Decomposed Newton algorithm-based three-phase power-flow for unbalanced radial distribution networks with distributed energy resources and electric vehicle demands

This paper proposes a three-phase power-flow algorithm using graph theory, injected current, and matrix decomposition techniques for unbalanced radial distribution networks. A decomposed Newton-Raphson (DNR) method is applied to solve the set of nonlinear power equations described in polar form. Unlike conventional Newton-Raphson-based methods, the proposed DNR algorithm does not involve calculating the lower and upper triangular matrix (LU) factorization, Gaussian elimination, and inversion of the full bus admittance matrix or Jacobian matrix and building the bus impedance matrix; it also requires less computation time and has high robustness with respect to the X/R ratio and load changes. The mathematical component models, such as three-phase conductors, transformers, automatic voltage regulators (AVRs), ZIP load demands, shunt capacitors/reactors, inverter-based distributed energy resources (DERs) and electric vehicle (EV) demands can easily be integrated into the proposed algorithm by using the injected current technique. Therefore, a three-phase power-flow problem can be decomposed into three single-phase power-flow problems with individual phase representation. To validate the performance and effectiveness of the proposed algorithm, four three-phase IEEE test systems and a practical Taiwan Power Company (Taipower) distribution system are used for comparisons. The results reveal that the proposed algorithm has good potential for improving the computational efficiency of optimal planning and design and also real-time power dispatch applications, even for ill-conditioned distribution networks.