# FEA-Based Design Procedure for IPMSM and IM for a Hybrid Electric Vehicle
## 1 Introduction
### Background and Literature Review
The larger saliency ratio of the V-shape configuration compared to the U shape allows for the production of a larger reluctance torque [25]. The V-shape design has been shown to be more robust against demagnetization [23; 26]. The promising characteristics of V-shape PMs have encouraged researchers to optimize the dimensions and V angle in several studies [27]. The V angle has usually been investigated as a variable in iterative optimization studies [18; 28]. In Ref. [29], it was shown that increasing the V angle can increase the torque in the constant torque region but reduces the maximum operating speed of the machine. The design of line-start induction machines is well understood. The National Electrical Manufacturers Association (NEMA) and the International Electrotechnical Commission (IEC) have standardized IM dimensions and power ratings for line-start applications and the required geometry, number of rotor and stator slots, and slot types are specified to achieve the required performance while meeting the thermal and mechanical constraints [30; 31]. The literature has shown that IMs can be a suitable choice for the propulsion systems of EVs and HEVs. They offer comparable efficiency with PMSMs in the field weakening region, and are of lower cost due to the absence of PM material in their rotor, but generally have a lower power density. A large number of papers have discussed the design of IMs based on the sizing equations [32]. These methods are not useful for the design of IMs in EVs because they are only optimal for operation at a single operating point. Some literature employs sizing equations in population-based iterative optimization studies. However, these studies cannot produce a true optimal design because the sizing equations used are not reliable over a wide range of dimensions and loading levels [2]. The number and shape of the rotor bars play an important role in the performance parameters of IMs. Different optimization problems have been defined to achieve desired outputs such as high torque or efficiency [33; 34]. An optimization study for an axial-flux IM was performed in Refs. [6; 35]. Although optimal designs were determined, the effect of slot shape on the performance parameters has not been discussed. In Ref. [30], the authors showed that the optimal number of rotor bars depends on the type of the supply (line start or inverter driven) and the number of pole pairs. Round rotor slots reduce the vibration and noise as compared to rectangular slots [36]. It has been shown that deeper and wider rotor bars increase the efficiency while improved starting and power factor are obtained by shorter bars [37]. Thirteen different shapes of rotor slots was studied in Ref. [38] to find the optimal shape of the bars which offer the highest efficiency and starting torque. These studies discussed the characteristics for a particular operating point and do not consider the performance analysis for a wide range of torque and speeds. Moreover, these papers just describe the effect of their considered variables on the case studies and do not cover the complete procedure to develop a baseline design. The aforementioned design processes ignore the temperature effect or assume some constant values to guarantee the feasibility of the design in terms of the thermal stress [16; 35]. For instance, a constant value of current density, whose value depends on the cooling method used, is often assumed to determine the slot area [39; 40]. Considering the above limitations of the design procedures in the literature, there is a lack of a systematic design procedure for preparation of a baseline design for PMSMs and IMs.