Enhancements to the Floquet Method for Analysis and Design of Power Converter Systems
Open Access
- Author:
- He, Mu
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 29, 2016
- Committee Members:
- Jeffrey Scott Mayer, Dissertation Advisor/Co-Advisor
Jeffrey Scott Mayer, Committee Chair/Co-Chair
Constantino Manuel Lagoa, Committee Member
Minghui Zhu, Committee Member
Alok Sinha, Outside Member - Keywords:
- Floquet Method
Power Converter Systems
Design Optimization
Genetic Algorithms - Abstract:
- Switch-mode power converters provide critical infrastructure for most electronic systems. As infrastructure, there are stringent demands to minimize cost and maximize performance. These conflicting goals increasingly require methods of analysis and design that are more sophisticated than conventional linear system techniques and serial design of converter subsystems. For example, linear small signal models fail to predict sub-harmonic oscillations that arise under certain operating conditions. Most power converter systems can be modeled using a switched state space model that includes piecewise linear time invariant (LTI) state space models for each topology along with a set of switching surfaces. In addition, most converters operate in a periodic manner, so the Floquet method can be applied to assess stability. Previous work yielded a closed-form expression for the Floquet-theoretic monodromy matrix for a piecewise LTI system with piecewise constant inputs. It also provided a method for calculating the periodic steady state response of such a system. The work presented here extends the previous derivation and method to systems having multi-period behavior (sub-harmonics) and sinusoidal inputs. This permits calculation of frequency response characteristics that are more accurate than those that can be obtained from small signal models. Tradeoffs are inevitable when one designs power converter systems. Decreasing the size of the energy storage elements - inductors and capacitors - reduces cost and volume but also reduces steady-state and transient power quality margins in ways that are difficult to determine using conventional models. To minimize cost and volume while ensuring that power quality specifications are satisfied, an automated design process based on Genetic Algorithms and extended Floquet method is presented.