Математична модель визначення екстремальної за напругою точки в дальній лінії електропередачі змінного струму

Abstract

The paper presents the results of the study of the voltage regime at intermediate points of the long-distance AC power line. Mathematical models of distribution of reactive power and voltage profile along the actual and idealized line are presented. A method and mathematical models for determining the coordinates of the extreme points of the flow section by reactive power and voltage along the line route are proposed. It is proposed to use mathematical models of linearized power transmission, as well as more detailed models of the second and third order to determine the coordinates of the extreme point on the voltage along the power transmission. It is shown that the increase of accuracy of calculations can be reached in case of application of mathematical models of the second and third order. Increasing the detail of modeling causes an increase in the accuracy of the model, but is associated with an increase in the cumbersomeness of the mathematical model, and the application of the third-order model generally requires the involvement of complex numbers to implement appropriate calculations. The influence on the accuracy of calculation of the coordinate of the extreme point of the magnitude of the active and reactive load, as well as the loss of active power during the corona discharge is investigated. The possibility of application of the offered models in problems of regulation and adjustment of parameters of flexible power transmissions on the basis of lines of ultrahigh nominal voltage is shown. Thus, for typical designs of main power transmission systems of the UES of Ukraine, sufficient accuracy of calculations is provided by first- and second-order models, and only for ultra-long power transmission lines it is expedient to use a third-order mathematical model.