基于磁感的变压器和感应电机等效矢量磁路分析

doi:10.19595/j.cnki.1000-6753.tces.231300

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Abstract The analysis of the working principle of transformers and induction motors mainly employs the equivalent electrical circuit in the traditional electrical machine theory. This approach represents actual magnetic quantities as electrical quantities, adding complexity to analysis. The traditional magnetic circuit theory, which only has reluctance elements, fails to characterize the phase differences between flux and magnetomotive force or iron losses, becoming a bottleneck.
This paper introduces a novel magnetic parameter called magductance. By vector magnetic circuit theory, an equivalent vector magnetic circuit is established and applicable to transformer and induction motor analysis. Firstly, the equivalent magnetic circuit for different working conditions is derived. At no-load conditions, the core loss is expressed in terms of magductance L₀. The phase difference between flux and magnetomotive force corresponds to the iron loss angle. The effect of the secondary side can be reflected through magductance L₂. When the load is zero, the expression for magductance is based on the original definition. The phasor diagram of the transformer derived from equivalent vector magnetic circuit takes magnetic flux Φ_m as the common reference phasor, and links among the primaryside, secondary side, and core are directly expressed by magnetic quantity. Secondly, the equivalent vector magnetic circuit for the induction motor is derived. It adds the airgap reluctance R_g, and the rotor squirrel cage is equivalent to the magductance L₂. Finally, the equivalent vector magnetic circuits for the transformer and induction motor are analyzed. (1) Vector magnetic circuit comprises reluctance R, equivalent magductance of core lossL₀, and equivalent magductance of secondary side (the rotor squirrel cage in the induction motor) L₂. (2) Loads of the transformer and induction motor can be directly considered in the equivalent magductance L₂. (3) For the transformer, R is equal to core reluctance R_Fe, and there is R=R_Fe+2R_gin the induction motor. (4) Electrical frequency ω is the excitation electrical frequency of primary winding in the transformer, and electrical frequency sω is the slip frequency of the rotor relative to the magnetic field in the induction motor. Experimental measurements agree well with the calculated results of the transformer and induction motor.
Compared with the existing equivalent electrical circuit, the proposed equivalent vector magnetic circuit saves the necessary turns referring and frequency referring. It characterizes the effect of L₀ on the magnetic flux and phase difference and calculates their output performance, providing a novel and intuitive method for analyzing, designing, and controlling electromagnetic equipment.

Key words： Magductance equivalent magnetic circuit vector magnetic circuit theory transformer induction motor electrical machinery

Received: 10 August 2023

PACS:	TM301
	TM401
	TM14

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