Analytical optimization and comparison of torque densities between permanent magnet and electrically excited machines

This paper compares the torque densities, i.e. torque per volume (T/V) and torque per weight (T/G), between permanent magnet (PM) and electrically excited (EE) machines for low speed applications when they have the same overall size and copper loss. The machines are optimized individually and analytically. The optimal split ratio and flux density ratio are derived. The influence of pole number and machine size is investigated as well. The analytical models are verified by finite element (FE) analyses. It shows that PM machines exhibit more than √2 times torque densities of EE machines. For EE machines, there is an optimal pole number to maximize torque densities and they prefer large volume applications. The comparison also shows that the T/G designs have significantly higher split ratio than the T/V designs to balance torque and weight.