基于磁感的变压器和感应电机等效矢量磁路分析

Equivalent Vector Magnetic Circuit Analysis of Transformer and Induction Motor Based on the Magductance

电机学等传统电机理论对变压器和感应电机的工作机理分析多采用等效电路的方法,将实际磁量等效为电量来表示,在一定程度上让二者的分析变得复杂化。可是,传统磁路理论中仅有磁阻元件,难以定量表征磁通与磁动势之间存在的相位差和铁心中的损耗等,进而成为分析的瓶颈。为此,该文引入新的磁路参数——磁感,并利用磁阻和磁感双元件构成的矢量磁路理论,建立适用于变压器和感应电机分析的等效矢量磁路,推导了不同工况下的磁路方程,并以变压器为例,从磁路角度绘制了相量图。对变压器和感应电机在不同工况下的主要特性进行定量计算,通过实验结果验证了分析方法的有效性。相较于等效电路分析方法,该文所提的等效矢量磁路分析方法省去了匝数归算、频率归算等过程,因而概念清晰、计算简洁。该文研究不仅为电机等电磁装备的分析设计提供了全新的方法,而且有望推动《电机学》教材的改革,降低电机学相关内容的学习难度。

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 fluxΦm 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 Rg,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 RFe,and there is R=RFe+2Rg in the induction motor.(4)Electrical frequencyωis the excitation electrical frequency of primary winding in the transformer,and electrical frequency sωis 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.