Magnetic equivalent circuit approach for AC copper loss calculation and optimal winding design for electrical machines

Abstract

The rapidly growing interest in aircraft electrification, known as more electric aircraft (MEA), has propelled the development of high-power-density machines, which are characterized by high-speed or high pole-pair number. These machines inherently encounter significant AC copper losses due to the high frequency of input voltage. The AC copper loss in electrical machines refers to the additional copper losses in the windings that occur due to alternating current (AC) effects, which are not present under direct current (DC) conditions. This phenomenon will not only cause partial overheating in the winding but also accelerate insulation aging, ultimately resulting in additional challenges in thermal dissipation or winding failure, which severely restricted the further improvement of power density of an electrical machine.
To reduce the burden on thermal management systems and increase the power density of electrical machines, various techniques for mitigating AC copper loss have been extensively studied, especially for innovative winding structures. However, the current solutions are not sufficiently satisfactory. For example, litz wire can effectively reduce the AC copper loss up to several kHz, at the cost of low copper filling factor and high manufacturing price, which severely restricts its further application in electrical machines.
In addition, a novel winding structure using transposed rectangular bundle with rectangular conductors and its design procedure are proposed to provide another optimal solution for high power density machines. The proposed winding can effectively reduce the AC copper loss in electrical machines without significantly compromising copper fill factor, thus enhancing power density.
The thesis comprises the following contributions:
1) Proximity Loss Calculation Method: Based on mesh-based magnetic equivalent circuit (M-MEC), a novel method is proposed to calculate the proximity loss and magnetic flux leakage according to precise slot positions of the conductors in electrical machines. This method demonstrates high flexibility and can be extended to accommodate slots of various shapes. Using an existing machine as an example, the modelling process of the proposed method is illustrated, showing close alignment and efficiency compared with FEA. Experimental tests on a motorette further validate the effectiveness of the proximity loss calculation method.
2) Circulating Current Loss Calculation Method: Based on the flux leakage calculation method mentioned above, a rapid circulating current calculation method is introduced. This method involves the electrical circuit of each strand and calculating parameters using M-MEC. The process is illustrated with a baseline machine, demonstrating shorter computation times and comparable precision to FEA. Experimental validation on a motorette further confirms the validity of the circulating current loss calculation method.
3) Innovative Winding Structure: A new winding structure aiming at reducing AC copper loss in high-frequency electrical machines is presented. This winding can suppress circulating current loss without significantly compromising copper fill factor. The optimization process, involving the calculation of circulating current loss for form-wound windings with different strand numbers and transpositions, is illustrated on the baseline machine. Experimental results validate the effectiveness of the optimized winding in reducing circulating current loss.

Date of Award	21 May 2025
Original language	English
Awarding Institution	University of Nottingham
Supervisor	Alan Zhang (Supervisor), Xiaochen Zhang (Supervisor) & David Gerada (Supervisor)