Mathematical optimization techniques for the design of permanent magnet synchronous machines based on numerical field calculation

Numerical field calculation and mathematical optimization methods are used to find the most appropriate design of synchronous machines with rare-earth permanent-magnet excitation. The efficiency of optimization procedures for the resulting constrained and unconstrained vector-optimization problems is examined. It is shown that for an efficient optimization procedure it is necessary to combine suitable methods for the transformation of vector optimization problems to scalar ones and methods for the transformation of constrained to unconstrained problems, and algorithms for unconstrained optimization. As a first attempt, it is recommended to use the preference-function method with a search algorithm such as Rosenbrock´s algorithm. When the Marglin method is used, the combination of SUMT with a search algorithm, and the combination of the augmented Lagrange multiplier method with the conjugate gradient algorithm, are appropriate. The combination of this optimization procedure with numerical field calculations yields a powerful tool for the design of permanent-magnet machines