A Hybrid Vector Magnetic Network Model Based on the Magductance Principle for Eddy-Current Loss Calculation in Permanent Magnets of Flux-Switching PM Machines

Flux-switching permanent-magnet (FSPM) machines feature high torque density and a mechanically robust rotor structure, making them suitable for high-speed applications. However, the stator-mounted permanent magnets (PMs) are exposed to rich spatial and temporal flux harmonics, which induce substantial eddy-current losses, increase the risk of irreversible demagnetization, and reduce operational reliability. Although finite-element analysis (FEA) offers high accuracy, its computational cost is considerable. Conventional equivalent magnetic network (EMN) methods are computationally efficient but have difficulty directly representing the eddy-current reaction field, which can limit prediction accuracy. This paper proposes a hybrid vector magnetic network (VMN) model based on the magductance principle. A rotor-saliency-modulated air-gap magnetomotive-force (MMF) model avoids repeated network reconstruction, while frequency-dependent magductance branches incorporate PM eddy-current coupling directly into the network without a separate post-processing correction. A three-dimensional PM subnetwork is combined with Schur-complement condensation to represent axial eddy-current distributions while reducing the system matrix order. Validation on a 12-slot/10-pole, 10 kW prototype shows maximum torque deviations of 1.9% relative to measurement and 2.0% relative to 3D FEA. Compared with 2D and 3D FEA, the computational speed is increased by approximately 15 and 280 times, respectively. The proposed model provides an efficient tool for PM-loss evaluation and segmentation assessment in the investigated FSPM machine.