A Matrix-Inversion-Free Fixed-Point Method for Distributed Power Flow Analysis

The power flow (PF) problem is a fundamental problem in power system engineering. Many popular solvers like PF and optimal PF (OPF) face challenges, such as divergence and network information sharing between multi-areas. One can try to rewrite the PF problem into a fixed point (FP) equation (more stable), which can be solved exponentially fast. But, existing FP methods are not distributed and also have unrealistic assumptions such as requiring a specific network topology. While preserving its stable nature, a novel FP equation that is distributed in nature is proposed to calculate the voltage at each bus. This distributed computation enables the proposed algorithm to compute the voltages for multi-area networks without sharing private topology information. Unlike existing distributed methods, the proposed method does not use any approximate network equivalents to represent the neighboring area. Thus, it is approximation-free, and it also finds use cases in distributed AC OPFs. We compare the performance of our FP algorithm with state-of-the-art methods, showing that the proposed method can correctly find the solutions when other methods cannot, due to high condition number matrices. In addition, we empirically show that the FP algorithm is more robust to bad initialization points than the existing methods.