MMF Harmonics Effect on the Embedded FE-Analytical Computation of PM Motors

Abstract

This paper aims to define a minimum set of finite element solutions to be used in the design and analysis of saturated permanent-magnet motors. The choice of the finite element solutions belonging to this set is strictly associated with the classical d - q axis theory and it is described in terms of key points on the Flux-MMF diagram. When synchronous machine are considered, such a diagram has a regular shape, so that a huge reduction in finite element field solutions is possible with no loss of accuracy. It is also shown that the torque computed by using the d - q axis theory is almost independent of variation of the flux linkage with the rotor position. At last, the paper describes a technique in which few finite element solutions allow the identification not only of the average torque, but also the main torque harmonics. As a results, the torque behavior versus rotor position can be rapidly predicted

Modeling and Analysis of Electric Motors: State-of-the-Art Review

“…where uαβ, i αβ and ψαβ are the voltage vector, current vector and flux linkage vector in the αβ reference frame respectively; ψdq is the flux linkage in the dq reference frame, which is determined by id and iq together; p is the number of pole pairs. Wj' is the magnetic co-energy [18].…”

“…To improve the accuracy of the interpolation, the rotor dependency of LUT is often considered in spatial harmonics. For a healthy three-phase synchronous motor, the spatial harmonics have order of multipliers of 6 [13,18]:…”

“…where ω is the rotational speed in rad/s, v is the kinematic viscosity of the fluid (in this case air) and rm is the mean radius of the annulus. Evaluating the Taylor number for an air temperature of 50 ºC, the kinematic viscosity is 1.785 × 10 -5 m/s and, thus, substituting all the values into (18), it results in 1.7905 × 10 3 for Ta. It should be noted that the thermal network should be solved to estimate the temperature of all the nodes, and then temperature-dependent properties such v as should be updated.…”

Nonlinear Analytical Model for a Multi-V-Shape IPM With Concentrated Winding

“…where and are the center angular position of the coils A+ and A- (Fig.2), m is the number of coils per phase per electrical period, N cs and N cp are the number of circuits in R rot series and in parallel respectively, L is the stack length The dq axis currents (i d , i q ) and flux linkages ( , ) are then computed using Park's transformation. The average torque (T avg ), the power factor (PF) and the voltage (V) are computed at 4 static positions for an accurate estimation [15]. They are expressed by (34), (35) and (36) respectively.…”

“…It is less than 5% which confirms the validity of the analytical model. [15]. The analytical and the finite element models are computed using Intel® Core™ i7-4600U CPU @2.10 GHz 2.70GHz with 16GB RAM.…”