Estimation of Time-Varying Harmonic Impedance Using Probability Distribution-Based Approach

In previous studies, harmonic impedance estimation was typically assumed to be a constant value. However, due to the randomness of renewable energy and the time-varying nature of control strategies in modern power systems, this assumption is no longer valid. Therefore, this paper presents an approach for estimating time-varying harmonic impedance (TVHI). First, a relational equation for TVHI estimation is formulated based on the harmonic voltage and current at the point of common coupling. Then, TVHI is represented as a polynomial function, and an optimization model for its estimation is developed considering the probabilistic distribution characteristics of the equivalent harmonic voltage. Next, a hybrid optimization algorithm, integrating the butterfly optimization algorithm and particle swarm optimization, is utilized to solve the optimization model, determining the polynomial coefficients and the polynomial function of TVHI. Finally, the accuracy of the TVHI estimation method is validated using standard test cases on the CloudPSS platform.