Small Signal Modeling And Stability Study Of DC Microgrid

With the depletion of fossil energy and the increase in global energy demand,the development of renewable energy is imminent.Renewable energy is uncertain and intermittent,and direct access to the grid will affect the reliable operation of the grid.In response to the above problems,the use of DC microgrids to integrate distributed energy and power loads can provide efficient and reliable power supply solutions.However,with the massive access of distributed power,energy storage and loads,the interaction and influence of multiple converters connected to the DC bus can easily cause the instability of DC bus voltage,threatening the safe operation of the system.Therefore,studying the stability of the DC microgrid system and its evaluation method is of great significance to ensure the safe and stable operation of the system.This thesis has carried out the small-signal modeling and stability research of the DC microgrid system.The main content includes two parts:the first part studies the small signal modeling of the switching converter subsystem in the DC microgrid system,and proposes a unified model unit to simplify the model of the entire DC microgrid system and provide a theoretical basis for the stability of the DC microgrid system;the second part,based on the research content of the first part,studies the stability of the multi-bus DC microgrid system and the bipolar DC microgrid system.Part 1:Small signal modeling and stability of the switching converter subsystem in the DC microgrid systemTaking the ripple-controlled buck converter as an example,the limitations of the existing average modeling method are revealed.The averaging method is improved by introducing the unified sample-hold effects of inductor current and output voltage respectively,and improved small signal models of the buck converter for ripple controls(including current mode control,V~2 control,and V~2C control)are proposed,which are simplified by the SIMPLIS simulation.The frequency domain characteristics of different ripple controls when the equivalent series resistance of the capacitor and the duty cycle change are analyzed in detail,and the relevance of each ripple control is revealed.The stability of the converter is analyzed using the Routh-Hurwitz criterion.The validity of the improved small signal model and the accuracy of theoretical analysis are verified through experiments.The research results show that the improved small-signal model of the buck converter with ripple controls(current mode control,V~2 control,V~2C control)have the advantages of simplicity and accuracy.It not only reveals the sub-harmonic oscillation well,but also effectively predicts the stability regions,which provide design guidelines for practical application.Moreover,introducing of the output voltage into the inner loop will increase the transient response of the current mode control,while introducing of the inductor current into the inner loop can expand the stability range of the V~2 control.The output voltage ripple of boost converter is different from the output voltage ripple of the buck converter,which is a discontinuous form.So the modeling of the valley V~2controlled buck converter cannot be applied to the valley V~2 controlled boost converter.According to the concept of average output voltage area,an average small-signal model of the valley V~2 controlled boost converter is established.The continuous virtual output voltage is constructed,then the sample-hold effect of the continuous output voltage is obtained through the sampling data method.based on that,adding the sample-hold effect of inductor current,an improved small signal model of the valley V~2 controlled boost converter is obtained.The effects of output capacitor equivalent series resistance(ESR),duty cycle,slope compensation slope,and compensator parameters on the transient performance and stability of the valley V~2 controlled boost converter is investigated by frequency domain analysis.It provides guidance for the design of valley V~2 controlled boost converter.The research results show that the improved small signal model of valley V~2 controlled boost converter is accurate to one-half of the switching frequency,which is simple and provide an idea for modeling switching converters with intermittent output voltage ripple.When the ESR or duty ratio is small,the valley V~2 controlled boost converter has better load transient performance and poor stability;when the ESR or duty ratio is large,the valley V~2 controlled boost converter has better stability performance,poor transient performance.The basis of the stability study of the DC microgrid system is to model the various subsystems in the DC microgrid system.However,for switching converters with different control technologies,or switching converters with different topologies,the small signal models of the switching converter and its control system are different,which makes the small signal model of the entire system complicated and irregular.Based on a comprehensive summary of the existing switching converter and controller modeling,this paper reveals the differences and connections of various control technologies,and further unifies the small signal model unit of the switching converter and its controller.The power stage model unit of the basic switching converter is proposed,and eight complete transfer functions are given.The model unit with introduction of two coefficients F_c and F_L is used to represent the controller which reveals the unity of various control technologies.On the basis of the model unit of the power stage and the controller and introduction of the sample-and-hold effects of inductor current and output voltage is introduced,the unified model unit of the basic switching converter with different control technologies is obtained.The proposed unified model unit can not only design the converter from the subsystem level,but also provide theoretical support for the stability analysis of the system composed of switching converters from the system level.Frequency domain analysis and experiments are used to verify the accuracy of the unified model unit and the effectiveness of the stability analysis of the system composed of switching converters.The research results show that the proposed unified model unit unifies the small signal models of the basic switching converters using different control technologies,which is simple and accurate.The unified model unit is used for system stability analysis,revealing the sub-harmonic oscillation in the system consisted of the switching converter which has been neglected in traditional stability studies.Part 2:Stability of multi-bus DC microgrid system and bipolar DC microgrid systemAccording to the operation of the multi-bus DC microgrid system,a generalized voltage source,a generalized current source and a two-port model are used to describe the subsystems in the microgrid system.Then,the basic form of the multi-bus DC microgrid system is obtained.According to Thevenin and Norton theorem,the multi-bus DC microgrid system is simplified,and the impedance and admittance of different bus ports are derived.The equivalent conversion between the Nyquist diagram and the Bode diagram is analyzed,and the generalized Bode diagram criterion is used to evaluate the stability of the multi-bus DC microgrid system.The process of judging the stability of the multi-bus DC microgrid system is studied.Regarding the intermediate bus voltage converter and its connected single-bus DC microgrid system as a whole part,an expansion unit is proposed to explore the scalability of the stability evaluation method of the multi-bus DC microgrid system.The research results show that the proposed multi-bus DC microgrid system stability evaluation method does not limit the subsystems,that is,it will not restrict the subsystems with the right half plane zero and pole.This method can judge the stability of each DC bus ports in the microgrid system separately which is simple,accurate and suitable for plug-and-play applications.By introducing the expansion unit,the proposed method can be extended to the more complex DC microgrid system stability research;by deleting the expansion unit,the stability of the single bus DC microgrid system can be studied.The simplified form of the bipolar DC microgrid system is discussed in detail from the perspective of the relevance of the three bus ports.The stability criterion based on impedance sum is adopted to obtain the stability conditions for the bipolar DC microgrid system.The proposed stability evaluation method can separately evaluate the stability of each bus port in the bipolar DC microgrid system,and the judgment method is intuitive and simple which is easy to expand.Three cases are used,namely:1)positive voltage PG and the negative voltage GN bus port loads are symmetrical or asymmetric;2)the negative voltage GN bus port introduces photovoltaic units and energy storage units;3)the positive and negative voltage PN bus port introduces photovoltaic units and energy storage units,to verify validity and accuracy of the stability evaluation method.The mutual influence of the stability of different bus ports is explored,and the instability phenomenon that may be caused by asymmetrical loads connected to the symmetrical bus port is analyzed and revealed.The research results show that the oscillation of the positive voltage PG bus port and the negative voltage GN bus port has almost no effect on the positive and negative voltage PN bus port,but the stability of the PN bus port will affect both the PG and GN bus ports.The stability of the PG and GN bus ports will influence each other.When the load resistance connected in the bipolar DC microgrid system is relatively small,the system will become unstable;when an unbalanced load is connected to the symmetrical bus port,both bus ports will oscillate.The introduction of photovoltaic unit and energy storage unit can improve the instability in the bipolar DC microgrid system.