A Fast Hybrid Analytical Model of PM Machine with Halbach Magnets and Saturation Effects

Surface-mounted permanent magnet (SPM) machines using Halbach magnet arrays offer enhanced magnetic performance but are prone to increased magnetic saturation due to their assembled magnetic effects. This study aims to develop a hybrid analytical model that accurately predicts the electromagnetic behavior of Halbach-based SPM machines while accounting for magnetic saturation. The proposed approach couples the sub-domain method with an equivalent magnetic network (EMN). The subdomain model computes the unsaturated air-gap field, and the EMN introduces equivalent surface currents at saturation-prone boundaries to represent the nonlinear permeability. The proposed model demonstrates excellent agreement with finite element method (FEM), with the average torque deviation below 5% while requiring only about 3% of the FEM computation time. Experimental measurements of a prototype further validate the accuracy of the analytical predictions. The hybrid model therefore provides a fast, accurate, and physically transparent tool for the analysis and design of Halbach-based SPM machines under magnetic saturation.