Power Flow in Unbalanced Three-Phase Power Distribution Networks Using Matlab: Theory, analysis, and quasi-dynamic simulation

Context: The power flow is a classical problem for analyzing and operating power distribution net-works. It is a challenging problem due to a large number of nodes, the high r/x ratio-typical in low voltage networks-and the unbalanced nature of the load.Method: This paper review four methods for power flow analysis, namely: the conventional Newton's method, Newton's method in a complex domain, the fixed-point algorithm using Ybus representation, and the backward-forward sweep algorithm. It is well-known that Newton's method has quadratic convergence, whereas the backward-forward sweep algorithm has linear convergence. However, the formal analysis of this convergence rate is less known in the engineering literature. Thus, the convergence of these methods is presented in theory and practice.Results: A set of simulations in the IEEE 900 node test system is presented. This system is large enough to demonstrate the performance of each algorithm. In addition, a Matlab toolbox is presented for making numerical simulations both for the static case and for quasi-dynamic simulations.Conclusions: Fixed point algorithms were faster than Newton's methods. However, the latter required less number of iterations.