Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Engineering (PhD)

Degree Level



Electrical Engineering


Roy A. McCann

Committee Member

Jingxian Wu

Second Committee Member

Mark E. Arnold

Third Committee Member

Yue Zhao


modeling method, modified describing function (MDF) method, converter dynamics, boost converters


The increasing use of renewable energy has resulted in the need for improved a dc-dc converters. This type of electronic-based equipment is needed to interface the dc voltages normally encountered with solar arrays and battery systems to voltage levels suitable for connecting three phase inverters to distribution level networks. As grid-connected solar power levels continue to increase, there is a corresponding need for improved modeling and control of power electronic converters. In particular, higher levels of boost ratios are needed to connect low voltage circuits (less than 1000 V) to medium voltage levels in the range of 13 kV to 34 kV. With boost ratios now exceeding a factor of 10, the inherent nonlinearities of boost converter circuits become more prominent and thereby lead to stability concerns under variable load conditions. This dissertation presents a new method for analyzing dc-dc converters using fractional order calculus. This provides control systems designers the ability to analyze converter frequency response with Bode plots that have pole-zero contributions other than +/- 20 dB/decade. This dissertation details a systematic method of deriving the optimal frequency-domain fit of nonlinear dc-dc converter operation by use of a modified describing function technique. Results are presented by comparing a conventional linearization technique (i.e., integer-order transfer functions) to the describing-function derived equivalent fractional-order model. The benefits of this approach in achieving improved stability margins with high-ratio dc-dc converters are presented.