Influence Of Modulation Method On The Dynamic Behavior Of Switching Converter

As the core component of the switching power supply,the switching converter is a strongly nonlinear time-varying system with abundant nonlinear dynamic phenomena such as sub-harmonic oscillation,period-doubling bifurcation,low-frequency fluctuation and chaos.However,these phenomena often lead to unpredictable working conditions,greatly affecting the performance of switching converters and even make them unable to work.Therefore,in-depth study of nonlinear dynamic behavior in switching converters will help to further reveal the mechanism of nonlinear phenomena and optimize the design of converter parameters.As an important part of circuit control,the modulation method will directly affect the performance of the converter.Based on the theory of nonlinear dynamics,this paper conducts in-depth research on the dynamic modeling,dynamic behavior and stability of switching converters from the perspective of different modulation methods.First,taking buck converter as the research object,the discrete mapping model of voltage-mode controlled buck converter with pulse width modulation(PWM)is established.Based on the model,the bifurcation diagram is used to analyze the dynamic phenomena such as period window,Hopf bifurcation,period-doubling bifurcation and chaos of the converter when the circuit parameters change.The system z-domain closed-loop transfer function,eigenvalue equations,the boundary equation between stable and unstable state of the circuit are derived,and the distribution of the converter’s working state domain is described.The existence of Hopf bifurcation and period-doubling bifurcation and the difference between the two Hopf bifurcations are proved theoretically.The influence of different PWM methods on the working stability of the converter is studied in detail to guide the selection and design of circuit parameters.Secondly,the double-loop V~2 control,which has a faster load transient response than the voltage control,is applied to the buck converter,and the discrete mapping and sampling data models of V~2 controlled buck converters with trailing-edge and leading-edge modulations are established respectively.The complex nonlinear dynamic behavior of V~2 controlled buck converters with different modulation methods when circuit parameters change is analyzed in detail.Introducing ramp compensation in the control loop,the critical expression of the converter from unstable to stable state is derived,and its working state domain is divided.The research results indicate that trailing-edge and leading-edge modulated buck converters have symmetrical dynamical behaviors,such as symmetrical bifurcation,symmetrical time-domain waveforms,symmetrical phase portraits and symmetrical period-doubling bifurcation boundaries.By ramp compensation,the range of stable working conditions of the converter can be effectively expanded.Finally,the V~2 controlled cascaded buck-buck converters with trailing edge-trailing edge modulation and trailing edge-leading edge modulation are proposed,and the influence of adding the latter-stage converter on the dynamic behavior of the front-stage converter is studied.By analogy with a single converter,a complete two-dimensional sampled data model under different working conditions is established,and the impact on the cascaded system when the front-stage converter and the latter-stage converter adopt different modulation methods is analyzed.The research results show that when a single converter is in an unstable state,adding a post-stage converter to the cascade system can eliminate the oscillation of single-stage converter,make it stable,and expand the stable range of the converter.Moreover,different modulation methods will have different effects on the dynamic behavior of the cascade converter and broaden the stability range.