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  3. Volume 7, Number 1, 2025
  4. Mathematical Model of a Synchronous Machine With Permanent Magnets Based on the Method of Average Voltages in the Integration Step

Mathematical Model of a Synchronous Machine With Permanent Magnets Based on the Method of Average Voltages in the Integration Step

SEPES.
2025;
Volume 7, Number 1
: pp. 39 - 51
https://doi.org/10.23939/sepes2025.01.039
Authors:
  1. Andriy Kutsyk
  2. Аndrii Lishchuk
1
Lviv Polytechnic National University, Department of Electromechatronics and Computerized Electromechanical Systems
2
Lviv Polytechnic National University, Department of Electromechatronics and Computerized Electromechanical Systems

Synchronous machines with permanent magnets (SMPM) have become widely used in modern electric drives and generator sets due to their combination of high energy efficiency, compact size and reliability. They are characterised by increased specific power, no losses in excitation circuits and reduced energy consumption. At the same time, the fixed magnetic flux created by permanent magnets imposes specific requirements on mathematical modelling, especially when developing control algorithms and researching operating modes.
Models in phase or orthogonal coordinates are traditionally used to analyse such machines. Simplified models in rectangular coordinates allow for quick calculations, but they are unable to reflect the behaviour of the machine in asymmetrical modes, different winding connection schemes, or in multiphase configurations. This significantly reduces their suitability in complex energy and electromechanical systems.
This paper presents a mathematical model of a synchronous machine with surface-mounted permanent magnets, implemented in phase coordinates. The model was constructed using the method of average voltages in the integration step, which ensures high numerical stability of calculations and increases the numerical integration step, allowing for faster calculations. The proposed approach expands the possibilities of analysis: it allows considering not only symmetric but also asymmetric modes, as well as implementing various load connection schemes.
A comprehensive verification of the proposed model was carried out: on the one hand, by comparing the results of mathematical modelling for generator operation mode with analytical calculations of the external static characteristics of a synchronous machine with permanent magnets, and on the other hand, using a similar model implemented in the Matlab/Simulink environment to study the behaviour of the machine in transient modes. The results obtained confirmed the adequacy of the proposed model for both steady-state and dynamic modes of operation.

synchronous machine with surface-mounted permanent magnets
mathematical model
method of average voltages in the integration step
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