Analytical Calculation of Magnetic Field in Fractional-Slot Windings Linear Phase-Shifting Transformer Based on Exact Subdomain Model

Fractional-slot windings linear phase-shifting transformers (FW-LPSTs) are a new type of transformer that can be used as an important component of multi-rectifier and multi-inverter systems. The FW-LPSTs are proposed for the first time, and few scholars have studied their magnetic field. However, accurate calculation of magnetic field distribution of the FW-LPSTs is the premise of the optimal design of the ontology, and the establishment of an accurate analytical model which remains a challenging task is the key to solving the magnetic field distribution. In view of the limitation of traditional analytical theory in solving the magnetic field, the FW-LPST model based on the exact subdomain method is proposed to obtain the exact magnetic field distribution. Considering the influences of the permeability and the structural parameters of the slot subdomain and the interaction of all slots on the distribution of the magnetic field, the governing equations of the air gap and slot subdomains are established using magnetic vector potential as the variable. According to the boundary conditions of each subdomain, all equations of the boundary condition are listed based on the Fourier series method. Finally, the vector magnetic potential and open-circuit magnetic flux density distribution of each subdomain are solved. The model accurately analyzes the influence of the cogging effect on the magnetic field distribution. The inductances of the primary side and the induced potentials of the secondary side are solved using the magnetic flux linkage method. The accuracy of the proposed analytical model is verified by comparison of the results obtained with those obtained by the finite element method.