Nonlinear Modeling And Transient Synchronous Stability Analysis Of PLL-based VSC Systems

With large-scale development and utilization of renewable energy,an increasing amount of it is being integrated into power systems through power electronic apparatuses.Due to the essential differences between the power electronic apparatus and the synchronous generator(SG)in physical characteristics,the dynamic processes of renewable-dominated power systems(RDPS)have changed considerably.Recently,transient instability incidents induced by the power electronic apparatus have occurred occasionally,threatening the operation of power systems and restricting the consumption of renewable energy.In the realm of the transient synchronous stability of SG-dominated power systems,it has developed a mature modeling and analysis framework based on the rotor swing motion within the electromechanical timescale,which has successfully guided operations and analyses.For the voltage source converter(VSC),its dynamic behaviors are determined by multi-timescale cascading control and system parameters,which results in fundamental changes in the synchronous mechanism and characteristics of power systems.Based on the multiple timescale’s characteristics and the singular perturbation theory,existing studies have analyzed the transient stability mechanism of the VSC based on reduced-order models.However,when the bandwidths of different controller are close,the dynamic behaviors of different control loops are close,which induces strong couplings.These make it difficult to identify dominant loops and reduce the original high-order models.In addition,there exist distinct differences between the VSC and SG in the modeling and dynamic behaviors.Thus,traditional modeling and analysis methods are not applicable to multi-VSC power systems.To address these problems,the nonlinear modeling and transient synchronous stability of phase-locked loop based(PLL-based)VSC power systems are analyzed and studied based on the theory of the basin of attraction(BOA),manifold,and bifurcation analysis.First,this dissertation carries out the modeling and analysis of a single-VSC system based on the higher-order model.Then,the transient dominant branches and state variables are identified based on the proposed controlling unstable equilibrium point(CUEP)based method.Correspondingly,the reduced-order models are established for analyzing the transient synchronous stability.Meanwhile,the synchronous stability of the single-VSC system is revealed based on the proposed generalized swing equation.Moreover,based on the reduced-order model and the theory of BOA,the transient stability of multi-VSC systems is analyzed and revealed.The main findings are given as follows.(1)The nonlinear dynamics of the single-VSC system is analyzed and revealed,and the mechanism of sustained oscillations is revealed.Based on the nonlinear dynamics methods,Hopf bifurcation,saddle node bifurcation,saddle-node bifurcation of the limit cycle,and stable/unstable limit cycles are analyzed and studied.Meanwhile,the time-domain characteristics of sustained oscillations are quantitatively analyzed through Bessel expansion.It shows that the current signals in the three-phase coordinate perform multiple sideband frequencies which are symmetric about the fundamental frequency.(2)A CUEP-based participation factor method is proposed to determine the transient dominant branches and state variables.Based on the proposed method,the dominant branches of the PLL-based(grid-following)and grid-forming VSC are quantitatively analyzed,respectively.It is found that synchronous controls dominate the transient stability of both types of VSCs,while the active power balance branches play a secondary role.Accordingly,two reduced-order models are proposed.By additionally comparing the roles of different branches in the VSC and SG,it is also found that angle synchronization and power balance of the VSC are reflected respectively by the synchronous controls and the DC capacitor,while they are combinedly reflected by the rotor swing.(3)A second-order model(generalized swing equation)is proposed to evaluate the transient synchronous stability of the single-VSC system considering only dynamics of the PLL.Based on the equal area criterion,the critical clearing angle under different faults is quantitatively calculated.The normalized generalized swing equation is established by normalizing the time variable.The nonlinear dynamics of the single-VSC system have been analyzed,including generalized saddle-node,Hopf,and homoclinic bifurcations.(4)The hyperplanes method is extended to the realm of transient synchronous stability of multi-VSC systems.Based on the second-order model of the VSC and the quasi-steady-state network model,the hyperplanes method is applied to quantitatively calculation of the fault critical clearing time in the single VSC,parallel VSC,IEEE3-machine-9-bus,and 10-machine-39-bus systems.The accuracy and effectiveness of the proposed method are verified by comparison with electromagnetic transient simulations.Within the limit of established models,the resilience of the RDPS is considerably smaller than that of the traditional power system in the transient stability,implying that faster control and relaying may be imperative.