Analysis of Magnetic Coupling Between Armature and Field Windings of Variable Flux Reluctance Machine

Abstract

I. INTRODUCTIONNon-permanent magnet machines are having growing interest recently due to the volatility of permanent magnet (PM) prices. Variable flux reluctance machine (VFRM) is a non-permanent magnet machine and it is a candidate for high-performance applications such as electric vehicles [1,2]. There are several slot/pole combinations of VFRM, such as 6/4, 6/5, 6/7, and 12/10 [3,4]. The 6/4 topology has a large torque ripple [5]. The 6/5 and 6/7 topologies have low torque ripple, but they have an unbalanced magnetic force (UMF) issue which causes mechanical stress and acoustic noise due to the odd rotor poles [6]. The 12/10 topology has a low torque ripple and balanced UMF.Although the structure of the VFRM is similar to the switched reluctance machine (SRM), VFRM has DC winding in the stator as well as three-phase AC windings. Therefore, the back-EMF waveform of the armature winding is sinusoidal. The control of the VFRM is easier than SRM due to the sinusoidal back-EMF.There is a magnetic coupling between armature and field winding because they have a common flux path as seen in Fig. 1. However, the field winding is fed by a DC current while armature windings have an AC current. In this study, the magnetic coupling between armature and field winding is analyzed and how VFRM can operate having DC and AC windings is explained.II. FLUX LINKAGE ANALYSIS OF FIELD WINDINGEvery tooth of VFRM has a field winding as shown in Fig. 1. Blue ones are field windings, red, green and yellow ones are armature windings. Firstly, the field winding is separated and called DC1, D2, D3, DC4, DC5, and DC6. Field windings are excited by DC current while armature windings are not excited. The flux of a single excited magnetic circuit is determined by Eq. (1).θ=NI/R(θr) (1)Where N is turns number, I is current, R is magnetic reluctance and θr is rotor position. The magnetic reluctance of the motor depends on rotor position because effective airgap changes with rotor position. Flux linkages of DC field windings and resultant flux linkage of field winding are obtained using the FEA, as shown in Fig. 2. Reluctance function of DC1 winding is obtained by FFT analysis of flux linkage, turns number and DC current. R0 is the DC component of reluctance, n is harmonic order, Rn is the magnitude of nth harmonic, and α is the angle of harmonic with respect to rotor position.RDC1=R0+∑Rnsin(nθr+α) (2)Flux linkage of DC1 winding is obtained using Eq. 1 and Eq. 2. Each of stator and rotor poles are not aligned at the same time, so there is a phase difference between DC windings. Therefore, the flux linkage of the DC2 winding is given in Eq. 4.λDC1(θr)=λ0+∑λnsin(nθr+α) (3)λDC2(θr)=λ0+∑λnsin(nθr+α+π/3) (4)Eventually, resultant flux linkage of when all DC windings are connected series is obtained by Eq. 5.λT(θr)=6λ0+∑λnsin(nθr+α)+∑λnsin(nθr+α+π/3) +∑λnsin(nθr+α+2π/3)+∑λnsin(nθr+α+3π/3)+∑λnsin(nθr+α+4π/3)+∑λnsin(nθr+α+5π/3) (5)λT(θr)=6λ0 (6)As shown in Fig. 2, all of the AC components eliminate each other and the resultant flux linkage has only a DC component. In this analysis, armature windings are not excited. Also, both field and armature windings are excited and flux linkage of the field winding is obtained by FEA, core material is assumed it has infinite magnetic permeance. Although magnitudes of the harmonic orders are changed, all AC components are eliminated and resultant flux linkages consist of DC components. Flux linkage of field winding has little harmonic if core material is steel, due to the magnetic saturation and leakage flux. These results could not be presented in this digest due to the figure limits. However, all of the results will be given in the final paper.III. CONCLUSIONVFRM has DC field winding and armature windings in the stator. Although armature and field windings have a common flux path and magnetic coupling, field winding can be excited by DC current. Thus, the flux linkage of the DC field winding is analyzed while armature windings are excited by AC current. The field winding is separated, and flux linkages of every winding are obtained by FEA. Every winding has a DC biased AC flux linkage. However, all DC windings are connected series, AC components of resultant flux are eliminated. Eventually, field winding has only a DC component even if there is a magnetic coupling between armature and field windings. The magnetic circuit of analysis and results at full load will be given in the final paper due to the figure limits of the digest. **