In the modern power grid, characterized by the increased penetration of power electronics and extensive utilization of renewable energy, inverter-based power plants play a pivotal role as the principal interface of renewable energy sources (RESs) and the grid. Considering the stability characteristics of grid-following (GFL) inverters when the grid is relatively weak, the application of grid-forming (GFM) controls becomes imperative in enhancing the stability of the entire power plant. Thus, there is an urgent need for suitable and effective models to study the interaction and stability of the paralleled inverters employing GFL and GFM controls. Thus, the small-signal modeling with full-order state-space model and eigenvalues analysis are presented in this paper. First, the small-signal state-space model of the individual GFL and GFM inverters is obtained, considering the control loop, interaction, reference frame, transmissions, and time delays. Then, the models of the individual inverter are extended to the hybrid inverters to study the effects of the GFM inverters on the small-signal stability of the entire system. And the impacts of the inertia and damping are analyzed by the eigenvalues of the state-transition matrix. A case comprising three parallel GFL inverters and two GFL inverters with one GFM inverter, respectively, are studied to examine the effectiveness and accuracy of the model. Finally, the stability margin obtained from the eigenvalue analysis of the entire system is verified by time-domain simulations.

With the rapid development of renewable energy sources such as wind power and photovoltaics, the penetration rate of power electronic equipment represented by grid-forming (GFM) and grid-following (GFL) converters in the power system has been increasing. The development of modern power systems is gradually showing a trend of high proportion of renewable energy and high proportion of power electronic devices (double-high), which profoundly changes the dynamic characteristics of modern power systems. Most of the converters in the power system adopt the GFL control strategy, which lacks the ability to support frequency and voltage. The converter with GFM control have gradually been incorporated into high-proportion renewable energy systems due to their voltage support and inertial response capabilities. However, the proportion configurations of GFM converter in the GFM/GFL hybrid system still needs to be further investigated. Therefore, this paper compares the basic principles and control methods of converters based on GFM strategy and GFL strategy, establishes the small-signal model of 100% REI system, and comparatively analyzes the dynamic characteristics of GFM and GFL converters. Secondly, a proportional configuration method for the GFM converter in 100% renewable electricity independent system (100% REI system) is proposed, and then through the small-signal model, the influence of different proportions of GFM converters and control mode on the stability of 100% REI system is discussed, the minimum configuration proportion of GFM converter to satisfy the stable operation of the system is explored. Finally, the correctness of the proportional configuration of GFM converters proposed in this paper and the engineering feasibility of independent operation of 100% REI system is verified.

High-voltage direct current (HVDC) technology based on Line Commutated Converter (LCC) is widely used in modern power systems due to its numerous benefits. However, as a typical power electronic device, LCC-HVDC has caused significant changes in the dynamic behavior of modern power systems due to largely replaced conventional power supplies in power systems. The interactions among sending-terminal and receiving-terminal system become stronger and have caused some stability issues, but the mechanism behind this has yet to be fully revealed. In order to analyze the interactions among sending-terminal and receiving-terminal system of LCC-HVDC, a small-signal model of modular HSS modeling is proposed based on Harmonic State Space (HSS) theory. Comparison of time-domain response with detailed switching model shows that the proposed can well reflect the dynamic behavior of the detailed switching model. Based on the model, the influence of controller’s parameters on system stability is analyzed, as well as the dynamic interactions of LCC-HVDC among sending-terminal and receiving-terminal system are investigated. Analytical results demonstrate that there exists interactions among sending-terminal and receiving-terminal system which have an influence on the stability of the system.

In some areas, such as Gansu in China and Texas in the USA, lots of wind power bases are located far away from load centers. Transmitting large amounts of wind power to load centers through long transmission lines will lead to wind turbines being integrated into a weak grid, which decreases the stability limits of wind turbines. To solve this problem, this study investigates the stability limits of a Doubly Fed Induction Generator (DFIG) connected to a weak grid in a DC-link voltage control timescale. To start with, a model of the DFIG in a DC-link voltage control timescale is presented for stability limit analysis, which facilitates profound physical understanding. Through steady-state stability analysis based on sensitivity evaluation, it is found that the critical factor restricting the stability limit of the DFIG connected to a weak grid is ∂P_e/∂ (−i_rd), changing from positive to negative. As ∂P_e/∂ (−i_rd) reaches zero, the system reaches its stability limit. Furthermore, by considering control loop dynamics and grid strength, the stability limit of the DFIG is investigated based on eigenvalue analysis with multiple physical scenarios. The results of root locus analysis show that, when the DFIG is connected to an extremely weak grid, reducing the bandwidth of the PLL or increasing the bandwidth of the AVC with equal damping can increase the stability limit. The aforesaid theoretical analysis is verified through both time domain simulation and physical experiments.

Grid-forming wind turbines (GFM-WTs) based on virtual synchronous control can support the voltage and frequency of power system by emulating the synchronous generator. The dynamic characteristics of a GFM-WT decided by virtual synchronous control, dq-axis voltage, and current control is significant for small-signal stability analysis. This paper builds a small-signal model of a GFM-WT in active power control (APC) and DC voltage control (DVC) timescale from the perspective of internal voltage. The proposed model describes how the magnitude and phase of the internal voltage are excited by the unbalanced active and reactive power when small disturbances occur. Interactions in different control loops can be identified by the reduced order model. We verify the accuracy of the proposed model in APC and DVC timescales by time domain simulations based on MATLAB/Simulink. Case studies show how the control parameters interact with each other in the two timescales.

In the modern power grid, characterized by the increased penetration of power electronics and extensive utilization of renewable energy, inverters-based power plants play a pivotal role as the principal interface of renewable energy sources (RESs) and the grid. Considering the stability characteristics of grid-following (GFL) inverters when the grid is relatively weak, the application of grid-forming (GFM) controls becomes imperative to enhance the stability of the entire power plant. Thus, there is an urgent need for suitable and effective models to study the interaction and stability of the paralleled inverters employing GFL and GFM controls. Thus, the small-signal modeling with full-order state space model and eigenvalues analysis is presented in this paper. First, the small-signal state-space model of the individual GFL and GFM inverters is obtained considering the control loop, interaction, reference frame, transmissions, and time delays. Then, the models of the individual inverter are extended to the hybrid inverters to study the effects of the GFM inverters on the small- signal stability of the entire system. And, the impacts of the inertia and damping are analyzed by the eigenvalues of the state-transition matrix. Case comprising three parallel GFL inverters and two GFL inverters with one GFM inverter, respectively, are studied to examine the effectiveness and accuracy of the model. Finally, the stability margin obtained from the eigenvalue analysis of the entire system is verified by time-domain simulations.