Abstract:The gradual penetration of grid-forming (GFM) converters into new power systems with renewable energy sources may result in the emergence of small-signal instability issues. These issues can be elucidated using sequence impedance models, which offer a more tangible and meaningful interpretation than dq-domain impedance models and state-space models. However, existing research has primarily focused on the impact of power loops and inner control loops in GFM converters, which has not yet elucidated the precise physical interpretation of inner voltage and current loops of GFM converters in circuits. This paper derives series-parallel sequence impedance models of multi-loop GFM converters, demonstrating that the voltage loop can be regarded as a parallel impedance and the current loop as a series impedance. Consequently, the corresponding small-signal stability characteristics can be identified through Bode diagrams of sequence impedances or by examining the physical meanings of impedances in series and in parallel. The results indicate that the GFM converter with a single power loop is a candidate suitable for application in new power systems, given its reduced number of control parameters and enhanced low-frequency performance, particularly in weak grids. The results of PLECS simulations and corresponding prototype experiments verify the accuracy of the analytical analysis under diverse grid conditions.

Abstract:Oscillations caused by small-signal instability have been widely observed in AC grids with grid-following (GFL) and grid-forming (GFM) converters. The generalized short-circuit ratio is commonly used to assess the strength of GFL converters when integrated with weak AC systems at risk of oscillation. This paper provides the grid strength assessment method to evaluate the small-signal synchronization stability of GFL and GFM converters integrated systems. First, the admittance and impedance matrices of the GFL and GFM converters are analyzed to identify the frequency bands associated with negative damping in oscillation modes dominated by heterogeneous synchronization control. Secondly, based on the interaction rules between the short-circuit ratio and the different oscillation modes, an equivalent circuit is proposed to simplify the grid strength assessment through the topological transformation of the AC grid. The risk of sub-synchronization and low-frequency oscillations, influenced by GFL and GFM converters, is then reformulated as a semi-definite programming (SDP) model, incorporating the node admittance matrix and grid-connected device capacities. The effectiveness of the proposed method is demonstrated through a case analysis.

Abstract:The integration of converter-interfaced generators (CIGs) into power systems is rapidly replacing traditional synchronous machines. To ensure the security of power supply, modern power systems require the application of grid-forming technologies. This study presents a systematic small-signal analysis procedure to assess the synchronization stability of grid-forming virtual synchronous generators (VSGs) considering the power system characteristics. Specifically, this procedure offers guidance in tuning controller gains to enhance stability. It is applied to six different grid-forming VSGs and experimentally tested to validate the theoretical analysis. This study concludes with key findings and a discussion on the suitability of the analyzed grid-forming VSGs based on the power system characteristics.

Abstract:This paper presents a Phillips-Heffron model for the generation unit with current-controlled (CC) voltagesource converter (VSC) as the interface. A concept of current angle is put forward for the CC-VSC, and the relationship between the current angle and the power angle is also quantified. Based on the current angle, a PhillipsHeffron model is established for the generation unit with CC-VSC, considering the dynamic of phase-locked-loop (PLL) in the weak grid. The model demonstrates that small-signal dynamics of the generation unit is similar to that of the traditional synchronous generator (SG) which is characterized by the electromechanical swing equations. Then the dynamics can be depicted by the famous inertia, synchronizing and damping coefficients. Small-signal stability of a CC-VSC-based single machine infinite bus system is analyzed by means of the traditional theory of power system. Based on the relationship between the current angle and the power angle, the Phillips-Heffron model of the CC-VSC is also used in stability analysis of multimachine power system, and parameter optimizations of the CC-VSC are also studied for stability improvement.

Abstract:With the rapid growth of grid-connected wind power penetration level, it is necessary to study the impacts of wind power on power system stability. The small-signal stability of power systems with large-scale wind power is explored using the eigenvalue analysis method. A prototype sample system, the two-synchronous-generator system with awind farm, is proposed for the oretical analysis. Then, simplified models of wind turbines (WTs) and the corresponding equivalent models of wind farms are analyzed. Three kinds oftypical WT models, i.e., squirrel cage induction generator,doublyfed induction generator, and permanent magnet synchronous generator are used. Furthermore, based on thesimplified equivalent models, effects of large-scale windfarms on the electromechanical oscillation modes (EOMs) of synchronous systems are discussed. Simulation results indicatethat wind farms of the three kinds of WTs have positive effects on EOMs. However, long transmission lines connecting wind farmto the system may produce negative effectson the small-signal stability of the system.

Abstract:Active damped LCL-filter-based inverters have been widely used for grid-connected distributed generation (DG) systems. In weak grids, however, the phase-locked loop (PLL) dynamics may detrimentally affect the stability of grid-connected inverters due to interaction between the PLL and the controller. In order to solve the problem, the impact of PLL dynamics on small-signal stability is investigated for the active damped LCL-filtered grid-connected inverters with capacitor voltage feedback. The system closed-loop transfer function is established based on the Norton equivalent model by taking the PLL dynamics into account. Using an established model, the system stability boundary is identified from the viewpoint of PLL bandwidth and current regulator gain. The accuracy of the ranges of stability for the PLL bandwidth and current regulator gain is verified by both simulation and experimental results.

Abstract:To tackle emerging power system small-signal stability problems such as wideband oscillations induced by the large-scale integration of renewable energy and power electronics, it is crucial to review and compare existing small-signal stability analysis methods. On this basis, guidance can be provided on determining suitable analysis methods to solve relevant small-signal stability problems in power electronics-dominated power systems (PEDPSs). Various mature methods have been developed to analyze the small-signal stability of PEDPSs, including eigenvalue-based methods, Routh stability criterion, Nyquist/Bode plot based methods, passivity-based methods, positive-net-damping method, lumped impedance-based methods, bifurcation-based methods, etc. In this paper, the application conditions, advantages, and limitations of these criteria in identifying oscillation frequencies and stability margins are reviewed and compared to reveal and explain connections and discrepancies among them. Especially, efforts are devoted to mathematically proving the equivalence between these small-signal stability criteria. Finally, the performance of these criteria is demonstrated and compared in a 4-machine 2-area power system with a wind farm and an IEEE 39-bus power system with 3 wind farms.

Abstract:The renewable energy sources (RESs) dominated power grid is an envisaged infrastructure of the future power system, where the commonly used grid following (GFL) control for grid-tied converters suffers from lacking grid support capability, low stability, etc. Recently, emerging grid forming (GFM) control methods have been proposed to improve the dynamic performance and stability of grid-tied converters. This paper reviews existing GFM control methods for the grid-tied converters and compares them in terms of control structure, grid support capability, fault current limiting, and stability. Considering the impact of fault current limiting strategies, a comprehensive transient stability analysis is provided. In addition, this paper explores the typical applications of GFM converters, such as AC microgrid and offshore wind farm high-voltage direct current (OWF-HVDC) integration systems. Finally, the challenges to the GFM converters in future applications are discussed.

Abstract:This paper proposes a dynamic-decision-based realtime dispatch method to coordinate the economic objective with multiple types of security dispatch objectives while reducing constraint violations in the process of adjusting the system operation point to the optimum. In each decision moment, the following tasks are executed in turn: ① locally linearizing the system model at the current operation point with the online model identification by using measurements; ② narrowing down the gaps between unsatisfied security requirements and their security thresholds in order of priority; ③ minimizing the generation cost; ④ minimizing the security indicators within their security thresholds. Compared with the existing real-time dispatch strategies, the proposed method can adjust the deviations caused by unpredictable power flow fluctuations, avoid dispatch bias caused by model parameter errors, and reduce the constraint violations in the dispatch decision process. The effectiveness of the proposed method is verified with the IEEE 39-bus system.

Abstract:In the existing small-signal stability constrained optimal power flow (SSSC-OPF) algorithms, only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold, e.g., damping ratio threshold and real-part threshold of eigenvalue, are considered in the small-signal stability constraints. The effect of steady-state, i.e., operating point, changes on eigenvalues is not fully taken into account. In this paper, the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane. The small-signal stability constraint is embedded into the standard optimal power flow model for generation rescheduling. The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach, while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues. To improve the computation speed, a hybrid algorithm for eigenvalue computation in the optimization process is proposed, which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation. The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.