Probabilistic three-phase power flow in a distribution system applying the pseudo-inverse and cumulant method

A new, analytical approach using the cumulant method is proposed for the three-phase probabilistic power-flow (PPF) analysis. The approach to forming the sensitivity matrix is based on quantifying the pseudo-inverse instead of the inverse jacobian matrix, since it is commonly singular in a distribution power network. The results are compared with those obtained using the point-estimate method (PEM) and the Monte Carlo (MC) method, which is a commonly used reference method for the PPF analysis in a distribution power network.