## 1 Introduction  
The conventional compressor installed with internal combustion engine for air conditioner is driven by being connected with a timing belt, which is so called belt-driven compressor. However, this sort of compressor has a disadvantage in efficiency since its operating point depends on the speed of crank shaft of engine, and thus, the compressor is not allowed to be independently driven at desirable operating points where high efficiency is ensured. As electric vehicles get to be supplied broadly, innovation in the involved subsystem is needed to save energy. Especially in the air conditioning system, as it is possible for subsystems to share battery pack as power source with power train, the adoption of an electrified motor and inverter is considered so as to utilize the independent operation for high efficiency. Energy consumed by air conditioner would be significant. Since one of the most important factors in electric vehicles is the extension of driving distance, high efficiency and power density (per unit weight or unit volume) of subsystems belong to the most important factors. Conventional actuators used for air conditioner are in the form of induction machines and scalar control method for low cost and simple implementation. Because, in the common environments of air conditioner system, induction machine is usually fixed somewhere in factories or buildings, power density is not considered as important as in mobile machine-like electric vehicles. Actually, the type of motor that achieves high efficiency and power density is interior permanent magnet synchronous motor (IPMSM) [1,2]. By adopting IPMSM with rare earth permanent magnet (PM) such as NdFeB in place of induction machine (IM), it is possible to meet and improve the most requirements in efficiency, power density and power factor [3, 4, 5]. Throughout the literature, the efficiency of IPMSM ranged from 93 to 95%while IM achieved from 85 to 87% in the same size [3]. In another literature, power factor of PMSM, 0.95, was significantly higher than the one of IM, 0.89, and power density of PMSM was improved by 17.3% [4]. However, in addition to the performances mentioned above, there are two more parameters to be suppressed: torque ripple, electromagnetic interference (EMI) noise and cost. The inherent cause of torque ripple is originated from magnetomotive force (MMF) subharmonics of a certain winding method in stator and no-load flux density on air gap formed by interior PM and the shape of magnet cavity in rotor. Moreover, the external causes exist like switching harmonics and imperfect fabrication. These reasons lead to fluctuation of speed in open-loop or closed loop system whose sampling time is long and, as a result, uncomfortable acoustic noise and mechanical vibration inside vehicles may be generated [6; 7; 8]. Thus, in the various industry applications, torque ripple should be suppressed for low acoustic noise via dedicated control methods or initial system design [9; 10; 11; 12]. Likewise, EMI noise is caused in the almost same reasons, switching harmonics and harmonics in control input in the control system [13]. Electromagnetic compatibility requirements in the automotive sector are most stringent; inherent causes must be excluded as much as possible in motor design. Now that raw material cost is considered here, the most expensive material is rare earth PM. In case of mass production, such as automotive, raw material cost is a sensitive issue. Therefore, design optimization is needed, where PM volume should be minimized ensuring enough performance [14]. That is, the goal of machine design for air conditioning compressor in electric vehicles is to optimize for maximized efficiency and power density, while at the same time, suppressing torque ripple and PM volume [15]. IPMSM is comprised of stator and rotor that has interior magnet cavity and inserted PM there.