Posynomial models of inductors for optimization of power electronic systems by geometric programming

When optimizing power electronic converters for multiple objectives, such as power density and efficiency, the optimization of the magnetic components is often the most challenging and time-consuming task. In order to perform optimization quickly and efficiently, it would be advantageous to formulate converter optimization as a geometric program, a proven convex optimization method. In order to optimize for losses and volume via a geometric program however, all loss and volume models of the various components must be in the form of posynomials. While some loss models, such as those of semiconductors, are naturally in posynomial form or easily transformed, this is not the case for inductors. This paper presents a derivation of posynomial loss, volume, temperature, and saturation models for families of inductive components, based both on simulation and on adapting familiar analytical models into approximate posynomial form. The terms of the derived posynomial models are the inductor design variables, such as the number of turns, the air gap, and so forth. This allows inductors to be optimized for multiple design objectives as a geometric program.