Research On V~2 Controlled Cuk Converter

Compared with conventional second-order converter,such as buck and boost converters,Cuk converter,consisting of two inductors and two capacitors,is a fourth-order converter with complex circuit structure.And there exist various operation modes for Cuk converter on the basis of different operation modes of inductor and capacitor.However,Cuk converter shares many advantages,such as the ability to step up and step down,its input and output current can be kept continuous,and so on.Thus,it has been widely applied to power factor correction,wind energy and photovoltaic power generation systems and some other occasions.At present,the research on the control method of Cuk converter mainly focues on current control,but the current controlled Cuk converter has the disadvantage of poor transient response speed,which cannot meet the requirements of some occasions that require fast transient response speed.V~2 control strategy behaves fast transient response speed and has been successfully applied to converters like buck and boost converters,however,very few literatures have discussed the feasibility whether V~2 control can be applied and the excellent performance be maintained in the fourth-order Cuk converter.Therefore,in order to improve the transient performance of Cuk converter,it is of great importance to study the V~2 controlled Cuk converter and its control performance.Firstly,Cuk converter is taken as the object of research in this paper,its operation principle and characteristics in continuous conduction mode(CCM),discontinuous conduction mode(DCM),continuous capacitor voltage mode(CCVM),and discontinuous capacitor voltage mode(DCVM)are analyzed detailedly,respectively.The critical expression of inductance of Cuk converter between CCM and DCM,and the critical expression of intermediate capacitance between CCVM and DCVM are further deduced.The small signal equivalent model of Cuk converter in CCM mode is developed on the basis of time average equivalent modeling method,the DC steady-state gain and the AC small signal transfer functions are derived.Frequency domain simulation results verify the the correctness of derived small signal model.Secondly,based on the detailed analysis of the operation principle of the V~2 controlled CCM Cuk converter,the closed-loop small signal model of the V~2 controlled CCM Cuk converter is established,and the expression of the sample-and-hold transfer function for Cuk converter is derived.As a comparison,the small signal model of current controlled CCM Cuk converter is established,and the control-to-output transfer function and output impedance are derived respectively.In frequency domain,the transient performance of CCM Cuk converter controlled by these two methods mentioned is analyzed detailedly.It is clearly revealed that compared with current control,V~2 controlled CCM Cuk converter has wider bandwidth of the control-to-output transfer function and lower low frequency gain of the output impedance,so it has better transient performance.Time domain simulation and experiment are presented to verify the correctness of the closed-loop small signal model and the transient performance analysis.Finally,the sampled data model as well as the discrete iterative map model of the V~2controlled CCM Cuk converter is established,and the dynamic behavior of the Cuk converter is analyzed based on the sampled data model under the variations of circuit parameters.The boundary condition expression of V~2 controlled CCM Cuk converter with slope compensation from stable periodic state to unstable state is derived.The results indicate that the stability of V~2 controlled CCM Cuk converter is related to the time constant composed of the output capacitance and its equivalent series resistance(ESR).When other circuit parameters are fixed,the larger the output capacitance or ESR is,the more stable the converter is.The stability range of V~2 controlled CCM Cuk Converter can be broadened by introducing slope compensation into the control loop to some extent.Results of time domain simulation verify the validity of the theoretical analysis.