# Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy
## 1 Introduction
However, the inclusion of more points will still make the calculation more complicated. The other solution is choosing representative points (RPs) to represent the driving cycle and the application torque-speed profile [23; 24]. The accuracy of this solution depends on the number and values of the RPs and the corresponding current calculation under different RPs. At present, motor optimizations using RPs to consider driving cycles mainly use the ideal current value, which ignores the influence of controllers [25; 26]. However, individually optimizing motor structure parameters cannot ensure optimal performance for the entire drive system, especially when the difference in the impact of the PWM carrier harmonic on the loss is significant under different control strategies and control parameters [27; 28]. On the other hand, for the control part, although there is much literature related to control strategies focusing on torque ripple reduction or motor efficiency improvements, such as advanced angle field weakening control, loss minimization direct torque control, and robust adaptive current control with disturbance observer [29; 30; 31], they usually consider the influence of harmonics or control parameters on the performance of the motor after the motor geometry structure is determined. It means that the proposed control strategies are generally designed and optimized at the control level and have not been combined with the motor design. As previously discussed, it can hardly achieve optimal system performance with this component-level-based optimization based only on motor or control. Therefore, to meet the challenging requirements and satisfy the wide operating range of EVs, it is necessary to optimize the driving motor, considering the inverter control strategy throughout the whole driving cycle in the product design phase. To deal with the aforementioned issue, this paper presents an effort to develop a system-scale multi-objective optimization procedure for driving motors based on the clustering technique under different operating conditions. And a full-speed domain vector controller with maximum torque per current (MTPA) and flux weakening control strategies [32; 33; 34] is adopted to meet the requirements of EVs. The main contributions of this paper are shown as follows:  
* The K-means clustering analysis is proposed as a preprocessing step to obtain insight into the distribution of operation points in two typical driving cycles, and the RPs of the torque-speed profile with their energy weights are identified. * The semianalytical efficiency model and torque model of an interior PMSM (IPMSM) based on FEM results are deduced to consider the influence of magnetic saturation, space harmonics, and cross coupling between d-axis and q-axis magnetic fields. * An optimal method to tune the motor and control parameters based on the multi-objective particle swarm optimization (MOPSO) algorithm is proposed, where the control model is added to consider the performance of IPMSMs under different control strategies in the whole driving cycle. This paper is organized as follows: Section 2 describes the clustering optimization design procedure for the IPMSM driving motor. Section 3 presents the motor-scale, control-scale, and system-scale optimization models. Based on these models, a comparative study has been carried out under three working condition requirements: one is under the rated operation point, and the other two are under driving cycles. And the optimization results are discussed and verified by experiments in Section 4, followed by the Section 5.