On-Load Analytical Modeling of Slotted Interior Magnet Synchronous Machines Using Magnetic Islands Method

Abstract

In general, the Magnetic Circuit (MC) is an effective and valuable tool for calculating the PM flux and predicting machine behavior during the no-load operation. Since the rotor PMs are the sole source of the flux, the flux path and the respective MC model is independent of the rotor position. However, this is not the case for the loaded operating condition. As the rotor spins, the path of the armature flux necessarily changes to pass through the rotor with minimum reluctance. Therefore, the MC model would vary at every rotor position and is no longer a feasible solution particularly, for cases with complex rotor structure. To resolve this, an analytical solution procedure based on the concept of the Magnetic Islands (MI) is presented to predict the on-load response of the motor such as armature flux and the winding inductance. The air-gap is defined as a function along the perimeter of the stator to include the stator slotting effect. In addition, the presented method accounts for the magnetic saturation. To assess the accuracy of the model, analytical results are compared against the finite element results.

Simplified Analytical Model for Rapid Evaluation of Interior PM Traction Machines Considering Magnetic Nonlinearity

“…Based on the continuity theory of the magnetic flux, the Ud_arm for the range (-0.5αpa, 0.5αpa) could be derived via (16) where r is the airgap radius, (Dor/2) ≤ r ≤ (Dis/2) [9]- [11], [27]. For simplicity, r is selected as Dis/2 in the paper.…”

“…For simplicity, r is selected as Dis/2 in the paper. Substituting (15) and (16) into (14) to obtain (17) for determining the d-axis armature-reaction airgap flux density.…”

“…Combination of EMC model and exact conformal mapping technique for calculating IPM machine open-circuit airgap field distribution was proposed in [14]. Analytical models for IPM machine considering slot effect and cogging torque was introduced in [15] and [16]. However, only analysis result as a function of phase current (q-axis) was presented in [15] and analysis result of one specific operation point was shown in [16].…”

“…Analytical models for IPM machine considering slot effect and cogging torque was introduced in [15] and [16]. However, only analysis result as a function of phase current (q-axis) was presented in [15] and analysis result of one specific operation point was shown in [16]. In [17], a high fidelity EMC model considering individual stator slot reluctances, segmented airgap reluctances, and segmented rotor reluctances was suggested.…”

Analytical Design of Sculpted Rotor Interior Permanent Magnet Machines

“…Results are validated with finite elements and utilized to improve the torque harmonic characteristics of an existing industrialized machine. This is because finite elements accurately predict experimental results across a broad range of machines [33][34][35][36] and have been utilized to evaluate and compare machine types [37][38][39] and validate analytical solutions [40][41][42][43][44][45][46][47][48][49][50]. Section 2 introduces the topics relevant to the design of IPM motor construction and control.…”