**Hang Zhao 1,2, Chunhua Liu 1,2,\*, Zaixin Song 1,2 and Jincheng Yu 1,2**


Received: 11 April 2019; Accepted: 13 May 2019; Published: 17 May 2019

**Abstract:** The exact mathematical modeling of electric machines has always been an effective tool for scholars to understand the working principles and structure requirements of novel machine topologies. This paper provides an analytical modeling method—the harmonic modeling method (HMM)—for two types of consequent-pole magnetic-geared machines, namely the single consequent-pole magnetic-geared machine (SCP-MGM) and the dual consequent-pole magnetic-geared machine (DCP-MGM). By dividing the whole machine domain into different ring-like subdomains and solving the Maxwell equations, the magnetic field distribution and electromagnetic parameters of the two machines can be obtained, respectively. The two machines were applied in the propulsion systems of hybrid electric vehicles (HEVs). The electromagnetic performances of two machines under different operating conditions were also compared. It turns out that the DCP-MGM can reach a larger electromagnetic torque compared to that of the SCP-MGM under the same conditions. Finally, the predicted results were verified by the finite element analysis (FEA). A good agreement can be observed between HMM and FEA. Furthermore, HMM can also be applied to the mathematical modeling of other consequent-pole electric machines in further study.

**Keywords:** harmonic modeling method; magnetic-geared machine; hybrid electric vehicle; magnetic field; electromagnetic performance; analytical modeling
