Research On The Modeling And Control For The Quadratic And PCCM Boost Converter Based On The Fractional Calculus Theory

In 1983,Mandelbort points out fractional phenomena are abundant in nature and many fields of science and engineering technology.As the discovery of its applications in practical background,the fractional calculus has been widely studied in machinery,physics,engineering,information science,material science and other areas.Fractional calculus has memory characteristics and the physical processes it described are essentially dissipative.The fractional order models can give a more accurate description and yield a deeper insight into the physical processes than the integral order models.The researches about modeling of inductors and capacitors indicate that the fractional order models of inductors and capacitors can better reflect the electrical characteristics than the integral order models,namely the inductors and capacitors are of fractional order in nature.And the inductors and capacitors are essential circuit components for the switching power DC/DC converters,which have many functions such as transmit and store electricity and filtering.With the development of renewable energy systems such as wind power generation systems,solar photovoltaic systems and fuel cell systems,higher requirements for the DC/DC converters are put forward,so the quadratic Boost converter and the PCCM Boost conveter come into being.As the quadratic Boost converter can provide a wider input voltage and a higher output voltage and the PCCM Boost converter has a better performance in closed-loop stability and transient response,they have attracted much attention recently.Therefore,the dissertation relies on the theory of fractional calculus,regards the quadratic Boost converter and the PCCM Boost converter as study objects and studies the following three aspects:(1)The quadratic Boost converter based on the operating models of its input inductor and energy storage inductor can be divided into four types: the CCM-CCM?CCM-DCM?DCM-CCM and DCM-DCM quadratic Boost converters.Based on the fact that the inductors and the capacitors are of fractional order in nature,the four types' mathematical models of the fractional order quadratic Boost converter are established by using fractional calculus theory.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 quadratic Boost converter are gained and the relations between the regions and the orders are found.On the basis of the chain fractance and the Oustaloup fractional order calculus for filter approximation algorithm,the approximate circuit models of the fractional order inductors and capacitors can be obtained.The influence of the orders on the performance of the quadratic Boost converter in four types are verified by numerical and circuit simulation.Simulation results demonstrate the correctness of the fractional order models and the efficiency of the proposed theoretical analyses.(2)The tri-state mode Boost converter that contains an additional switch across the inductor makes the inductor current operates in the pseudo continuous conduction mode.PCCM is the third operating mode of the Boost converter that between CCM and DCM.Based on the fact that the inductor and the capacitor are of fractional order in nature,the fractional order mathematical models of the PCCM Boost converter and the PCCM quadratic Boost converter are established by using fractional calculus theory.In the view of the direct current and alternating current equivalent models,the quiescent operation points and the corresponding transfer functions are obtained,and the influence of the orders on the performance of the PCCM Boost converter and the PCCM quadratic Boost converter are analyzed and verified by the numerical and circuit simulation.Simulation results demonstrate the correctness of the fractional order models and the efficiency of the proposed theoretical analyses.Finally,the relations and the differences among the PCCM Boost converter?the PCCM quadratic Boost converter and the quadratic Boost converter are indicated.(3)Due to the affine non-linear nature in the fractional order mathematical models of the PCCM Boost converter and the PCCM quadratic Boost converter,and according to the stability theorem of the fractional order non-linear system,non-linear controllers are designed.On the basis of the fractional order circuit models,the non-linear controllers are verified by the Matlab/Simulink software.Simulation results show that the controllers enhance the dynamic and steady-state performance of the fractional order systems during large fluctuation of power supply and load disturbance.