摘要
在级联功率变换器中,源变换器与负载变换器之间的开关纹波交互可重塑公共耦合点处的电压纹波。当输出电容等效串联电阻(ESR)较大时,源变换器的输出电压纹波对负载变换器的稳定性具有显著的影响。为了揭示开关纹波交互作用对负载变换器稳定性的影响,本文以级联的谷值电压(VVR)控制Buck变换器为例,通过动力学建模和稳定性分析等方法来阐述负载变换器的稳定性机理。首先,分析了源变换器与负载变换器公共耦合点处电压纹波的特性,利用分岔图展示了负载变换器随源变换器和负载变换器电感值变化时的动力学行为。然后,明确了级联VVR控制Buck变换器在一个开关周期内的3种开关状态序列,建立了相应的近似离散映射模型,并推导了不动点邻域内的Jacobi矩阵及其特征根;通过监测Jacobi矩阵的特征根随源变换器和负载变换器电感值变化的运动轨迹,明晰了开关纹波交互作用下负载变换器的失稳机理。特征根分析结果表明,增大源变换器的电感值可以提高负载变换器的稳定性,而增大负载变换器的电感值将降低负载变换器的稳定性。最后,搭建了级联VVR控制Buck变换器的实验样机,结合理论分析给出了相应的电路仿真结果和实验结果。电路仿真结果和实验结果验证了理论分析的正确性。
In a cascaded power converter,the switching ripple interaction between the source converter and the load converter reshapes the voltage ripple at the common coupling point(CCP).When the equivalent series resistance(ESR)of the output capacitor is large,the output voltage ripple of the source converter significantly affects the stability of the load converter.This study examines the effect of the switching ripple interaction on the stability of the load converter using the cascaded valley voltage-ripple(VVR)controlled Buck converter as an example.The operation principle of the VVR-controlled Buck converter is detailed in its schematic diagram and steady-state operation waveforms.When the source converter possesses a large output capacitor ESR,the voltage ripple at the CCP is determined by the voltage across the output capacitor ESR of the source converter.The characteristics of the voltage ripple at CCP are analyzed when the input current ripple of the load converter is fed forward to the output capacitor of the source converter.Based on the relationship between the duty cycles of the source converter and the load converter,the voltage ripple at CCP has three types of waveforms.Typical circuit parameters of the cascaded VVR-controlled Buck converter are selected for circuit simulation to demonstrate the stability effect of the voltage ripple at CCP on the load converter.Based on the typical circuit parameters,two sets of circuit simulation results are obtained.When the load converter is supplied by a constant input voltage(in standalone operation),it operates in a stable period-1 state,whereas when the load converter is supplied by the output voltage of the source converter(in cascaded operation),it operates in an unstable period-2 state.Both the inductance of the source and load converters(L1 and L2)can affect the characteristics of voltage ripple at CCP and are selected as bifurcation parameters to analyze the bifurcation behaviors of the load converter.The bifurcation diagrams with variations of L1 and L2 are presented in this study.As L1 increases from 2 to 20μH,the operation state of the load converter transitions from a chaotic state to an unstable period-2 state through a border-collision bifurcation at L1=6.6μH and then to a stable period-1 state via inverse period-doubling bifurcation at L1=13.2μH.As L2 increases from 40 to 100μH,the operation state of the load converter shifts from a stable period-1 state to an unstable period-2 state via period-doubling bifurcation at L2=53μH.The stability of the VVR-controlled Buck converter in standalone operation is independent of inductance;however,when the converter is in cascaded operation,its stability relates to the inductance of the source and load converters.When both the source and the load converters operate in continuous conduction mode(CCM),the cascaded VVR-controlled Buck converter has four switching states.A map between the state variables at the initial moment and the termination moment of the mth switch state is established by solving the state equation of the mth(m=1,2,3,4)switching state.Under the switching ripple interaction,the cascaded VVR-controlled Buck converter exhibits three switching state sequences in one switching cycle.With consideration of these three switching state sequences,an approximate discrete-time map model of the cascaded VVR-controlled Buck converter is developed.Based on this model,the corresponding Jacobian matrix around the fixed point and its eigenvalues are derived.The stability of the cascaded VVRcontrolled Buck converter can be determined by monitoring the eigenvalues of the Jacobian matrix with variations in the chosen circuit parameters.As L1 decreases or L2 increases,the eigenvalueλ1 exits the unit circle via−1 at L1=13μH or L2=52μH,while the other three eigenvalues,λ2,λ3,andλ4,remain inside the unit circle,resulting in the occurrence of period-doubling bifurcation.Accordingly,typical eigenvalues for different L1 and L2 are listed in this study.The results of eigenvalue analysis are consistent with those of bifurcation analysis.The results showed that increasing the inductance of the source converter enhances the stability of the load converter,whereas increasing the inductance of the load converter diminishes its stability.Circuit simulation results for different L1 and L2 are presented to visually demonstrate the effects of L1 and L2 on the stability of the load converter.Finally,the experimental prototype of the cascaded VVR-controlled Buck converter is established.Based on the circuit simulation results,corresponding experimental results are provided.The experimental results confirm the accuracy of the simulation analysis and theoretical analysis.These results provide theoretical guidance for the parameter design of load converters in cascaded power converters.The research method can also be applied to load converters with other control methods,such as peak-current-mode control.
作者
张希
陆大辉
金立强
闫冠宇
包伯成
ZHANG Xi;LU Dahui;JIN Liqiang;YAN Guanyu;BAO Bocheng(School of Microelectronics and Control Engineering,Changzhou University,Changzhou 213159,China)
出处
《工程科学与技术》
北大核心
2025年第2期256-266,共11页
Advanced Engineering Sciences
基金
国家自然科学基金面上项目(62271088)
江苏省研究生科研与实践创新计划项目(KYCX22_3045)
江苏省高等学校大学生创新创业训练计划项目(202310292040Z)。
