Transient Stability Analysis For Grid-Connected Converters Based On Nonlinear Decoupling Method

The new power system plays a crucial role in achieving the "dual carbon" objective.The "dual high" power system integrates various distributed power sources,energy storage,and new loads.As a result,the system characteristics of the new power system have undergone significant changes when compared to conventional power systems that are predominantly reliant on synchronous generators(SGs).In order to integrate renewable energy power generation units to the power grid,power electronic devices such as voltage source converters(VSCs)are required.Consequently,the dominance of synchronous machines,with their physical characteristics,has been replaced by power electronic devices that are controlled by algorithms.The integration of numerous power electronic devices in the system has led to low inertia and weak damping characteristics,where the dynamic features have shifted from electromechanical transient to electromagnetic transient,primarily due to specific control strategies.The overall dynamics and interdependencies of various control elements have made power systems,with converters acting as interfaces,more susceptible to complex stability issues.Simultaneously,the VSC grid connected system exhibits the low inertia characteristic,resulting in significant changes in state variables during system disturbances,highlighting the prominence of transient stability issues.For an extended period,the lack of effective analysis tools for analyzing the transient stability of grid-connected VSC systems is attributed to the complexities associated with high-order nonlinear,strongly coupled models.The transient stability of high-order nonlinear systems can be examined using the Lyapunov method.However,there is no universally accepted theoretical framework for the selection of Lyapunov functions,leading to considerable variations in stability analysis conclusions based on these choices.The application of the equal-area criterion in gridconnected VSC systems necessitates the reduction of the VSC model’s order to an equivalent second-order model,akin to the swing equation of a synchronous machine.Oversimplification of models and disregard for damping terms pose the risk of erroneous transient stability analysis findings.Therefore,it is urgent to propose new transient stability analysis methods.In response to the above issues,this thesis first clarifies the mathematical essence of the existing mature linear system analysis methods,which is the idea of decoupling.Inspired by the decoupling idea,combining with the normal form method,the innovative coupling-factor-based nonlinear decoupling(CFND)method is proposed.Coupling factor indicators are first established to assess the degree of coupling among different state variables,which enables the classification of state variables into isolated variables and coupling pair variables according to their coupling degree.Next,the nonlinear transformation is derived to transform the higher-order nonlinear model into a series of lower order modes,and mature inverse trajectory as well as phase diagram methods are used to analyze the lower order modes,indirectly reflecting the transient stability of the original system.The CFND method possesses universality,adaptability,insensitivity to system order,and obviates the necessity of constructing corresponding Lyapunov functions for various nonlinear systems,effectively surmounting the inherent limitations of conventional analysis methods.On the basis of the proposed CFND method,transient stability analysis is conducted for gridfollowing and grid-forming VSC systems.Grid-following and grid-forming VSC system exhibit different adaptability to the weak and strong power grid,and there are also significant differences in the control factors that dominate the stability of their grid-connected systems.Currently,the transient stability analysis of the grid-following and grid-forming VSC systems relies on the reduced-order nonlinear model considering the phase-locked loop and the quasi-steady-state model considering the active power outer loop,respectively.The over-simplified reduced-order model completely disregards the influence of the control inner loop and circuit topology,and there is no clear quantitative research on the applicable conditions of the reduced order model.Further,the main factors influencing the transient stability of different grid-connected VSC systems have not been comprehensively analyzed.Therefore,this thesis establishes the full-order large-signal model for grid-following and grid-forming grid-connected VSC system,and applies the CFND method to analyze the model.For grid-following VSC systems,the influence of phase-locked loop bandwidth,current inner loop bandwidth,and the transferred power during low voltage ride through process on system transient stability is clarified.By comparing the transient stability analysis conclusions obtained by the reduced-order model and the full-order model,the quantitative applicable conditions of the reduced-order model are derived.For grid-forming VSC systems,it is explained that the system’s attraction domain is mainly affected by the grid voltage magnitude drop,key parameters in active and reactive power loops,and the control inner loop.Increasing the voltage-reactive droop coefficient will lead to an expansion of the critical mode’s ROA and an inward shift of the initial operation point position.Therefore,increasing the reactive loop voltage droop coefficient can effectively enhance the transient stability performance of the system.Due to the complexity of the topology and control of the grid-connected VSC system,the order of multi-VSC system has sharply increased.Directly considering the detailed mathematical model of the multi-VSC system will impose a huge computational burden on transient stability analysis.Therefore,from the perspective of practical engineering applications,a reduced-order model for multi-VSC grid-connected system is derived.The proposed transient stability analysis method is applied to a three-VSC grid-connected system,which serves as an example.It is revealed that in a grid-connected system,a single large drop in grid voltage is more likely to cause instability compared to a staged drop,and VSCs with higher output active power are more prone to experience transient instability.