A review on analytical models of brushless permanent magnet machines

This study provides an in-depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite-element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time-consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent circuits (MEC) or solving Maxwell's equations can be faster and more flexible, but less accurate for complex machine structures. The paper focuses on the recent development of analytical models for brushless permanent-magnet (PM) machines that have become increasingly popular in low and medium-power applications. The literature review covers the recent developments in analytical models for PM machines with respect to various machine quantities such as magnetic flux density components, induced voltage, inductances, electromagnetic force/torque, efficiency, or unbalanced magnetic force (UMF). It outlines the advantages and disadvantages of different analytical models such as the zero-dimensional (0-D), one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical methods, as well as the Maxwell and basic mathematical analysis. Although the MEC models are faster than the numerical model, they are not as accurate for various structures of electrical machines including a great magnetic air gap. They also note that the analytical models based on the Maxwell equations are faster than the numerical ones and have the potential to obtain acceptable accuracy similar to the numerical models in electrical machines. Overall, this literature review provides valuable insights for researchers and engineers in selecting appropriate analytical models for PM machines. It highlights the trade-offs between accuracy and computational efficiency when choosing between numerical and analytical models, and the flexibility of analytical models to address changes in machine geometries or input values. Additionally, this helps researchers save time in determining appropriate references regarding the analytical models of brushless PM machines.