Three-phase probabilistic load flow in radial and meshed distribution networks

With the introduction of higher levels of renewables and demand response programs, traditional deterministic power system tools fall short of expectations. Probabilistic load flow (PLF) takes into account the inconsistency or the unknown loads, and generation in the fundamental load flow analysis. This study proposes a PLF solution for both balanced and unbalanced, radial and weakly meshed networks without explicitly using the Y-bus matrix. It allows for discrete probability density functions as input variables without having to assume a predefined distribution. The nodal voltages and the power flows can be calculated independently from one another. The proposed method is applied to the IEEE 123 Node Test Feeder and the IEEE 13 Node Test Feeder in both its original radial configuration and a modified mesh configuration, including a load replaced with a wind turbine. The results are validated by comparison of the proposed method's solutions to those obtained using cumulants and Monte Carlo simulation. The proposed PLF method provides an accurate and practical way for finding the solution to stochastic problems occurring in power distribution systems allowing for real-system data to be analysed.