A Complex-Valued Three-Phase Load Flow for Radial Networks: High-Performance and Low-Voltage Solution Capability

Abstract

Load flow methods for distribution networks, such as backward forward sweep (BFS) have a good computational performance and can find solutions with accuracy. However, some studies may demand the determination of low voltage solutions, and this poses a problem for these methods since they cannot find these solutions due to convergence issues. This paper presents a load flow method based on a novel complex-valued formulation developed for distribution networks, which works well on radial topologies by using an incidence matrix to avoid complicated series element models, allow high-performance and low-voltage solution capability. The formulation is solved by Newton's method via Wirtinger's calculus. To prove the low-voltage solution capability, both sides of QV curves, i.e., unstable and stable regions were traced on balanced and unbalanced networks. Performance tests in the IEEE test feeders show that the runtime is less than or equal to the runtime of the BFS method. Furthermore, the line R/X ratio and the number of controlled voltage node or volt-var functions do not affect the computational performance, yielding advantages over the classic Newton and BFS methods.