# Computationally Efficient PM Power Loss Mapping for
###### Abstract  
This paper proposes a computationally efficient approach for mapping permanent magnet (PM) power loss in permanent magnet synchronous machines (PMSMs). The PM loss mapping method here uses time-step finite element analysis (FEA) to determine the function parameters representing the loss variation with speed (frequency), amplitude modulation ratio, carrier ratio, and stator current and is suitable for rapid evaluation of machine performance over the entire torque-speed envelope. The PM loss can be accurately mapped across the full operational envelope, including the field-weakened mode. The loss mapping procedure takes into account the equivalent resistivity of axial segmentation of the PM array calculated by three-dimensional (3-D) FEA. The effect of temperature on the PM loss is also considered. The proposed methodology is validated on two surface-mounted PMSM designs. The results of the loss mapping procedure are consistent with those from direct 3-D finite element prediction and experimental results of PM power loss at each operating point of the machine. permanent magnet synchronous machines; computationally efficient methodology; PM loss mapping; permanent magnet (PM) power loss; PWM +
Footnote †: 2021: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Scholars from the University of Sheffield and the University of Bristol put forward a series of analytical methods and theoretical models. Their research mainly focused on obtaining the energy flow density of the boundary of the rotor permanent magnet by solving the two-dimensional electromagnetic field model and then obtaining the overall loss of the rotor permanent magnet [6]. [PERSON] and [PERSON] et al. from the University of Southampton, UK calculated the PM power loss of a high-speed permanent magnet synchronous motor at no load and load using the analytical method and the finite element method and compared and analyzed the two calculation methods [7,8]. [PERSON] et al. from Chiba University of Technology, Japan, analyzed the effect of the rotor shape on PM power loss by using the three-dimensional finite element method and proposed a new rotor structure to restrain the eddy current of the permanent magnet [9]. [PERSON] et al. from Gifu University, Japan, used the three-dimensional (3-D) finite element method to analyze the effect of permanent magnet block partitioning on PM power loss in a surface-mounted permanent magnet synchronous machine (SPMSM) [10]. [PERSON] of Tianjin University established two-dimensional and three-dimensional finite element models of the motor and analyzed the variation in the internal magnetic field of the motor and the eddy current of the permanent magnet under load and no load [11]. [PERSON] of Shenyang University of Technology analyzed the influence of spatial and temporal harmonics of stator magnetomotive force on PM power loss by the analytical method and the finite element method and established the analytical model and the time-varying finite element model of PM power loss [12]. [PERSON] et al. of Harbin Institute of Technology studied the influence of motor design parameters on PM power loss and analyzed the eddy current loss and temperature field distribution of a permanent magnet by the finite element method [13]. Currently, there are two calculation methods for PM power loss: the analytical method and the finite element method. However, these two methods are difficult to be used for efficient calculation of PM power loss in the whole working field in the actual motor design process. The analytical method is often error prone due to a series of assumptions and is not applicable to different topological structures of the motor. It takes a long time to calculate the PM power loss at a single working point by the 3-D finite element method, and the time to calculate the PM power loss in the whole working field is immeasurable.