Mathematical Simulation of Modes and Characteristics of Asynchronous Motors under Asymmetrical Power Supply

The purpose of this article is to develop a method and algorithm for the calculation of the steady-state mode and static characteristics of the squirrel-cage asynchronous motors that are supplied by a three-phase network with an asymmetrical voltage system. The aim is achieved by developing a method where the mathematical model of the motor takes into account the saturation of the magnetic core and the current displacement in the short-circuited rotor bars. Magnetization characteristics of the main magnetic flux and the leakage fluxes paths are used to account for the saturation. To account for the current displacement in the rotor winding the bars are divided into several layers throughout the height, resulting in a number of windings on the rotor with mutual inductive couplings. In the mathematical model, the processes in the asynchronous motor are described by a system of the nonlinear differential equations of electromagnetic equilibrium, composed in the fixed three-phase coordinate axes. The solution of this system in the steady-state mode is the periodic dependence of the currents, which are determined by solving the boundary problem. For this purpose, their algebraization is carried out by approximation of the periodic dependences at the nodes’ grid of the period of repeatability of the process by the third order splines. The solution of the problem is to determine the nodal values of coordinates on the period from the obtained nonlinear system of algebraic equations. For this purpose, the continuation method and iterative refinement by the Newton method were used. Calculation of the static characteristics was performed by the differential method