilistic analysis. Reducing the computational burden while maintaining high level of accuracy is one of them. The proposed method can deal with correlated problems. This method is tested on some valid and conventional networks containing renewable energy resources, nonstationary loads, and their correlations. The results are compared against more accurate results obtained from Monte Carlo simulation, which demonstrate the high level of accuracy according to the error indices. Results confirm the high capacity of the proposed method in accuracy and speed response compared to other methods.