Моделирование Феррорезонансных Режимов В Нелинейных Электрических Цепях С Учетом Магнитного Гистерезиса

Abstract

The article provides a solution to the problem of numerical simulation of the resonant modes of voltages and cur-rents in electrical circuits arising from the serial and parallel connection of nonlinear inductive and capacitive elements. The Weber-ampere characteristic of the inductive element is set taking into account the hysteresis. Fer-roresonance modes arise in electrical circuits containing capacitive and nonlinear inductive elements, including power transformers, arc-extinguishing reactors, current and voltage measuring transformers, electric motors. The nonlinearity of the characteristics of inductive elements is the reason that when their magnetic systems are saturated, differential inductances change, resulting in ferroresonance, often abnormal and even emergency modes. A modified inverse Jiles-Atherton model is used to simulate magnetic hysteresis. Numerical integration of differential equations describing dynamic processes in electrical circuits is performed by the explicit Euler meth-od. As a result of the calculations performed, it is shown that as a result of ferroresonance, a trigger effect oc-curs, which manifests itself in the form of an abrupt change in the state of the circuit caused by the ambiguous nature of the volt-ampere characteristic for the input voltage and current. The proposed method of modeling transient and steady-state modes in nonlinear electrical circuits, taking into account magnetic hysteresis, can be generalized to the case of arbitrary circuits, including those with complex topology.