Optimal Design of Inductors Based on Homothetic Shape and using Geometric Programming

Abstract

The efficiency and power density of a converter are two major characteristics but they are antagonists so the designer has to find a tade-off between them. This is generally formulated as a multi-objective optimization problem giving a pareto front, and it can be encoutered at the system level, at subsystem level or even at the component level. In general the formulation needs to be different at each level because optimization algorithms are not robust enough and cannot guarantee convergence on large scale problems. This paper proposes a design method for inductors, using a mathematical formalism known as Geometric Programming (GP) that gives strong guarantees of convergence whatever the size of the problem. The design model describes objective and constraint functions using monomials and posynomials to comply with GP rules and works with homothetic shapes. A first formulation using continuous parameters allows selecting the region of operation and provides a good estimate of attainable size and losses, then a second formulation shows how to truncate parameters that need to be discrete values to obtain feasible objects (integer number of turns, discrete core size,) and account for non linear permeability. An evaluation case is presented to test the performance of the proposed algorithm. Last, a finite element analysis is included to account for some non linearities such as fringing and proximity effects, and improve the design accuracy. Because of the GP formulation, it should be possible in future work to use such an inductor model for sub-system level optimization (for example 2nd or 4th order filter) and still guarantee convergence towards a global optimum.