Probability Density Assessment of Voltage Sag Based on Hamiltonian Monte Carlo Method

In this paper, a method for evaluating the probability density of voltage sags based on Hamiltonian Monte Carlo (HMC) is proposed, which realizes a more accurate and reliable evaluation of the probability distribution of voltage sag events. Firstly, by introducing the Hamiltonian equation of motion, the evolution of voltage sag events affected by uncertain factors is regarded as a Hamiltonian system, and the probability of voltage sags in a bounded domain under random disturbance is solved. Secondly, taking Poisson distribution as the target probability density distribution, Bayesian inference is used to estimate the function parameters, and a large number of data with common distribution characteristics are generated from a small number of original voltage sag observation data, which solves the problem of insufficient data samples. Finally, the simulation analysis of IEEE 24 bus system and IEEE 1772 bus system verifies that the HMC method has a higher acceptance rate. The probability density distribution of the proposed method and the original data is compared, and the correctness and effectiveness of the proposed method are verified.