Multi-Objective Optimization of Unidirectional Non-Isolated DC/DC Converters

Engineers have to fulfill multiple requirements and strive towards often competing goals while designing power electronic systems. This can be an analytically complex and computationally intensive task since the relationship between the parameters of a system's design space is not always obvious. Furthermore, a number of possible solutions to a particular problem may exist. To find an optimal system, many different possible designs must be evaluated. Literature on power electronics optimization focuses on the modeling and design of particular converters, with little thought given to the mathematical formulation of the optimization problem. Therefore, converter optimization has generally been a slow process, with exhaustive search, the execution time of which is exponential in the number of design variables, the prevalent approach. In this thesis, geometric programming (GP), a type of convex optimization, the execution time of which is polynomial in the number of design variables, is proposed and demonstrated as an efficient and comprehensive framework for the multi-objective optimization of non-isolated unidirectional DC/DC converters. A GP model of multilevel flying capacitor step-down converters is developed and experimentally verified on a 15-to-3.3~V, 9.9~W discrete prototype, with sets of loss-volume Pareto optimal designs generated in under one minute. It is also demonstrated how the GP model can be used to determine the sensitivity of the optimized designs to the design parameters. Furthermore, a general procedure for deriving GP models is presented and demonstrated on the example of inductors for higher power applications. Finally, using the example of the seven-switch flying capacitor converter, it is shown how in cases where a converter-level GP model is not possible, component-level GP models can be coupled with a circuit simulator to perform efficiency optimization quickly. This hybrid approach is used to design a wide input and output voltage range, 2~A output current converter IC. The results show that GP is of great value to both researchers and practicing engineers. The methods demonstrated for deriving GP models of power converters are extendable to other converter topologies, allowing for the creation of a rigorous mathematical framework for the optimization of power electronics that guarantees globally optimum designs generated quickly.Ph.D.2018-12-19 00:00:0