Finite element based phase-variable model in the analysis of double-star permanent magnet synchronous machines

Abstract

This paper describes a finite element (FE) based phase-variable model for double-star permanent magnet synchronous machines. In a double-star configuration where two three-phase windings are spatially shifted by 30 electrical degrees, a high amount of the 5th and 7th current harmonics may be excited because of the winding layout. However, a conventional d-q axis model considers only fundamental components, and thus, the machine model may be oversimplified. Improvement in the accuracy can be obtained by introducing an FE-based phase-variable model that includes the higher-order harmonics occurring in the no-load flux linkages and in the self-and mutual inductances. Moreover, when compared with an FE analysis with controlled power electronics, significant reduction in the computation time can be achieved. The effects of the harmonics on the machine behavior are evaluated by simulations, and the accuracy of the proposed model is verified by measurements.

Comparison of Finite-Element-Based State-Space Models for PM Synchronous Machines

“…The models of [12] and [13] neglected saturation based on the assumption that the total flux linkage of the windings is dominated by the PM flux. The same was assumed in [15] and [16] which used 2-D FEM to identify the linear inductances for both phase-domain and two-axis models of a double-star interior-magnet machine. All the circuit models of [12], [13], [15], and [16] were implemented in the MATLAB/Simulink environment using look-up tables (LUT).…”

“…The same was assumed in [15] and [16] which used 2-D FEM to identify the linear inductances for both phase-domain and two-axis models of a double-star interior-magnet machine. All the circuit models of [12], [13], [15], and [16] were implemented in the MATLAB/Simulink environment using look-up tables (LUT). In [17] and [18], saturation was also included in both phasedomain and two-axis PM machine models which were implemented on a real-time FPGA simulator.…”

“…This would not be beneficial in the linear cases of [12], [13], [15], and [16] in which one inductance function describes the behavior for the whole range of currents. In general, however, it is easier to obtain the flux linkages than the inductances from the FE solution.…”

“…Several different approaches were applied in the reviewed papers. In [12], [13], and [15], the torque was obtained by calculating the fluxcurrent contribution assuming a linear material and summing to this the cogging torque determined by FE analysis, while [16] completely neglected the cogging torque. In a general nonlinear case, however, the torque should be obtained by the virtual work principle as a partial derivative of the magnetic field energy W f or co-energy W c with respect to the mechanical rotor angle, keeping the other variables constant:…”

Study of multiphase modular stator SPM based on phase variable model

“…Phase variable model(PVM) [4][5][6][7], which is essentially an field-circuit coupled method, combines the accuracy of FE model and the high simulation speed of d-q model. PVM utilizes the machine parameters obtained from the nonlinear transient FE solutions, then the details of the machine can also be considered using PVM.…”