Small-Signal Transfer Functions of the Classical Boost Converter Supplied by Ultracapacitor Banks

Ultracapacitor is an emerging device for energy storage that can replace batteries in some short-term applications. Due to the fact that the terminal voltage of an ultracapacitor varies with the level of energy stored, a power electronic converter with voltage boosting capability is usually needed at its terminals to interface with a load operating at a constant voltage. For the case of a classical boost dc-dc converter supplying a resistive load by drawing energy from a bank of ultracapacitors, the paper derives small-signal transfer functions by considering a time-varying steady-state. To reduce the complexity of resulting exact expressions of poles, highly accurate approximate expressions are also derived. Furthermore, it compares how the control characteristics change when a constant voltage source such as a battery replaces the ultracapacitor bank. A numerical example is presented to demonstrate the accuracy of the approximate values of poles and zeros and to describe how the poles and zeros vary with the duty ratio.