Fast Simulation and Chaos Investigation of a DC-DC Boost Inverter

Intensive and repetitive simulations are required to study static and dynamic behaviours of systems. Particular phenomena such as bifurcation and chaos require long simulation times and analysis. To check the existence of bifurcations and chaos in a dynamic system, a fine-tuning procedure of a bifurcation parameter is to be carried out. This increases considerably the computing time, and a great amount of patience is needed to obtain adequate results. Because of the high switching frequency of a boost inverter, the integration process of the dynamic model used to describe it uses an integration step that is in general less than one microsecond. This makes the integration process time consuming even for a short simulation. Thus, a fast, but accurate, method is suitable to analyse the dynamic behaviour of the converter. This work contains two topics. First, we develop a like-discrete integration process that permits precise results in a very fast manner. For one switching period, we compute only two or a maximum of three breaking points depending on whether we treat a continuous conduction mode (CCM) or a discontinuous conduction mode (DCM) of the inductor current. Furthermore, with each segment of the dynamic trajectory, an exact analytic formula is associated. The second goal is to use this result to develop a discrete iterative map formulated as in standard discrete time series models. The Jacobian matrix of the found iterative map is defined and used to compute Lyapunov exponents to prove existence of chaos. Performance of the developed study is positively evaluated by using classical simulations and fine-tuning a bifurcation parameter to detect chaos. This parameter is the desired reference of the inductor current peak. Results show that the proposed scheme is very fast and accurate. The study can be easily extended to other switching topologies of DC-DC inverters.