# Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy
## 1 Introduction  
With the deepening of vehicle electrification in the global market, the driving motor as the main power of the electrical vehicle (EV) drive system holds promising growth potential and attracts extensive attention [1, 2]. At present, more than 80% of driving motors in the electrical drive system of pure and hybrid EVs on the market adopt permanent magnet synchronous motors (PMSM) for wider speed regulation range, higher efficiency, and power density [3, 4, 5], such as Toyota Prius, Chevrolet Bolt, BMW i3, BYD E6, and so on. To obtain a better driving experience and a longer driving range, it is of great significance to improve PMSM performances through optimization design technologies [6, 7]. Generally, the optimization design of PMSM for an EV can be based on a single operation condition, such as the rated operation point of the torque-speed curve, which could ensure satisfactory working performance at this specific point. Yet, once the condition changes, the PMSM performance will deteriorate and even result in undesired reliability in the power train. The operating conditions of EVs are very complex and involve frequent starting and braking, frequent accelerating and decelerating, cruising, and climbing. Therefore, the optimized PMSM at the rated operation point could not guarantee the whole operation requirements within the considered driving cycle of an EV, which puts forward inevitable demands for the PMSM design considering the driving cycle [8; 9; 10; 11]. Different from the PMSM that operated at the rated operation point, the actual performance of the PMSM at each operating point in different driving cycles is closely related to the control strategy and control parameters. To achieve high system-level performance, the perfect cooperation of the motor and its control systems, considering the driving cycle, must be investigated synchronously. Although both motor and control are important to the system's performance, not much work has been reported in the literature. The design and optimization are mostly at the component level of motors [10; 11], which can be classified into two types of single-objective and multi-objective optimization. For single-objective optimization, any one of efficiency, torque ripple, cost, or weight can be used as the optimization objective. In [12; 13], by using the finite element method (FEM)-based model and the exact subdomain model with intelligent optimization algorithms, the torque ripple and cogging torque are respectively obtained minimally in the PMSM. For multi-objective optimization, two or more design objectives are selected simultaneously [14; 15]. Efficiency and cogging torque are selected as the two design objectives for optimization of a PMSM in [16], where two-stage design optimization using the Taguchi method and response surface model are used to identify the three design variables. In [17], the multi-objective genetic algorithm is adopted to achieve low cost and low torque ripple for a PMSM optimization, and the resulting motor performances meet all the given design demands. The above optimization on the component level of motors is generally conducted under the rated operation point. When component-level-based optimization involves more operation points in the driving cycle, the simple way is to repeat the performance calculation process in rated point optimization at all operation points and then use the optimization algorithm to select the optimal scheme [18; 19]. However, the optimizations with a precise model that includes all operating points will be very time-consuming, with a significant increase in computational cost and complexity. There are two main solutions to this problem. One is using approximate models for as many operating points as possible to obtain the global optimal design. The approximate models for the former solution could be the Kriging model, equivalent circuit model, and response surface model [20; 21; 22], which are generally used to replace the finite element precise model and reduce the computer cost.