Multi-objective optimization of multi-level DC-DC converters using geometric programming

Multi-objective optimization of power converters is a time-consuming task, especially when multiple operating points and multiple converter topologies must be considered. As a result, various steps are often taken to simplify the design problem and restrict the size of the design space prior to going through an optimization procedure. While this saves time, it produces potentially sub-optimal designs, and existing approaches must tradeoff between running time and design optimality. This paper presents an optimization-oriented method for modeling power converters and their components as posynomial functions, allowing multi-objective optimization of converters to be formulated as a geometric program, a type of convex optimization problem. This allows the use of fast, powerful solvers that guarantee global optimality of solutions. The method is demonstrated using the example of low-power multi-level flying capacitor step-down converters. Results show that, using geometric programming, sets of globally Pareto-optimal designs of two-, three-, and four-level converters with respect to efficiency and power density, for one design space and one operating point, can be generated in as little as 25 s, on a mid-to upper range laptop computer. Thus, optimal designs for three different converter topologies for hundreds of different operating points and/or design spaces can be generated in several hours-less than the time required to globally optimize one converter topology at one operating point for one design space using currently prevalent methods. This paper also demonstrates how geometric programming can be used to quickly perform sensitivity and tradeoff analysis of optimal converter designs.