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.

A general framework is given for applying the Newton-Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton-Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ) buses and generator (PV) buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.

Steady-state power flow models are essential for daily operation of the electricity grid. The changing electrical environment requires a shift from separated power flow models to integrated transmission-distribution power flow models. Integrated models incorporate the coupling of the networks and the interaction that they have on each other, representing the power flow within this changing environment accurately. In this paper we conduct a comparison study on the numerical performance of methods that solve the integrated power flow problem. The methods of study can be divided into unified or splitting methods. In addition, the integrated networks can be modeled as homogeneous or as hybrid networks. Our study shows that the methods have several advantages and disadvantages, but that unified methods in combination with hybrid network models have the best numerical performance. Splitting methods running on hybrid network models have an advantage when full network data sharing between system operators is not allowed.

In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are validated by comparing it with the Newton power flow algorithm and a commercial network design tool Vision on various distribution networks including real network data. Results show that our method can be as accurate as classical Nonlinear Power Flow (NPF) methods using a constant power load model and additionally, it is much faster than NPF computations. In our research, it is shown that voltage problems can be identified more efficiently when MV and LV are integrally evaluated. Moreover, Numerical Analysis (NA) techniques are applied to the Large Linear Power Flow (LLPF) problem with 27 million nonzeros in order to improve the computation time by studying the properties of the linear system. Finally, the original computation times of LLPF problems with real and complex components are reduced by 2.8 times and 5.7 times, respectively.Energies 2019, 12, 4078 2 of 15 distribution network, such as radial or weakly meshed structure, high R/X ratio, line's length and unbalanced loads. Many methods [6-9] have been developed on distribution power flow analysis and the most of them are based on the Backward-Forward Sweep (BFS) algorithm. Several reviews on distribution power flow solution methods can be found in References [10][11][12].All iterative power flow solution methods use a direct solver eventually for the linearized NPF problem in every iteration. It has been shown that iterative linear solvers can result in faster performances over sparse direct solvers for very large power flow problems [13][14][15]. In other words, the computational time of NPF computations can be improved by studying the properties of the linear system solved in every iteration and applying Numerical Analysis (NA) techniques such as different reordering schemes, various direct solvers and numerous Krylov subspace methods on them.Another way to ease the calculation and to speed up the computational time is to linearize NPF equations using some approximations and assumptions in order to obtain the Linear Power Flow (LPF) equations. After the linearization, the resulting LPF equations can be computed only once by direct solvers. Therefore, LPF computations are generally faster than NPF computations and are more suitable to be applied on very large networks with millions of cables for real time simulation. The best-known example of the LPF problem is the DC load flow [16] where linear relations are determined between the active power injections P and the voltage angles δ and the reactive power injections Q and the deviations of the unknown voltage magnitudes ∆|V|. Furthermore, the linear power flow formulation is obtained based on a voltage dependent (ZI) load model and some numerical approximations on the imaginary part of the nodal voltages in Reference [17]. Another linear power flow model based ...

No abstract