Abstract
Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load, load connection, transformer, and distributed generation (DG) are presented. A three-phase power flow formulation is described for both power and current mismatch functions. Extended versions of the Newton power flow method are compared with the backward-forward sweep-based algorithm. Furthermore, the convergence behavior for different loading conditions, R / X ratios, and load models, is investigated by numerical experiments on balanced and unbalanced distribution networks. On the basis of these experiments, we conclude that two versions using the current mismatch function in polar and Cartesian coordinates perform the best for both balanced and unbalanced distribution networks.
Highlights
The electrical power system is one of the most complex system types built by engineers [1].Traditionally, electricity was generated by a small number of large bulk power plants that use coal, oil, or nuclear fission and was delivered to consumers through the power system in a one-way direction.Due to the modernization of the existing grid, a large number of new grid elements and functions including smart meters, smart appliances, renewable energy resources, and storage devices are being integrated into the grid
Newton power flow (NR)-c-pol and NR-c-car versions were more stable for the changes and they can be applied to any unbalanced distribution networks with high R/X ratios and loading conditions
The Newton power flow method and its six possible versions are introduced for three-phase power flow problems
Summary
The electrical power system is one of the most complex system types built by engineers [1]. There are conventional power flow solution techniques for transmission networks, such as Gauss–Seidel (GS), Newton power flow (NR), and fast decoupled load flow (FDLF) [7,8,9] which are widely used for power system operation, control and planning These conventional power flow methods do not always converge when they are applied to the distribution power flow problem due to some special features of the distribution network:. Compared to existing versions of the Newton power flow method, our versions use different equations for PV buses in the Jacobian matrix that result in better convergence and robust performance We present how these versions can be applied to unbalanced distribution networks by studying loads, three-phase load connections, three-phase transformers, and DGs. This paper is structured as follows.
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