Grid-forming inverters (GFMIs) are anticipated to play a leading role in future power systems. In contrast to their counterpart grid-following inverters, which employ phase-locked loops for synchronization with the grid voltage and rely on stable grid connections, GFMIs primarily employ the power-based synchronization concept to form the voltage. Hence, they can not only stably operate in regions of the grid characterized by low strength but also provide critical ancillary services to power systems, including voltage, frequency and inertia support. Several control strategies have been employed for GFMIs, making it crucial to comprehend their stability characteristics for the analysis of small-signal stability and low-frequency oscillations. This article examines the performance of GFMIs when equipped with four different control strategies, namely: droop-based GFMI, virtual synchronous generator (VSG)-based GFMI, compensated generalized VSG (CGVSG)-based GFMI, and adaptive VSG (AVSG)-based GFMI. The comparative analysis assesses the performance and robustness of these four control strategies across various operational scenarios in frequency and time domains. Initially, the impedance-based stability analysis method is employed to evaluate these control strategies across different case studies in terms of grid strengths, grid impedance ratios, the dynamics with/without virtual impedance and inner voltage and current loops, and variations in the inverter's operating points. Subsequently, time domain verification using the electromagnetic transient models are conducted for these case studies as well as to assess the power tracking capability of these control strategies in response to changes in power references. Finally, the robustness of these four controllers is explored against external grid disturbances, including grid frequency deviations, phase jumps, and voltage sags, considering varying levels of disturbance magnitudes in both weak and strong grid connections. In conclusion, the evaluation of these control techniques in various operational scenarios reveals their strengths and weaknesses, offering valuable guidance for the selection of the most appropriate control technique to suit desired practical applications.

The conventional virtual synchronous generator (VSG) is typically designed to meet certain operational and control requirements in the islanded mode. However, once the VSG is switched to grid-connected mode (GCM), the robust operation cannot be guaranteed under different grid conditions. It can lead to poor dynamic performance, especially in strong grids, such as significant oscillation, long settling time, and large overshoot. To improve the VSG performance in the GCM, this article first analyzes in depth the inherent coupling between the active and reactive power and its dependence on grid conditions, such as the short circuit ratio and the grid impedance ratio. Subsequently, an adaptive VSG (AVSG) control strategy based on online grid impedance estimation is proposed to ensure robust operation of the VSG considering both strong and weak grid conditions. This technique allows the operator to specify the desired settling time of the output power and damping ratio. To estimate the grid impedance in real time without additional hardware and reduce the associated impacts on power quality, an online event-based grid impedance estimation algorithm is embedded in the control loop of the AVSG. The simulation and experimental results indicate that, compared with the conventional fixed-parameters-based controller design method, the AVSG exhibits desired performance such as no oscillation, specified time duration for the settling time, and minimal overshoot regardless of the grid conditions.

This article presents a comprehensive comparison of three control strategies used for grid-following inverters (GFLIs). The first strategy is the phase-locked loop (PLL)-based vector current control (VCC), and the other two PLL-less controllers are the voltage-modulated direct power control (VMDPC) and the linear-parameter-varying power-synchronized control (LPV-PSC). The VCC relies on the PLL to synchronize with the grid frequency to control the exchanged real and reactive power with the grid, which may result in instability issues under weak grid conditions. To prevent this, the VMDPC and LPV-PSC are proposed recently as PLL-less approaches to overcome the difficulties of the VCC in weak grid conditions. The performances of the VCC, VMDPC, and LPV-PSC are comprehensively reviewed in this article, considering the operations of the GFLIs under both strong and weak grids. In each operation mode, the provided tests investigate: 1) step response of active and reactive power, 2) frequency jump in the grid voltage source, 3) phase jump in the grid voltage source, and 4) voltage sag in the grid voltage source. In addition to evaluating the three controllers in the time-domain, the frequency-domain impedance-based stability analysis based on the generalized Nyquist criterion is also considered, which confirms the time-domain findings in terms of accurate predictions of the stable/unstable operations of the GFLIs that are equipped with these controllers. It is found that, compared to the conventional VCC and the VMDPC, the LPV-PSC has promising performance under various test conditions in both strong and weak grids, which may be a future solution for weak-grids connection of the GFLIs.

The phase-locked loop (PLL)-based grid-following inverters have been widely used as the interface between renewable energy resources (e.g., wind and solar power) and the utility grid. In addition to the basic PLL and inner current control loop that are responsible for tracking the phase angle of the point of common coupling (PCC) voltage and regulating the current injection according to the estimated phase angle, respectively, these grid-following inverters are commonly also equipped with outer power and voltage control loops. Some examples are outer active power/dc-link voltage control loops and outer reactive power/PCC voltage control loops, which provide the $dq$ -axis current references for the inner current control loop. However, the existing literature generally focuses on specific outer control modes within a specific small-signal modeling framework, e.g., state-space or admittance modeling framework. In addition, different research groups usually repeatedly derive these small-signal models without a systematic modeling and analysis procedure. Furthermore, the systematic and comprehensive comparative modal and admittance analysis of these outer control modes is still missing in the literature. To avoid reinventing the wheel, provide the small-signal stability analysis community with handy both state-space and admittance models, and investigate the effects of various outer control loops on the small-signal models, this article presents a comprehensive and systematic small-signal modeling, analysis, and comparison framework of the PLL-based grid-following inverters, where the state-space and $dq$ -domain admittance models of eleven control modes are derived step by step in a completely followable style. All of these derived small-signal models are verified by the time-domain step responses and frequency-domain $dq$ -domain admittance measurement. The insights into the effects of these outer control modes on the poles and residues of the $dq$ -domain admittance model are also explored, which help to understand how these outer control modes contribute to the $dq$ -domain admittance shaping.

Oscillation phenomena of offshore wind power plant (OWPP)in a wide frequency range can be caused due to impedance interactions between grid-connected inverters (GCIs) and transmission cables. In this paper, impedance model of GCI with outer power control loop, inner current control loop and phase-locked loop is first established in dq reference frame. The correctness is validated by frequency scanning method. Then, the effects of active and reactive power/current references on dq impedance characteristics of GCI with/without consideration of power control loop are investigated using complex space vectors and complex transfer functions. Furthermore, RLC circuit model of transmission cable considering frequency-dependent characteristics is also established for dq-domain IBSC. On the basis of them, it's found that low-frequency oscillation phenomena of OWPP under power control mode may occur if active power reference exceeds a certain threshold value, which can be mitigated by injecting a certain amount of negative reactive power. Impacts of PLL parameters, length of transmission cable and number of paralleled GCIs on required negative reactive power for low-frequency stabilization are further investigated. Both Matlab/Simulink-based simulation and OPAL-RT-based real-time verification are implemented in an OWPP with four permanent magnet synchronous generators to validate the correctness of the reactive power characteristic analysis.

This paper presents a gray-box hierarchical instability source identification method of multiple-inverter-fed power systems, which enables stability analysis at system, component, and parameter levels sequentially. Impedance frequency responses of all components are first obtained using frequency scanning method. System impedance network model is then established by connecting these individual components based on system topology, which is further lumped into a loop impedance model (LIM). The vector fitting (VF) algorithm is then used to generate system state-space model from the impedance frequency responses of the LIM for eigenvalues-based stability analysis. If the system is assessed to be unstable, problematic components are further identified by performing impedance-based stability criterion at terminals of all components, where the numbers of right-half-plane poles are obtained by the VF algorithm. Finally, circuit and controller parameters of the identified problematic components are further identified using the VF algorithm, which are re-tuned to improve system stability. The proposed hierarchical instability source identification method is implemented in a multiple-paralleled grid-connected inverter system. Simulation results obtained in Matlab/Simulink platform and real-time simulation verification results obtained in OPAL-RT platform are given to validate the correctness of the theoretical analysis results.