Three-Phase Probabilistic Power Flow Calculation Method Based on Improved Semi-Invariant Method for Low-Voltage Network

Power flow analysis of low-voltage network (LVN) is one of the most crucial methods for achieving refined management of such networks. To accurately calculate the three-phase (TP) probabilistic power flow (PPF) distribution in LVN, this paper first draws on the injection-type Newton method; by leveraging TP power measurements relative to the neutral point obtained from smart meters, the injected power is expressed in terms of injected current equations, thereby establishing TP power flow models for various components within the low-voltage distribution transformer area grid. Subsequently, addressing the stochastic fluctuation models of load power and photovoltaic output, this paper employs conventional numerical methods and an improved Latin hypercube sampling technique. Utilizing linearized power flow equations and based on the improved semi-invariant method (SIM) and Gram–Charlier (GC) series fitting, a calculation method for three-phase PPF in low-voltage distribution transformer area grids using the improved semi-invariant is proposed. Finally, simulations of the proposed three-phase PPF method are conducted using the IEEE-13 node distribution system. The simulation results demonstrate that the proposed method can effectively perform three-phase PPF calculations for the distribution transformer area grid and accurately obtain probabilistic distribution information of the TP power flow within the grid.