A contribution to identification of convex structures for global optimization of permanent magnet machines

Application of modern mathematical optimization has become an important tool for the design of permanent magnet machines. This paper focuses on identification of particular mathematical structures, which can be obtained by appropriate formulation of otherwise well-known analytical equations. This problem formulation can be used for reliable and efficient optimization, notably in regards to the certification of the optimality. In other words, locally optimal solutions are avoided, and it can be guaranteed that a solution is globally optimal. The tool for the certification of optimality is the exploitation of convexity characteristics during the problem formulation, as convex optimization has proven to be a very efficient and highly reliable optimization method. To this aim, the problem formulation for maximization of several performance parameters of a brush less DC permanent magnet motor with use of soft magnetic composites and 3D flux distribution is discussed. The results can be considered as elements of a library of tools leading towards reliable and efficient optimization of permanent magnet machines.