A subdomain model for armature reaction field and open‐circuit field prediction in consequent pole permanent magnet machines

Abstract

In this paper, the machine quantity, such as electromagnetic torque, self and mutual inductances, and electromotive force, is analytically calculated for non-overlapping winding consequent pole slotted machine for open-circuit field and armature reaction. The sub-domain approach of (2-D) analytical model is developed using Maxwell's equations and divide the problem into slots, slot-openings, airgap and magnets region, the magnet flux-density is calculated and analyzed for both permanent magnet (PM) and armature current reaction (AR) with radial magnetization pattern. The magnetization surface currents (MSCs) are considered at the borders of iron-pole magnets and the value of MSCs is accurately computed. The result obtained using proposed model compared with that of FEM, (2-D) analytical model required less computation time and achieve higher accuracy of AR and PM.

A review on analytical models of brushless permanent magnet machines

“…Secondly divide the machine into regions based on the Maxwell equations and by using the magnetic vector potential. Finally, after applying boundary condition all machine quantities can be computed 14,25,28–45 …”

“…Based on the mentioned methods, the sub‐domain 44,45 technique due to the high speed and precision is more famous. In this way, analytical models are divided to regions according to the shape and material characteristics, (i.e., magnet, air gap, and winding) and according to partial differential equations (PDEs) that are derived from Maxwell's equations, due to a set of assumptions, the problem is simplified and a general solution, which provides the PDEs and boundary conditions for each region.…”

“…In the most analytical papers, machine quantities such as magnetic field distributions, a back electromotive force (Back‐EMF) and electromagnetic torque (cogging torque and load torque) are computed with the proposed analytical method and verified by finite element analysis. Figure 5 a–c illustrates the ideal rectangular, six‐step rectangular and sinusoidal current waveforms, for electromagnetic torque 45 …”

“…A summarized review of AM techniques used to solve the magnetic field on PMSM presented in Table C1. In this table, the calculation of flux density and all other machine quantities for Sd / Ss , internal/external rotor machine using different magnetization pattern has been addressed 1–75 …”

“…Slotted machines preferred due to its higher airgap flux density and provide better heat removal, the comparison between Ss and Sd given in Table 3. The calculation of slotting effects has been considered in some papers using either conformal transformation techniques 1,4,7–9,13,24 or subdomain technique (SD) 10,11,16–21,25,30–32,41–45 . The advantage and disadvantages of conformal transformation technique has been explained briefly by Zhu et al 21 …”