High-performance electric drive applications necessitate a high fidelity model to predict the terminal characteristics of machines in the design stage to fulfill a system-level evaluation together with the converters. This article interprets winding function theory (WFT) from the field perspective and incorporates secondary effects, such as slotting and iron nonlinearity into it to accurately predict the main flux linkage in induction machines. The method is centered on resolving the magnetic scalar potential on the two sides of the air gap and computes the flux linkage via a winding function. Its performance is benchmarked against 2-D finite-element analysis (FEA) and the state-of-the-art magnetic equivalent circuit (MEC) method. Flux linkage and torque results indicate that the relative error is within 3.1% even in a highly saturated region when comparing to FEA, while MEC using the same circuit network may present a 20% error.

In view of the increasing demand in torque density, this article propounds the idea of looking for an upper bound of the torque production and average shear stress for surface permanent magnet (SPM) synchronous machines. The derivation is based on the assumption of an infinite permeability of the iron core and employs the transfer relation between the normal magnetic flux density and the tangential magnetic strength. The result is written as functions of the machine's major geometries and excitation conditions. The ratio of the actual value and this upper bound may be used as a metric of measuring the usage of materials’ electromagnetic capability, or reversely as an indicator of the marginal gain of the iron core of higher relative permeability. The result is further investigated to discuss the electromagnetic scalability and the sizing law of SPM machines. Specifically, the reason for increasing volumetric torque density as the machine size goes up is revealed. The optimal remanence flux density of permanent magnets is also predicted at 1.91T , providing that the lamination saturates at 2T .