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2. High-power density direct-drive in-wheel motors 2.1. Requirements overview The development of a direct-drive SPMSM, which will exhibit desirable performance, requires a large amount of problem variables, constants and constraints to be taken into account according to [20]. Moreover, meta-heuristic optimization techniques can be applied along with the classical design theory and the analytical equations. In this case, the multi-objective SPMSM optimization has to be modelled and performed carefully, especially when certain quantities are of primary concern [21]. The problem complexity is increased if an in-wheel PMSM is supposed to be incorporated into the powertrain of an HEV, whereas its operating point varies almost ceaselessly. Thus, the study of motor performance in the rated operat- ing point or in the point of maximum provided torque, using finite element method (FEM) or fixed permeability method (FPM) has been proven inefficient enough [22]. Consequently, various design approaches and optimization methodologies have been revealed so far and each of them has its own advantages and disadvantages. In classical HEV design process motor’s efficiency map or torque-speed curve is a convenient way to represent drive system’s performance. The determination of efficiency, torque and speed for different operating points permits the preliminary estimation of motor’s charac- teristics in agreement with vehicle’s attribute. Also, different topologies that are investigated as possible candidates for the same application can be easily compared to each other [23]. However, by using efficiency maps the motor is considered as a black box, which responds to certain inputs (voltage and current). These two variables are assumed to be optimal in order to achieve the highest efficiency at a specific torque and speed output. Furthermore, a map scaling factor model (MSFM), based again on the knowledge of an efficiency map, is generally used for the selection of motor’s output power rating and specifications. The efficiency and torque are scaled using a linear dependency on the rated power. At the same time, few HEV’s subsystems, such as the internal combustion engine, wheels, batteries and control scheme, can also be modelled constructing the appropriate equations and then a joint optimization of all the subsystems using dynamic programming can be performed [24]. Although the aforementioned procedure permits a better interaction between the electric motor/s and the other vehicle’s subsystems, the approximation of the dynamic behaviour of the entire system is not satisfactory enough. It lacks accuracy concerning energy management estimation and fuel consumption calculation. Additionally, there is no association between motor’s performance and its geometrical parameters. A compromise between FEA and MSFM method is introduced in [9], in which the detailed magnetic circuit model is incorporated in the optimization process. Starting from a preliminary topology, the final configuration can be derived when the user’s requirements are met. The drawback of this approach is that only a restricted number of variables can be treated simultaneously. Thus, some geometrical parameters, such as motor’s diameter and length, should be specified by the designer and this method should be applied only for the optimization of magnets and windings modula- tion. A fast magnetostatic FEA is proposed in [25] in order to address the specific problem. The derived results are now more precise and the computational time and complexity are Hybrid Electric Vehicles128