Analysis of the electrical system mode based on the solution of the boundary value problem

by

A.M. Oleinikov1, L.N. Kanov2

1Institute of Natural and Technical Systems, RF, Sevastopol, Lenin St., 28

 E—mail: oma091041@gmail.com

2.Sevastopol State University, RF, Sevastopol, Universitetskaya St., 33

DOI: 10.33075/2220-5861-2026-1-139-146

UDC 620.92                

EDN: https://elibrary.ru/lcruxg

Abstract:   

A mathematical model of an electric power system is substantiated, taking into account the distributed parameters of a long cable line, dynamic load and the application of modern provisions of sensitivity theory to solve boundary-value problems, which makes it possible to build an effective numerical algorithm for applying gradient methods. The possibility of numerical simulation of a system mode consisting of a synchronous generator loaded through a long transmission line, step-up and step-down transformers to an asynchronous motor based on analytical approximation of the dependence of specific parameters of the line on the distance along the length is demonstrated. Electromagnetic processes in the line under sinusoidal voltage conditions are described by complex differential equations, separating the real and imaginary parts. An algorithm for solving a boundary value problem for the model equations is described, and an example and calculation results for a typical operation are provided. Overall, the feasibility of solving complex steady-state analysis problems using gradient methods is demonstrated. These methods are more efficient than commonly used methods of directly searching for the optimal operation mode. A promising area of research is the further development of a method for calculating branched and closed systems for voltage regulation under varying loads, as well as the possibility of voltage regulation directly by the excitation current of a synchronous generator.

Keywords: electroenergy system, synchronous generator, asynchronous engine, transformer, areas of distributive line, up-diffused parameters, complex tension, current, loading, regional tasks

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