I. Introduction
Permanent magnet machines (PMMs) have been widely used in many applications our daily life because they have some advantages such as compact feature, simple, low size mechanical construction, easy maintenance, good reliability, high torque density, and efficiency. However, it has been found that one of drawback of PMM in applications is cogging torque (CT). The CT in any PMM can reduce the permanent magnet machine performance. As a consequence it leads to decrease the effectiveness of the machine function in application. The CT can generate vibration, noises, thus limit applications to a high-precision control system. In renewable energy applications, the CT can reduce the self-starting of the rotor rotation, particularly when the low-speed condition. Based on the investigation and discussion, it can be concluded the CT is one of the most important issues in PMM applications. In addition, in order to gain the achievement and effectiveness of any PMM in the application, the CT in PMM should be considered and overcome in the design phase. In fact, in the design phase of PMM, the CT has been identified that it is effected by the interaction force of magnetic flux of magnet in rotor core and the stator slot of machine. Thus, in order to minimize the CT in any PMM, it can be conducted by modifying the magnet structure, stator core, or combining the modification in both of magnet structure in rotor core and stator slot of the machine. For the purpose of task, the parameters affecting the CT in machine should be determined and optimized. As the CT is the effect of magnet structure and stator slot, authors have selected the magnet structure to be optimized, instead of other parts of the machine. The reason is the magnet structures are the parts in any PMM which have the highest impact on the CT peak value. Considering this fact, in the paper authors have conducted to optimize the magnet edge of machine in terms of applying the combination magnet edge slotting (MES) and pole arc optimization (PAO). The MES is one CT reduction technique as has been reported in past work [1]. The MES has been investigated and proposed the MES on the reduction of the CT. In the research, a-PMM of integral slot number with 24 slots and 8 poles is investigated. The slot opening width of the PMM investigated was 2 mm, and the air gap length was 2 mm was selected. The CT of the PMM proposed could be reduced to around 95 %, compared with the initial PMM structure. For achieving the CT reduction at least 98 % of the machine rated torque, the MES is developed in term of two steps of slotting (TSS) technique in magnet edge with combined PAO are developed in this study. In the present work, the length of machines studied have been reduced to 1 mm, but the slot opening width is kept 2 mm. This could achieve the CT reduction of the proposed PMM, and the effectiveness of the combining TSS and PAO is analyzed and validated using finite element analysis based on FEMM.