Permanent-magnet harmonic electric machines (PMHEMs) have attracted increasing attention in recent years due to their attractive features. This novel breed of electric machines has exhibited great potential for various industrial applications, such as low-speed direct-drive applications and hybrid propulsion systems for transportation. A typical characteristic of PMHEMs is the difference between the pole-pair number of permanent magnets (PMs) and the pole-pair number of armature windings. Due to the sharp magnetic permeance change caused by the modulator, the air-gap magnetic field within PMHEMs is modulated. Hence, new magnetic field harmonics can be produced and thereby used for energy conversion. However, due to the introduction of modulator structure, the magnetic field distribution within the PMHEMs become more complex compared to conventional electric machines, which makes performance prediction and analysis of PMHEMs extremely difficult. Furthermore, the modulator structure usually works at the magnetic saturation region, and the nonlinear characteristic of soft-magnetic materials must be considered to obtain a precise performance prediction. Although finite element analysis (FEA) can provide precise magnetic field distribution and performance prediction for PMHEMs, it is time-consuming and cannot offer a closed-form solution. Additionally, the FEA mesh for PMHEM analysis should be very dense to calculate various harmonic components accurately, which further increases the computation burden.

In this thesis, the key features of PMHEMs are first summarized systematically by analyzing various topologies that belong to this new breed of electric machines. Then, several analytical methods are introduced and compared with respect to the feasibility for solving the magnetic field distribution of PMHEMs. Based on the Fourier series expansion method, this thesis develops two effective analytical methods to evaluate the electromagnetic performances of PMHEMs, namely the subdomain method (SDM) and harmonic modelling method (HMM). Subsequently, the analytical method is combined with the nondominated sorting genetic algorithm (NSGA)-II to conduct geometrical parameters optimization for PMHEMs.

Based on the harmonic analysis of PMHEMs by using the proposed analytical method, two double-rotor harmonic electric machines (DRHEMs) belonging to PMHEMs are proposed, which possess two different types of PMs on two rotors. The multiple operation modes of DRHEMs are analyzed through an improved subdomain method that considers magnetic saturation. Furthermore, DRHEMs are applied to a hybrid propulsion system, and their parameters are optimized according to the requirements of various operation modes.

Finally, the proposed analytical methods and the feasibility of the DRHEMs are verified using both FEA and experimental results. Results demonstrate that the analytical methods can serve as a rapid and accurate tool for the design and optimization of PMHEMs at the preliminary design stage. Furthermore, the semi-analytical solution of PMHEMs can help designers better understand the working principle of PMHEMs and provide engineers inspiration for novel topologies for electric machines.