Transient virtual inertia optimization strategy for virtual synchronous generator based on equilibrium point state assessment

This paper investigates transient angle stability of parallel system of two virtual synchronous generators (VSGs) and hybrid system comprised by VSG and diesel generator (DG). Compared to single grid-connected VSG, the paralleled VSGs system and hybrid system are facing larger challenges on stability aspect during serious faults. Although there exist several publications on transient stability, the transient instability mechanism is rather ambiguous, especially for paralleled systems. Besides, swing equations of paralleled VSGs system and paralleled DG-VSG system are established to discuss the dynamic characteristics of the system during short-circuit fault. The increase of power angle between DG and VSG is caused by the different angular accelerations, which deteriorates the transient angle stability of paralleled DG-VSG system. Thus, paralleled DG-VSG system is more prone to instability than paralleled VSGs system, which can be illustrated by power angle (P-δ) characteristic curves. Finally, simulation results validate the correctness of theoretical analyses.

This paper presents a methodology that aims at identifying virtual inertia (VI) gain limitations from virtual synchronous generators (VSGs) while maintaining the frequency stability considering the delay associated with the frequency measurement process. The phase-locked loop (PLL) is typically used for frequency estimation that is used to calculate the rate of change of frequency (RoCoF) and it drives the VI loop. The PLL is generally accompanied by a low-pass filter that aims to suppress the impact of harmonics. This filter introduces a delay that when used with the VI control loop causes stability issues for high values of VI gain. A comparison of various PLL approaches suggests that certain variants tend to permit higher value of cut-off frequencies which can be utilized to increase the VI gain limit from VSG. This study presents a method by which the upper limit on VI gain can be quantified and related to the cut-off frequency of the PLL low pass filter that is indirectly representing the delay. It is performed using small signal frequency stability analysis on the frequency domain model of the grid with virtual inertia emulating VSG. The effective maximum VI gain from VSG is explored while satisfying the frequency measurement accuracy specification considering harmonics. The results show that the requirements of reaching a stable operation with sufficient stability margins can still be met with a faster PLL-based system and the potential increases in VI support from VSG can be quantified using the proposed method. The study has been first performed on a single machine single inverter bus (SMSIB) system and is generalized to the multi-machine and multi-inverter system.

Virtual synchronous generators (VSGs) are prone to over-current and instability issues when grid faults occur. However, directly restraining the current reference in the control system of the VSGs will lead to a loss of connection between the inner current control loop and the outer power loops resulting in synchronization control failure and power angle instability. Besides, the VSGs are also susceptible to transient angle instability issues caused by losing stable operating point during grid faults. Therefore, achieving current limitations and maintaining the stable operation of the VSG is a worthwhile research topic. Hence, this article analyzes the adaptive current limiting characteristics of the VSG with a virtual impedance (VI) method and investigates the transient stability of the VSG under different fault clearance angles. It finds that the inherent growth of the VI during the current limiting process increases the risk of power angle instability. An improved control method is proposed in this article by adjusting the active power reference to account for the changes of the grid voltage and the VI, which is beneficial to enhance the power angle stability of VSGs during grid voltage drops. Besides, an estimation method of the grid voltage is adopted to deal with the instability issues caused by the uncertain grid voltage at the fault point. Then, the influence of grid impedance variation on the proposed method is analyzed, considering the voltage estimation errors, the power angle change, and the active power waste. Finally, the effectiveness of the proposed method is verified through simulation and experiment.

A virtual synchronous generator (VSG) control for converters has been proposed as a method to provide virtual inertia from power electronics connected generation and storage. Most works to date have analyzed VSG control under the assumption that the VSG dynamics are much slower than that the converter. This work shows that when converter and line dynamics are taken into account, the virtual inertia and damping settings are constrained by stability considerations. These conditions for stability are analyzed based on a simple transfer function approach. It is shown that for the VSG to be stable and validly approximated by a second-order system, the ratio of damping to virtual inertia is a key parameter. This letter quantifies how these VSG parameters are constrained by stability. The transfer function analysis is validated using full switching model simulations of stable and unstable cases.

The conventional synchronous generator (SG) can regulate the active and reactive power for frequency and voltage stability, when the system fluctuates. In renewable energy generation system (RES), the stability problem of RES can be solved by adding virtual inertia and damping in the control strategy of the grid-connected inverter. The grid-connected inverter and renewable energy system with this kind of control strategy, called as virtual synchronous generator (VSG), acts as a synchronous generator. In this paper, the topology of grid-connected PV array and energy storage system is proposed. The VSG used in grid-connected inverter, is modelled as stator and rotor model by stator voltage equation and rotor motion equation, respectively. Meanwhile, the VSG control mechanism, based on droop control and model of VSG, can be divided as active power-frequency and reactive power-voltage control. Besides, the system stability is analyzed based on small signal model, for the design of inertia and damping. The simulation model is designed by MATLAB/Simulink for the implementation of VSG. In simulation, it is compared that the dynamic regulation performance of VSG with different control coefficient, such as virtual inertia, virtual damping, droop coefficient and integral coefficient. The optimization for regulation performance in simulation provides an appropriate selection method of the control coefficient for VSG.

In recent years, the proportion of grid-forming converters based on virtual synchronous generator (VSG) has gradually increased in power systems, but the transient synchronization stability after it is connected to the power grid lacks in-depth research. The transient synchronous stability mechanism of VSG is studied in this paper. The transient synchronous stability model of the VSG during grid voltage dropping faults is established. Based on the phase portrait curve method, the instability mechanism of the VSG and the influence of voltage variation on its transient synchronization stability are studied. According to the reactive power and voltage coupling effect, an enhancement measure is proposed to improve the transient synchronization stability by automatically changing the command value of output active power. Finally, through the electromagnetic transient simulation model built in PSCAD/EMTDC, the transient stability mechanism of the VSG grid-connected system and the availability of enhancement measures during grid faults are respectively studied.

This paper addresses the challenge of poor dynamic performance in Modular Multilevel Converter-based High-Voltage Direct Current (MMC-HVDC) systems within weak power grids when conventional control strategies are applied. To enhance system performance, a novel grid-connected power control method integrating Virtual Synchronous Generators (VSGs) and Passivity-Based Control (PBC) is proposed. The passivity characteristics of the MMC and the roles of virtual inertia and damping in VSG control are thoroughly examined. Based on the passivity property of the MMC, PBC is implemented in the current inner loop, while VSG control, leveraging its unique working characteristics, is incorporated into the power outer loop. To further optimize performance, adaptive virtual inertia and damping compensation mechanisms, utilizing sigmoid functions, are introduced within the VSG framework. The synergistic operation of PBC and adaptive VSGs significantly improves the dynamic response and robustness of the MMC-HVDC system. The effectiveness and feasibility of the proposed method are validated through simulation experiments in MATLAB/Simulink, conducted under power variations, grid voltage variations, and load changes.

• The paper focuses on optimising Virtual Synchronous Generator (VSG) control in Modular Multilevel Converter (MMC)-based HVDC systems to enhance power system stability and oscillation damping. • It introduces virtual inertia and damping to mimic synchronous generator behaviour, improving frequency and voltage regulation. • The proposed control strategy ensures smooth transitions between grid-connected and islanded modes, suppresses harmonics, and addresses challenges like low inertia and weak grid conditions. • Simulation results validate the effectiveness of the VSG-controlled MMC in maintaining stability during dynamic and transient events, making it suitable for future power systems with high renewable energy integration. This paper discusses the development of a Virtual Synchronous Generator utilizing a Modular Multilevel Converter. The control system employs an internal simulation of the electromechanical swing equation to replicate the inertia and damping characteristics of a synchronous generator, enabling the generation of the necessary frequency and phase angle for MMC control as a VSG. The ac-side management involves cascaded voltage and current controllers operating within a synchronous reference frame defined by the virtual swing equation. Simulation findings validate the performance of the VSG-controlled MMC when connected to an external AC grid and in islanded mode with a resistive load. This paper validates, through experimentation, the effectiveness of controlling a Modular Multilevel Converter (MMC) as a Virtual Synchronous Generator (VSG) designed to deliver virtual inertia and robust frequency stabilization in power systems with low physical inertia. The proposed control structure incorporates a virtual swing equation, cascaded voltage and current regulation loops, reactive power control, and emulated impedance. A 60 kVA MMC model was employed to demonstrate the system’s capabilities. During frequency disturbances such as a drop from 50 Hz to 49.8 Hz, the controller facilitated dynamic power injection up to approximately 35 kW while capping peak currents at 100 A. Frequency deviations were mitigated within 300 milliseconds, and the converter exhibited seamless transitions to islanded operation along with reliable voltage control during load variations. These findings confirm the proposed controller’s effectiveness in maintaining grid stability under diverse operating conditions.

Attributed to the ability of inertia provision and good regulation performance, the virtual synchronous generator (VSG) has been proven as a promising solution to the problems introduced by using converter interfaced generation. Although the small-signal stability control of the VSG has been widely analyzed, the transient characteristics still needs more study, which belongs to a large-signal problem. In this article, the transient angle stability control of the VSG is investigated. Two possible VSG emulation methods, i.e., the power-emulation and the torque-emulation, are compared from the perspective of transient characteristics. Then, the transient of the VSG internal voltage and its impact on the transient angle stability are quantitatively studied in details. Thereafter, an enhanced VSG controller is proposed, where a large-signal analysis is also presented to evaluate its influence on the acceleration and deceleration areas. Finally, the analysis and effectiveness of the enhanced VSG method are validated by the experimental results.

As a typical grid-forming control method, virtual synchronous generator (VSG) control enhances system inertia but introduces frequency oscillation issues. This problem becomes particularly severe in multi-VSG parallel systems when inconsistent virtual inertia exists among power sources, significantly compromising the security and stability of power system operation. Virtual inertia control can directly regulate the rate of change of frequency (RoCoF) under constant torque difference conditions to suppress frequency oscillations, offering faster response characteristics. Therefore, this paper proposes a distributed virtual inertia control strategy for multi-VSG parallel systems. First, a small-signal model of the multi-machine parallel system is established, and its small-signal stability is demonstrated. Second, a neighbor-communication-based distributed virtual inertia coordination control method is proposed. Through neighbor information exchange and local decision-making, this method enables dynamic adjustment of each unit's virtual inertia, driving frequency synchronization among all units in the system. This effectively suppresses post-disturbance frequency oscillations and enhances the dynamic performance of low-inertia power systems. Furthermore, the stability of the proposed control strategy is rigorously proven through the construction of a Lyapunov energy function. Finally, MATLAB/Simulink simulations verify that the proposed virtual inertia control strategy can effectively mitigate frequency oscillations while reducing their settling time.

Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time

The recently proposed concept virtual synchronous generator (VSG) has been intensively researched. Its core idea is to add a segment in traditional inverter control to simulate synchronous generator's rotor motion characteristic so that the distributed energy resources (DER) can have virtual inertia. VSG control usually contains output current amplitude limiting part to avoid too large current from damaging the inverter, so the output current may saturate under big disturbance, which could cause more complicated stability problems. This paper first analyzes the power-angle characteristic of VSG in stable operation and output current saturation condition, and then utilizes the equal area criterion used in synchronous generator stability analysis to calculate the fault critical clearing angle. On this basis, an adaptive control strategy of inertia and damped coefficient is proposed, which could significantly prolong the fault critical clearing time (CCT) and decrease frequency fluctuation, thus improving the system transient stability. Finally, the simulation results based on MATLAB/Simulink verify the validity and advantage of the proposed control method.

Transient stability analysis of a grid-connected type-4 wind turbine with grid-forming control during the fault

In recent researches on inverter-based distributed generators, disadvantages of traditional grid-connected current control, such as no grid-forming ability and lack of inertia, have been pointed out. As a result, novel control methods like droop control and virtual synchronous generator (VSG) have been proposed. In both methods, droop characteristics are used to control active and reactive power, and the only difference between them is that VSG has virtual inertia with the emulation of swing equation, whereas droop control has no inertia. In this paper, dynamic characteristics of both control methods are studied, in both stand-alone mode and synchronous-generator-connected mode, to understand the differences caused by swing equation. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results are verified by simulations and experiments. It is suggested that VSG control and proposed inertial droop control inherits the advantages of droop control, and in addition, provides inertia support for the system.

Virtual Synchronous Generator technology improves the frequency dynamic performance of the system by introducing virtual inertia and damping coefficients into the power electronic inverter. In order to further suppress power oscillations and solve the problem that constant virtual parameters cannot take into account the maximum frequency overshoot and response speed, firstly, a small-signal model of active and reactive power rings of virtual synchronous machine is established to study the influence of virtual inertia on the frequency stability and power equalization effect of parallel connection of multiple machines. Secondly, based on the fuzzy control method in variable universe, the control strategy of coordinated adaptive adjustment of the virtual inertia of the parallel system according to the output angular frequency is proposed, and at the same time, the automatic adjustment of the virtual damping coefficient with the inertia is realized by combining with the appropriate damping ratio. Finally, the parallel parameter matching principle is designed so that the output power can be distributed according to the capacity ratio. Two different virtual synchronous machine control strategies are compared and analyzed by matlab/simulink to verify the correctness and feasibility of the proposed adaptive control strategy.