Small-signal Modeling And Stability Analysis Of DC Grid Based On Voltage Source Converters

The high voltage direct current transmission technology based on voltage source converter(VSC-HVDC)has the advantages of decoupling control of active and reactive power,being accessible to passive power grid,et al.Moreover,it avoids the commutation failure problem.It is well acknowledged that the VSC-HVDC is a promising approach to the integration and long-distatnce transmission of bulk power of renewable energy.Up to now,normalized small-signal modeling method and systematic small-signal analysis are still insufficient regarding VSC based DC grid.This paper will thoroughly study the state-space model,steady-state model and small-signal model of three common VSCs.Key issues such as efficient modeling of bulk VSC based DC grid,impact of various parameters on the small-signal stability and schemes to enhance the small-signal stability will be discussed.The main contents and contributions are summarized as follows:(1)The generalized modeling methods of the state-space model,steady-state analytical model and small-signal model for the two-level VSC,half-bridge sub-module based modular multilevel converter(MMC)and hybrid sub-module based MMC are researched.The correctness of the modeling method is validated by comparing the time-domain response of the proposed models against electromagnetic models.The connection quantites between the electric system of converters,control systems of the converters,AC system and DC networks are normalized,which makes it convenient to create the state-space model and small-signal models of bulk VSC based DC grid.The generalized modeling methods provide a set of powerful tools for analytically analyzing the dynamic characteristics and the stability issue.(2)A calculation method for totally analytical analysis of the operating characterisitcs for VSC is realized.Based on the steady-state model,given the active power and reactive power of the converter,the steady-state values of the electric quantities including the internal dynamics of MMCs and the control quantities including the arm modulation signals are analytically calculated,which realizes the closed-loop analysis.The calculation method for the active and reactive power region considering multiple operating constraints is proposed.The influence of different VSC parameters on the operating region is analyzed,which provides a powerful tool aiming at designing the parameters and quantitatively analyzing the power ability of VSCs.(3)Focused on the bulk VSC-HVDC modeling,a modularized modeling method is proposed.The whole system is divided into three sub-systems,namely AC system,VSCs and DC networks.The state-space model and small-signal model of the sub-systems are provided.Based on the coupling relation among differnet sub-systems,the linking equations are established,then the whole model is created in a modularized way.Since tha generic controller equipped with control flags is adopted,VSC with different control modes can be modeled using the same modeling frame,which alleviates the derivation burden for bulk VSC based DC grid.(4)The impact of DC reactors on the small-signal stability of MMC based DC grid is analyzed.The critical values of the DC reactors are indentified using root loci analysis.The influence of the topology and operating status of the system is studied,which reveals the embedded interaction among the DC reactors,DC network topology and VSC operating status.The research results serve for the DC reactors sizing,DC network topology designing and power operating status configuration.Based on the parcipating factor analysis,the optimized input signals and installation points of the damping controllers are proposed.By the small-signal modeling of the system after introducing the damping controller,the optimized control parameters for the damping controller are analyzed.The electromagnetic simulation verifies the correctnees of the analysis and the effectiveness of the damping controller.The proposed damping control offers a solution to improving the stability.(5)The impact of different control parameters including the inner control loop,outer control loop,droop control and bandwidth of the signal filters is studied.The critical values of different control paramtes are identified using root loci method.The unstable modes and dominant state-variables are analyzed,which reveals the general rule of the impact of various control parameters.The influnece of the oprating status is analyzed,and the independency of some control parameters on the operating status regarding statbility issues is revealed.Suggestion regarding the value seclection for control parameters and operating status configuration is provided to maintain the stability of the system.