A Magnetic Circuit Model for an IPM Synchronous Machine Incorporating Moving Airgap and Cross-Coupled Saturation Effects

Analytical Modeling of Open-Circuit Air-Gap Field Distributions in Multisegment and Multilayer Interior Permanent-Magnet Machines

“…4, where . This simplification may cause some errors because of the variation in magnetic saturation level in the bridges under different loading conditions [3], [4]. However, since the bridges are usually designed to be highly saturated even at open-circuit, the accuracy of lumped magnetic circuit models will still be acceptable, as will be illustrated later.…”

“…Therefore, a lumped magnetic circuit model usually is a good compromise between simplicity and accuracy [3]- [9]. By way of examples, Laplacian or quasi-Poissonian field equations were directly solved analytically for SPM machines [10], [11] and inset PM machines [12], conformal mapping techniques were used for analyzing the influence of stator slotting [13]- [15] and rotor saliency in IPM machines [16], [17], while lumped magnetic circuit methods [3]- [9], [18]- [26] were extensively used for SPM machines [18]- [20], switched reluctance machines [21], linear brushless dc machines [22], hybrid stepping motors [5], salient-pole synchronous machines [23], flux-switching PM machines [24]- [26], inset PM machines [6], IPM machines [3], [4], [7]- [9], etc. In the lumped magnetic circuit analysis, the permeances of stator yoke and rotor yoke were often omitted for simplicity [5]- [7], [9], [18], [22], [25], [26], or handled with the nonlinear B-H curve of iron by iterative process for higher accuracy [3], [4], [8], [19]- [21], [23], [24].…”

“…However, since there is no significant magnetic saturation at yokes, neglecting the permeances of stator yoke and rotor yoke is usually acceptable and the results will still have fair accuracy [27]. To account for the slotting effect, [3], [6], [7] introduced Carter coefficient for predicting the average air-gap flux density, and [4], [5], [18], [20], [21], [24]- [26] analytically approximated the flux distributions in the slots by assuming straight and semicircular lines for predicting air-gap flux density distribution. However, the stator slots can be neglected if only the average air-gap flux density is considered [8], [9], [19], [23].…”

“…To investigate the end effect, a 3-D lumped magnetic circuit was employed in [20], [24], [25]. Furthermore, lumped magnetic circuits were also developed according to different rotor positions in order to account for rotor rotation [4], [5], [20], [21], [24], [26], much attention being paid to the nonlinear permeances in teeth [20] or pole tips [21], [24], [26] by employing iterative process [20], [21], [24] or by using saturated coefficients based on FEA [26]. Lumped magnetic circuits are particularly useful for IPM machines due to highly saturated rotor bridges and complicated rotor configurations.…”

“…Lumped magnetic circuits are particularly useful for IPM machines due to highly saturated rotor bridges and complicated rotor configurations. The rotor bridges could be modeled as constant flux leakage sources with preset values [6]- [8] or nonlinear permeance elements using iterative process [3], [4], [9]. Although the assumption in [6]- [8] might cause error since the saturation level of rotor iron bridge could be varied under different loading conditions, it was fairly acceptable for approximation as it resulted in significant simplification.…”