Method for the Analysis of Three-Phase Networks Containing Nonlinear Circuit Elements in View of an Efficient Power Flow Computation

The present paper is devoted to applying the Hănțilă method for solving nonlinear three-phase circuits characterized by different reactance values on the three sequences (positive, negative and zero). Nonlinear elements, which are components of the circuit, are substituted by real voltage or current sources, whose values are an iteratively corrected function of the voltage across or the current through them, respectively. The analysis is carried out in the frequency domain and facilitates an easy evaluation of the power transfer on each harmonic. The paper presents numerical implementations of the method for two case studies. For validation, the results are compared against those obtained using the software LTspice in the time domain. Finally, the power flow on the harmonics and the overall power balance are analyzed.

Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.