### 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 language | English |
---|---|

Pages (from-to) | 113-120 |

Number of pages | 8 |

Journal | Russian Electrical Engineering |

Volume | 90 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2019 |

### Fingerprint

### 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

*Russian Electrical Engineering*,

*90*(2), 113-120. https://doi.org/10.3103/S1068371219020081

**A Discreet Mathematical Model Based on the Bilinear Transformation of a Synchronous Electric Machine with a Turn-to-Turn Fault in the Rotor Winding.** / Polishchuk, V. I.; Timoshkin, V. V.; Glazyrin, A. S.; Bolovin, E. V.

Research output: Contribution to journal › Article

*Russian Electrical Engineering*, vol. 90, no. 2, pp. 113-120. https://doi.org/10.3103/S1068371219020081

}

TY - JOUR

T1 - A Discreet Mathematical Model Based on the Bilinear Transformation of a Synchronous Electric Machine with a Turn-to-Turn Fault in the Rotor Winding

AU - Polishchuk, V. I.

AU - Timoshkin, V. V.

AU - Glazyrin, A. S.

AU - Bolovin, E. V.

PY - 2019/2/1

Y1 - 2019/2/1

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.

KW - discrete mathematical model

KW - Laplace transform. z-transform

KW - rotor winding

KW - synchronous electric machine

KW - turn-to-turn fault

KW - Tustin transform

UR - http://www.scopus.com/inward/record.url?scp=85066239787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066239787&partnerID=8YFLogxK

U2 - 10.3103/S1068371219020081

DO - 10.3103/S1068371219020081

M3 - Article

AN - SCOPUS:85066239787

VL - 90

SP - 113

EP - 120

JO - Russian Electrical Engineering

JF - Russian Electrical Engineering

SN - 1068-3712

IS - 2

ER -