A Discreet Mathematical Model Based on the Bilinear Transformation of a Synchronous Electric Machine with a Turn-to-Turn Fault in the Rotor Winding

V. I. Polishchuk, V. V. Timoshkin, A. S. Glazyrin, E. V. Bolovin

Research output: Contribution to journalArticle

Abstract

Abstract: A number of requirements are imposed upon the group of promising discrete mathematical models: a small sampling interval, the guaranteed asymptotic (Lyapunov) stability, explicit nature of numerical methods, and program and algorithmic optimization of calculations. The application of bilinear transformation to construct a discrete mathematical model of a synchronous electric machine with a turn-to-turn fault of the rotor winding is considered. This approach makes it possible to tackle a number of problems which arise when standard methods for solving a Cauchy problem are used—namely, nonstationarity of dynamical systems and influence of the integration error on the accuracy. A transfer from a system of differential equations, describing the physics of synchronous generator operation, to difference equations is considered. Based on the difference equations obtained, a structural scheme is composed which allows the mathematical model software to be implemented on the microcontroller without involving additional mathematical functions. The experimental testing of adequacy of the discrete mathematical model of a synchronous generator with a turn-to-turn fault is performed. The proposed approach can be used to solve problems on identification of turn-to-turn faults, where an adequate high-speed and stable model is necessary.

Original languageEnglish
Pages (from-to)113-120
Number of pages8
JournalRussian Electrical Engineering
Volume90
Issue number2
DOIs
Publication statusPublished - 1 Feb 2019

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Electric machinery
Rotors
Mathematical models
Synchronous generators
Difference equations
Convergence of numerical methods
Microcontrollers
Numerical methods
Dynamical systems
Differential equations
Physics
Sampling
Testing

Keywords

  • discrete mathematical model
  • Laplace transform. z-transform
  • rotor winding
  • synchronous electric machine
  • turn-to-turn fault
  • Tustin transform

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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N2 - Abstract: A number of requirements are imposed upon the group of promising discrete mathematical models: a small sampling interval, the guaranteed asymptotic (Lyapunov) stability, explicit nature of numerical methods, and program and algorithmic optimization of calculations. The application of bilinear transformation to construct a discrete mathematical model of a synchronous electric machine with a turn-to-turn fault of the rotor winding is considered. This approach makes it possible to tackle a number of problems which arise when standard methods for solving a Cauchy problem are used—namely, nonstationarity of dynamical systems and influence of the integration error on the accuracy. A transfer from a system of differential equations, describing the physics of synchronous generator operation, to difference equations is considered. Based on the difference equations obtained, a structural scheme is composed which allows the mathematical model software to be implemented on the microcontroller without involving additional mathematical functions. The experimental testing of adequacy of the discrete mathematical model of a synchronous generator with a turn-to-turn fault is performed. The proposed approach can be used to solve problems on identification of turn-to-turn faults, where an adequate high-speed and stable model is necessary.

AB - Abstract: A number of requirements are imposed upon the group of promising discrete mathematical models: a small sampling interval, the guaranteed asymptotic (Lyapunov) stability, explicit nature of numerical methods, and program and algorithmic optimization of calculations. The application of bilinear transformation to construct a discrete mathematical model of a synchronous electric machine with a turn-to-turn fault of the rotor winding is considered. This approach makes it possible to tackle a number of problems which arise when standard methods for solving a Cauchy problem are used—namely, nonstationarity of dynamical systems and influence of the integration error on the accuracy. A transfer from a system of differential equations, describing the physics of synchronous generator operation, to difference equations is considered. Based on the difference equations obtained, a structural scheme is composed which allows the mathematical model software to be implemented on the microcontroller without involving additional mathematical functions. The experimental testing of adequacy of the discrete mathematical model of a synchronous generator with a turn-to-turn fault is performed. The proposed approach can be used to solve problems on identification of turn-to-turn faults, where an adequate high-speed and stable model is necessary.

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