A Fractional Order Approach for Modeling Nonlinear Behavior in Boost DC-DC Converters with CPL

The increasing use of renewable energy has resulted in the need for improved boost dc-dc converters. This type of power electronics-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 solar power levels continue to increase, the corresponding boost converter power levels also need to increase. Consequently, higher levels of boost ratios are needed in order 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 paper presents a new method for analyzing boost converters using fractional order calculus. This results in Laplace-domain transfer functions with non-integer order powers. 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 paper details a systematic method of deriving the optimal fit of actual boost converter operation by use of a modified describing function technique that is often used in nonlinear systems analysis. Results are presented by comparing a conventional linearization technique (i.e., integer-order transfer functions) to the describing-function derived fractional order transfer function. The benefits of this approach in achieving improved stability margins with high-ratio boost converters is presented.