Synchronization Stability Modeling And Analysis Of VSC-tied Systems Under DC-link Voltage Timescale

With the development of power electronic technology and the requirements of clean energy for economy and society,the traditional power systems based on fossil energy are gradually changing into the new generation power system dominated by renewable energy.The power system is undergoing a great revolution.In recent years,with great increasing penetration of wind and photovoltaic energy,the large-scale blackouts caused by power electronic devices have been reported,which seriously threatens the safe and stable operation of power systems.Different from the synchronous generators with rotor motion as the core,the dynamic of power electronic devices is dominated by diversified control.The traditional power system analysis based on the rotor synchronization is not suitable for current devices.Grid-following and grid-forming are two basic kind of controls of power electronic devices.Many of existing research on the two kinds of devices are focusing on the single-machine grid-connected system.A systematic and unified theory to understand the essential difference between their synchronization principle is still lacking.In addition to the complex interaction between multiple timescales,all these hinder the application and development of the power-electronic-based power systems.This paper focuses on the comparative analysis of the synchronization principle of grid-following and grid-forming devices.Furthermore,the synchronization models with only considering the synchronization loop and considering the influence of outer control loop are constructed and studied.Based on mathematical analysis,simulation and experimental verification,the research begins from the single-VSC grid-connected system and gradually goes deep into the multi-VSC system.The details are as follows:(1)According to the multi timescale characteristics of power electronic devices,with all the nonlinearities preserved,the DC voltage timescale model of single-VSC gridconnected system is constructed.Based on the theories of nonlinear dynamics,the characteristics of nonlinear dynamical systems such as Hopf bifurcation and the basin of attraction are analyzed in a high dimensional space.Under the voltage drop fault,it finds that the system stability of power-electronic-based power systems is still determined by whether the system state is within or out of the basin of the equilibrium point.In addition,the discontinuity of the amplitude and phase of the terminal voltage is found,and the relationship between fault depth and critical failure duration is studied.(2)For multi-VSC system,the detailed nonlinear model within electromagnetic timescale model is established.Then,by using the singular perturbation technique,a reduced-order model within the DC-link timescale is obtained.The relationship between the input and output variables of each subsystem is well clarified.The proposed model consists of differential algebraic equations and keeps slow dynamics in transient processes.Finally,the model is compared with the traditional electromechanical dynamical model of power systems,which are dominated by synchronous generators.(3)For the multi-VSC system with only synchronization loop considered,the paper researches the synchronization principle of the grid-following and grid-forming devices.The grid-forming devices mimics the synchronous generators and directly establishes the relationship between the active power and the voltage phase.In a sharp contrast,the gridfollowing devices is affected by both active power and reactive power.Its power factor angle drives the dynamic of the current phase.The synchronization small-signal stability models are established for multi-converter power system,within the framework of the classical Phillips-Heffron model for the traditional power system.Based on that,the influence of the control parameters of phase-locked loop and virtual synchronization loop on inertia and damping are revealed.(4)For the multi-VSC system with the outer loop control and synchronization loop both considered,the synchronization models of grid-following and grid-forming devices are constructed in the frequency domain.Extending the concept of participation factor in the modal analysis,the correlation factors between input/output ports and characteristic functions are defined,establishing a bridge from small-signal stability to the characteristic trajectory/function and then to the input/output ports.Based on that,the method of identifying the instability dominanted device is proposed,Finally,adopting two weak stability systems as examples,the stabilities are effectively improved by modifying the control parameters of the instability dominanted devices,which verifies the efficiency of the proposed method.This paper establishes the nonlinear models of single-VSC grid-connected system and multi-VSC system within the DC voltage timescale.From the perspective of nonlinear dynamics,the stability rules of single-VSC system under large disturbance are revealed.Focusing on the synchronization principle of the grid-following and grid-forming devices,the paper analyzes the small-signal stability of multi-VSC system.The influence of the control parameters of phase-locked loop and virtual synchronization loop on inertia and damping are revealed.Furthermore,considering the outer loop control,a method for identifying the instability dominanted devices in multi-VSC system is proposed.Hope these researches could provide a theoretical basis for understanding the synchronization stability of new generation power system dominated by renewable energy.