Probabilistic load flow calculation by using probability density evolution method

This paper presents a novel framework methodology based on the probability density evolution method (PDEM) for solving the probabilistic load flow (PLF) problem. By leveraging a constructed visual stochastic process, the joint probability density evolution equation of a system statement and random inputs is derived based on the principle of preservation of probability. The probability density function of the system statement can then be numerically solved by means of a TVD-based difference scheme. The proposed method is validated through case studies in which the active power and reactive power consumptions of buses are assumed to obey a normal distribution and Weibull distribution, respectively. The cumulative probability functions of the voltage magnitudes of buses and active power branches are computed using the PDEM with 100 samples. The mean, standard deviation, skewness, and kurtosis are also examined. The comparison to Monte Carlo of 10,000 simulations demonstrates the accuracy and efficiency of the proposed approach and verifies its suitability to solve the PLF problem.