Investigation of Chaotic Behaviour in a DC–DC Converter Using the v-Resolution Approach

Investigation of nonlinear phenomena such as bifurcation and chaos in DC-DC converters has usually been carried out by obtaining a discrete-time map of the closed-loop system (i.e. sampled-data method). In some cases, extracting such a map is not an easy task and may consist of more tedious algebra. Geyer, in 2004, proposed a method (as well-known as v-resolution method) to model the buck converter in the form of discrete-time. This model whose input and outputs are duty cycle and states-inductor current and capacitor voltage- is said to be valid for all operating regimes. Therefore, in this study, we aim at investigating nonlinear dynamics in a current controlled buck converter using v-resolution method. Precisely, we study the subharmonic instabilities by means of an open-loop model of the converter. By choosing the current reference as a bifurcation parameter, the obtained simulations show that the discrete-time v-resolution model of buck converter is nonlinear enough to manifest both fast-scale and slow-scale instabilities. This is verified by comparing bifurcation diagrams obtained by sampled-data method and v-resolution approach. Finally, we can apply this modeling method to other type of DC-DC converters to study nonlinear dynamics without dealing with difficulties in capturing the discrete-time map of the closed-loop system.