AC Losses in Windings: Review and Comparison of Models With Application in Electric Machines

Abstract

Industry is increasingly adopting high-speed electric machines due to their high-power density and low cost. However, increasing the speed leads to many challenges that are worth to study since they have relevant impact on the design of the machine. One of these challenges is the losses in stator winding assembly. At low frequency, losses in windings are usually assumed equal to DC losses. However, at high frequency some phenomena become noticeable and worth evaluating since they lead to noticeable losses. AC losses in windings are due to skin effect, proximity effect, and circulating currents. The main models of AC losses in windings in the literature are presented for both circular and rectangular wires. These models are compared using both interior and surface-mounted permanent magnet synchronous machines. Results show that for proximity effect, analytical model is convenient when considering armature reaction only, however, when considering on load case, hybrid model with simple FEA is suitable thanks to its interesting trade-off between accuracy and computation time, which makes it suitable for large-scale optimization. For circulating currents effect, finite element model is unavoidable. Moreover, two important properties concerning circulating currents are stated as well as their mathematical proofs.INDEX TERMS AC losses in windings, electric machine, circulating currents, high speed, proximity effect, skin effect.

Remanufacturing a Synchronous Reluctance Machine with Aluminum Winding: An Open Benchmark Problem for FEM Analysis

“…The losses of electric machines-excluding mechanical losses such as friction or ventilation-were calculated by summarising the DC and AC losses. Specifically, the winding losses at a high-frequency range were expressed as a combination of the DC loss (I 2 R), which was only affected by the amplitude of the applied current (I) and the DC resistance (R) skin and proximity effects, and the circulating current effect that was caused by uneven current sharing via the strands is shown in Equation (17) [81,82]. When alternating current flows through a conductor, the current density near the surface became greater than that in the core because of the generated eddy currents, which is known as the skin effect.…”

Circular Economy Aspects of Permanent Magnet Synchronous Reluctance Machine Design for Electric Vehicle Applications: A Review

“…When the armature field flux leaks into the slot during heavy load, an inductance imbalance between bundle strands can occur, generating circulating currents. AC loss depends on several factors, including conductor dimensions, frequency, and amplitude of the magnetic field [146,147]. For a more precise estimation of the eddy current loss, FEM-based magnetic field calculations are used, which consider both the axial (B ax ) and radial (B rad ) components of magnetic induction [148,149].…”