IPMSM can prevent the scattering of PMs in high speed and use reluctance torque caused by the difference of magnetic resistance as well as magnetic torque. Because of high speed and high efficiency of IPMSM, it is used in various field such as EV motors, industrial machine tools, and home appliances. IPMSM can be classified by its PM arrangement and various shape. Among various model of IPMSM, IPMSM with v-shape PM has advantage of high torque and high output in comparison with flat-type PM because the magnetic flux increases as PM cross-sectional area increases. However, IPMSM has the disadvantage of cogging torque that affects torque ripple and noise. Also, optimization of the objective function is difficult because of many design variables and the complicated shape of the rotors in IPMSM.
The random walk method is an optimization technique which improves the approximation to approach the optimal point from the preceding approximation by using random number for nonlinear function. It can be applied to case where the objective function is discontinuous at some point or non-differential, in which the relationship between the function value and variables is difficult to be explained.
The simplex method is an optimization technique to move the simplex gradually toward the optimal point by comparing the value of the objective function at each vertex of the simplex model formed by the set of n+1 points in an n-dimensional space. The movement of the simplex is performed by using reflection, expansion, and contraction. Simplex method has quick and efficient convergence of design variables than random walk method. However, design variables may converge to local (not global) optimum and whether finding of the global optimum is affected by initial simplex location and its volume or shape. Also, the random walk method takes a lot of iteration and may converge to local optimum in bad case because it depends on randomness or probabilities. Because these methods have their own disadvantages, this paper proposes a combination of two existing methods (random walk and simplex) that overcomes the limitation of each method and the optimal shape design of V-shape IPMSM using random walk and simplex method for minimizing cogging torque. The validity of our optimization technique can be confirmed by comparing cogging torque of the basic model and the optimized model. Random walk and simplex method is thought to be useful in designing electric machines which have complicated shapes and objective function difficult to be estimated.