Development of Differential Equations and their Solution Using the Simulink Matlab Program, which Calculate the Self-Swinging of Synchronous Machines with Traditional and Longitudinal-Transverse Excitation

Olimjon Toirov,Utkir Mirkhonov,Аllabergan Bekishev,Sardor Urakov,N Voropai,A Michalevich,S Senderov,H Guliev

doi:10.1051/e3sconf/202021601116

Abstract

The article presents the differential equations of a synchronous generator in phase coordinates and in the coordinate system (d, q). In addition, differential equations of synchronous machines with longitudinal-transverse excitation and a block diagram based on these equations are given. The system of differential equations is solved by the operator method. On the basis of a system of differential equations using the Simulink Matlab program, a structural diagram was created and a graph of the self-swinging processes taking place in synchronous machines with conventional and longitudinal-transverse excitation was obtained. On the basis of the obtained graph, the processes of self-swinging of synchronous generators with traditional and longitudinal and transverse excitation are compared.

Highlights

The relevance of the topic lies in the fact that the determination of the static and dynamic stability of synchronous generators of medium and high power in laboratory conditions using these generators requires a lot of money and time
The static and dynamic stability of synchronous generators with longitudinal-transverse excitation is a poorly studied area, and the study of this area is useful for studying the stability of generators by developing differential equations for synchronous generators with biaxial excitation
When we use a synchronous machine with biaxial excitation, it will give us the opportunity to control the direction of the magnetic flux vector, increase the static and dynamic stability of the machine and more effectively dampen the vibration of the rotor under alternating and shock loads [7]

Summary

Introduction

The relevance of the topic lies in the fact that the determination of the static and dynamic stability of synchronous generators of medium and high power in laboratory conditions using these generators requires a lot of money and time. The development of biaxial synchronous generators with magnetic axis control and their use in power plants is currently underway [8,9]. When we use a synchronous machine with biaxial excitation, it will give us the opportunity to control the direction of the magnetic flux vector, increase the static and dynamic stability of the machine and more effectively dampen the vibration of the rotor under alternating and shock loads [7]. The aim of the work is to study the effect of an additional excitation coil on the transverse axis on the self-swinging processes of synchronous machines with longitudinaltransverse excitation using a mathematical model and comparison with the self-swinging processes of a traditional synchronous generator

Construction of mathematical equations for traditional synchronous machines

Conclusion