基于线圈子单元的永磁同步电机健康与定子绕组短路故障数学模型

doi:10.19595/j.cnki.1000-6753.tces.211762

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Abstract To solve the issues existing in the mathematical model of stator winding short-circuit fault of permanent magnet synchronous motor (PMSM) with phase winding as the basic element, such as the influence of fault space location cannot be taken into account, different short-circuit faults need to be remodeled, and the contribution of coil to motor performance under healthy condition cannot be studied. This paper proposes a mathematical model based on coil sub-element for PMSM (APM) with health and stator winding short-circuit fault.
Firstly, each coil of PMSM is divided into multiple coil sub-elements, and the matrix equations of physical quantities such as voltage, impedance and no-load back EMF of each sub-element are established respectively. The voltage equations of all sub-elements are established by using Kirchhoff's voltage law, and the electromagnetic power and torque equations of the motor are established. Secondly, the finite element method is used to establish the no-load back EMF matrix of each wire turn considering the spatial position relationship in the slot, and the sub-element no-load back EMF matrix considering the position information is obtained by matrix transformation. Then, the finite element method and fitting method are used to establish the inductance matrix of each wire turn considering the spatial position relationship in the slot, and the sub-element inductance matrix considering the position information is also obtained by matrix transformation. Finally, the simulation model and graphical interface of APM are established in Matlab/Simulink. By modifying the tap number and the connection position of the short-circuit resistance module in the graphical interface, the electromagnetic characteristics of motor health and different types of stator winding short-circuit fault (WSF) are calculated.
By comparing the APM calculation results, finite element simulation results and experimental results, the correctness and accuracy of the APM are verified, and the following conclusions are obtained: (1) By modifying the tap number and the connection position of the short-circuit resistance module in the graphical interface, APM can conveniently and quickly calculate the voltage, current, torque and other electromagnetic characteristics of the motor health and different types of WSF. (2) Considering the influence of the motor winding structure, APM can subtly analyze the contribution of coils to motor performance under different operating conditions when PMSM is in a healthy state. Using APM to analyze coils at different positions, it can be found that the coils at different positions of the same branch have different voltages, different powers, and different loads. Due to the different voltages of different coils in the same branch, the fault probability of different coils in the same branch is different under the same coil insulation level. In the design of coil insulation, coils at different positions of the same branch can adopt different insulation levels to reduce motor manufacturing costs. (3) Without changing the internal structure, APM can efficiently, accurately and subtly analyze the motor performance under different types of WSF such as interturn short-circuit fault and interphase short-circuit fault. (4) Considering the influence of fault space position, APM can accurately analyze the influence of short-circuit fault at different positions of the coil in the PMSM slot on motor performance. It is found that when the short-circuit turns (R_f) and short-circuit resistance (N_f) are the same, the short-circuit current and average torque are different under ISF at different positions in the slot, which reveals the limitation of N_f and R_f as the criterion of fault severity.

Key words： Permanent magnet synchronous motor mathematical model coil sub-element stator winding short-circuit fault matrix equations

Received: 01 November 2021

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TM351

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