Probabilistic power flow calculation in asymmetric, unbalanced and distorted distribution networks

In this paper, the procedure for calculating power flows in three-phase asymmetric and unbalanced distribution networks with nonlinear loads and sources is presented. Due to the stochastic nature of the power generated from renewable energy sources (RESs), such as photovoltaic (PV) and wind turbine (WT) systems, as well as load power uncertainties, the power flow problem is treated as a probabilistic problem and solved using the Monte Carlo Simulation (MCS) method. The MCS method consists of applying a mathematical model by assigning probability density functions (PDFs) to the input stochastic variables and simulating PDFs of the model’s output variables of interest, thereby performing a large number of iterations. To model the input random variables - wind speed, solar irradiance, and load power, Weibull, beta, and normal probability distributions are used, respectively. The calculation of the harmonic voltage and current components is performed using the decoupled harmonic power flow (DHPF) algorithm which is adapted to the unbalanced and asymmetrical conditions. The MCS method is tested on the standard IEEE 13-bus network, where the typical harmonic spectrums of converter currents are used.