Mathematical Model of Electromagnetic Processes at Switching on the Power Transformer of the Power Supply System of the Agro-Industrial Complex at Idle Run

At present, the majority of agricultural electricity consumers are supplied from united power systems through networks that are also designed to supply electricity to industrial enterprises, cities, and electrified railway transport. An important element of rural power networks are power transformers of different voltage classes. Many transformer substations in rural power networks operate under difficult conditions and abnormal modes: overloads, operation in underloaded or unbalanced mode, and other emergency and near-emergency modes. To ensure the reliable operation of transformers when designing relay protection against overload currents, internal and external short circuits, and other faults of power transformers and supply lines, it is necessary to take into account the inrush currents when switching on the transformer at idle. The inrush currents at switching are caused by the nonlinearity of the magnetization curve of the ferromagnetic core of the transformer, linking its primary and secondary circuits. The mathematical model of electromagnetic processes in the transformer during its idle switching on includes differential equations of equilibrium of the primary electrical circuit. Transients in an electric circuit with a nonlinear ferromagnetic core are considered on the example of connecting a two-winding transformer in the no-load mode to a sinusoidal supply voltage. The transient mode of transformer connection is considered without taking into account losses in steel and taking these losses into account. The program for calculating the transient process when switching on the transformer at idle without taking into account losses and taking into account losses in steel is made using differential equations in matrix form and in Cauchy form. The methodology presented in the article allows for an accurate analysis of the transient process during transformer idle switching, to take into account the arising magnetizing current surges, their duration, and on the basis of this data to develop technical measures to reduce the negative consequences of these phenomena.