Abstract
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.
Highlights
DC-DC boost inverter, known as a step up inverters, are largely studied in literature [1,2,3]. ese power electronic devices transfer electric energy from a DC input voltage source to an output load that requires a higher voltage. e efficiency of DC-DC boost inverter is good in general which makes them largely employed in various applications
Results show that the proposed scheme is very fast and accurate. e study can be extended to other switching topologies of DC-DC inverters
Of the paper, the load resistance is chosen to ensure that the circuit operates theoretically in the continuous mode. e sequence of the braking points computed for a set of some consecutive switching periods is used to define a discrete iterative map process. e obtained time series added to the Jacobian matrix of the map permits the computation of Lyapunov exponents
Summary
DC-DC boost inverter, known as a step up inverters, are largely studied in literature [1,2,3]. ese power electronic devices transfer electric energy from a DC input voltage source to an output load that requires a higher voltage. e efficiency of DC-DC boost inverter is good in general which makes them largely employed in various applications. E switch is turned on at the beginning of each switching period and turned off if the inductor current becomes greater than a reference value and remains in the off state until the beginning of the cycle Simulations of this control system are frequently done in Matlab/Simulink environment. It includes the equivalent electrical circuit modelling the DC-DC boost inverter, commutation equations, properties of DCM and CCM regimes, and dynamical submodels associated with ON and OFF states. For both DCM regime and CCM regime, mean values of inductor current and output voltage are detailed and expressed.
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