Multi-objective optimization and comparison of multi-level DC-DC converters using convex optimization methods

Generation and Derivation of Practical Optimization-Oriented Models of Inductors

“…Recently it has been shown [1], [2], [3], [4], [5], that geometric programming [6], a class of convex optimization problems, can be used to accurately and quickly optimize power converters for multiple objectives. There are two main advantages of using this approach.…”

“…First, in a feasible convex optimization problem, a local minimum is guaranteed to be a global minimum. Second, many efficient solvers for convex optimization problems exist: in [2], [5] it was shown that complex converter topologies can be optimized for efficiency and volume in under one minute. A Geometric Program (GP) has the following form minimize (1) subject to…”

“…Therefore, in order to model a power converter as a GP, each component in the system must be modeled using posynomial functions. As shown in [2], [4], [5], semiconductor models are often already in posynomial form or can be manipulated to be in posynomial form in a relatively straightforward manner. Accurate models of magnetic models, such as those in [7], [8], are more difficult to put into posynomial form.…”

“…In [1], [4], comprehensive posynomial models of inductors were not considered. In [2], [5], low-power SMD inductors were considered and modeled in an application-specific way, with a posynomial model that is appropriate to the converters considered for optimization within the operating range envisioned for the studied application. Therefore, these models cannot be easily transferred to a different converter optimization problem, and in most cases, the models would need to be re-derived.…”

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

“…In the literature it is possible to find several methods for the optimization of the inductors, most of them focusing on analytic models, measurements and finite elements models [1], [4], with fixed or variable geometry [5], [6]. Our aim here is to develop a method that is sufficiently fast to be later used at subsystem or system level with up to hundreds of variables, and still accurate enough to be a very good starting point of a component optimization process.…”