Modeling And Chaos Analysis Of Fractional Buck-Boost Converters

In order to achieve carbon neutralization and carbon peak,the demand for renewable energy power generation systems such as wind energy,solar photovoltaic and fuel cell will be more,and the reliability of DC-DC converters are also put forward higher requirements.With the exploration of researchers,people found that using mathematical models based on fractional calculus can describe some natural phenomena more accurately,and the potential fractional characteristics of some circuit elements are also found one after another.Accordingly,a systematic study is presented in this work,in which a modeling and analyzing method based on fractional calculus for power electronic systems is proposed,the influence of fractional order characteristics of circuit components on nonlinear dynamics of Buck-Boost converter is discussed,and the chaos is controlled.The main contents of the thesis are as follows:(1)The fractional state averaged model of the Buck-Boost converter in continuous current mode(CCM)and discontinuous current mode(DCM)is built.Direct current analyses are conducted by using the direct current equivalent models and the transfer functions are derived from the corresponding alternating current equivalent models.The operating regions of the Buck-Boost converter are gained and the relations between the regions and the orders are found.On the improved Oustaloup fractional order calculus for filter approximation algorithm,the fractional order Simulation model of Buck-Boost converter in CCM and DCM mode can be obtained.Simulation results demonstrate the correctness of the fractional order models and the efficiency of the proposed theoretical analyses,and the open-loop response speed of the fractional order model is obviously better than that of the integral order model.(2)On the improved Oustaloup fractional order calculus for filter approximation algorithm,the fractional order Simulation model of peak current controlled Buck-Boost converter in CCM and DCM mode can be obtained.The influence of parameters on the period doubling bifurcation and chaos of systems was analyzed,by using current reference,symmetric fractional order,asymmetric fractional order as variables,from phase portraits and bifurcation diagrams of the systems.Phase portraits and other results show that compared with the integer order model,the fractional order model can show more abundant dynamic phenomena.The capacitor's and the inductor's fractional order have significant influence on the chaos of the Buck-Boost converter in CCM and DCM mode,and the inductor's fractional order is more effective than capacitor.(3)The methods of traditional and improved resonant parametric perturbation are applied to control the chaos in fractional order Buck-Boost converter.The stability criterion based on the reference current is derived,which provides the theoretical basis for the selection of optimal amplitude and optimal phase.The fractional order Simulink numerical model is established to verify the control method.The results show that the methods of traditional and improved resonant parametric perturbation can effectively transform the fractional order system from the chaos to the steady,and compared with the method of traditional,the method of improved can make the system reach steady state more quickly,and can minimize the influence of sinusoidal disturbance signal on the system.