Abstract
As more and more power electronic based generation units are integrated into power systems, the stable operation of power systems has been challenged due to the lack of system inertia. In order to solve this issue, the virtual synchronous generator (VSG), in which the power electronic inverter is controlled to mimic the characteristics of traditional synchronous generators, is a promising strategy. In this paper, the representation of the synchronous generator in power systems is firstly presented as the basis for the VSG. Then the modelling methods of VSG are comprehensively reviewed and compared. Applications of the VSG in power systems are summarized as well. Finally, the challenges and future trends of the VSG implementation are discussed.
Keywords
Inertia; virtual synchronous generator (VSG); frequency control; renewable energy source (RES); inverter
THE traditional power systems are dominated by synchronous generators (SGs), which are proved to have many inherent favorable features such as large inertia and damping that are beneficial for the stable operation of power systems. Meanwhile, the frequency and voltage regulation can easily be achieved by SGs with the governor and automatic voltage regulator (AVR). The inertia can be generally defined as the resistance of an object to the change in its state of motion. In terms of power system stability, the inertia implies the ability to maintain the rotor speed, and the frequency under disturbances, e.g., short circuits [
In the past decade, due to the potential shortage of fossil energy, the increase of energy consumption, and pollution of the environment, the renewable energy sources (RESs) such as solar and wind have drawn great attention worldwide. By the end of 2018, 17.6% of the power supply is provided by RESs in USA, in which the capacities of solar and wind are 51 GW and 94 GW, respectively [
In general, the low inertia of power systems will have impact on two key aspects. Firstly, a lower inertia introduces a poorer frequency nadir during the disturbances. There is not sufficient kinetic energy to keep the frequency at a specified level, which causes large frequency deviations and might be harmful to both generation and consumers. Besides, a lower inertia will lead to a large RoCoF, which triggers the active protection system to trip the generators [
One of the most promising solution is the virtual synchronous generator (VSG). Although different implementions have been proposed in the literature such as synchronverter [
This paper will give a comprehensive review of VSG including modelling, new developments and application in power systems, and will also discuss the future challenges. The remaining part of this paper begins with a review of both the SG and VSG models as well as their comparison and assessment given in Section II. New development of VSG corresponding to different models is also included in this part. The application of VSG in power systems is described in Section III. Afterwards, the challenges and future trends of VSG are presented in Section IV. Finally, the conclusions are drawn in Section V.
The VSG introduces the models of SG into the control system of the inverters, and then the static power electronic converter is able to operate like a rotating electrical machine. In addition, by emulating the governor and AVR, the VSG can easily achieve the functions of quick damping of voltage and frequency oscillations, sharing the power automatically, and synchronizing to the grid.
The basic principle diagram of the VSG is shown in

Fig. 1 Diagram of basic principle of VSG.
By introducing the models of SG into the control of the inverter, the VSG can make the power exchange between the DC source and the power system with the same characteristics as the SG. An inverter can be equivalent to an SG when the switching of power semiconductors is neglected. In the SG, the mechanical rotor and windings can provide the necessary inertia and damping for a stable operation, while in the VSG, the virtual inertia and damping should be provided by the ESS, which can be an additional battery, super-capacitor, or DC-link capacitor itself, etc.
The control system of the VSG consists of three levels, i.e., the inner control loop, SG modelling, and the frequency and voltage regulation. The inner loop is identical to other control structures such as droop control [
Generally, the VSG has the following features:
1) Enable the inverter to mimic the SG, especially its inertia and damping characteristics.
2) Enable the energy source to provide virtual inertia if necessary.
3) Enable to participate in frequency and voltage regulation via virtual governor and AVR.
4) Enable to feature “plug and play” in power systems.
5) Enable to operate in islanded mode for the grid-supporting VSG.
6) Select parameters flexibly without considering the physical constraints of the real SG.
7) Introduce problems of both SG such as power oscillation and inverter such as harmonics.
Before discussing the VSG, this part will firstly summarize the representation of SG in power systems. These SG models are the basis of the VSG.
According to different simplifications, the models of SG can be classified from the

Fig. 2 Summary of eight different representation levels for SG in power systems.
For the state-of-art solutions, the
As seen in the following, some literatures only use the swing equation to build the VSG model even without the electromagnetic part.
(1) |
where and are the mechanical and electromagnetic torques, respectively; is the damping factor; is the angle frequency; is the angle of the rotor; and is the moment of inertia, which will not influence the steady-state operation but have apparent impact on the dynamics. A large implies more energy released or absorbed during the disturbance, and stronger ability for frequency support.
A converter can be controlled as a grid-feeding inverter, a grid-forming inverter, or a grid-supporting inverter [
1)
As mentioned before, not all the models of SG have been used in the modelling of VSG. The highest order and most accurate model presented in the literature is the
The VISMA strategy requires much calculation burden due to the complicated dynamic model. Together with the potential instability of the model in unbalanced conditions [

Fig. 3 Control structure of VISMA Method-2.
Compared with the
2)
Neglecting the stator transient and sub-transient damping windings, the representation of SG can be simplified to a
In [

Fig. 4 Control structure of
Although the
3)
A simpler modelling of VSG is based on the

Fig. 5 Equivalent circuit of
In

Fig. 6 Control structure of steady-state model based VSG.
It is worth mentioning that the stator parameters should be designed carefully without leading to synchronous resonance [
As mentioned before, the swing equation represents the important inertia characteristics. Therefore, there are a lot of literatures implementing the VSG by just using the swing equation and focusing on the most important feature. One of the famous implementations is called synchronverter, as shown in

Fig. 7 Control structure of synchronverter.
The synchronverter can take the filter inductance as the stator windings. However, in terms of the control system, it is a
A simpler implementation of VSG is shown in

Fig. 8 Control structure of VSG based on swing equation [
It should be mentioned that, in the above figures of the control structure, it is assumed that the damping is included in the virtual governor or the droop characteristics, whose equation can be expressed as:
(2) |
where Pm is the mechanical power. This is because the damping provided by the rotor, which is much smaller than that provided by the governor, can usually be neglected due to an actual SG [
(3) |
where is the damping power; and is the frequency of the grid derived by a PLL. This can be seen as an independent loop, which means that it can be added into different VSG models. A detailed discussion on different damping terms can be found in [
To evaluate different implementations of VSG, some comparison results are given in this part, and the response of the SG is also investigated. The models of SG and their frequency characteristics are in focus, and therefore the inner loop and virtual AVR are not included in the control system as discussed in [

Fig. 9 Block diagram of power control loop of VSGs.

Fig. 10 Comparison of frequency characteristics of open-loop transfer functions for different VSG implementations.
After the system is in the steady state, a load step from 10 kW (14.44 ) to 20 kW (7.22 ) occurs at s. Then at s, the power set increases to 10 kW. Furthermore, a 0.5 Hz frequency decrease in the system is implemented at s. Finally, the VSG turns into islanded mode at s.

Fig. 11 Comparison results of frequency on load bus under different VSG implementations using data from Table I.

Fig. 12 Comparison results of RoCoF at load bus with different VSG implementations using data from Table I.
Based on the introduction and comparisons above, the different VSG emulation methods are summarized in detail in Table II.
As an increasing number of RESs are connected to power systems and the number of conventional generators are decreasing, the total system inertia decreases, which may lead to the increasing risk of unstable operation of the system during transient events. The VSG is a promising solution to the problem, and much research efforts have been devoted to this area.

Fig. 13 Simplified diagram of PMSG-based wind power system controlled as VSG.
In [
In addition, photovoltaic [
Microgrid is a promising solution to integrate, manage, and optimize the distributed generation (DG) units, which can operate either in grid-connected mode or in islanded mode. An islanded microgrid should build the voltage and frequency by itself. However, as a power electronic dominated system without SGs, the islanded microgrid comes across many problems such as lack of inertia, low power quality and robustness.

Fig. 14 Schematic diagram of AC microgrid using a VSG in connection with an ESS.
In [
As more and more DGs are connected into the distribution grid, microgrids are necessarily required to provide variable auxiliary services. The VSG can help DGs participate in the management of microgrids and improve the stability and economy of the system, which should be investigated further.
As an advanced power transmission technology,voltage source converter based HVDC (VSC-HVDC) transmission has many applications in system interconnection, wind power integration, and powering of islands, etc. However, traditional control strategies of HVDC cannot provide frequency support to a weak grid, where large frequency deviations appear when there is power unbalance, and a stable operation of the system is violated.

Fig. 15 Schematic diagram of VSC-HVDC controlled as VSG.
To solve the problem above, the swing equation can be introduced into the control strategy of the inverter station. It has been proved under different conditions that the VSG-based HVDC can help to improve the frequency stability of the low-inertia AC grid [
The VSG has its own special dynamics compared to the traditional grid-connected inverters, and changes the stability of traditional power systems [
Investigations in [
Transient stability is another important aspect of VSG. With a large disturbance, the power system with VSG is no longer a linear system, and the results from small-signal analysis are not available. To evaluate the transient stability, the classic Lyapunov method can be applied [
The VSG relies on the ESS to provide inertial energy no matter whether it is from additional sources or from the capacitors in the VSC. It has been proved that the ESS can effectively support the system frequency with different kinds of disturbances [
In practice, the ESS is limited by its power and energy density, and the actual state of charge, etc. A self-tuning VSG is proposed in [
It can be seen that there is still no effective method to determine the optimal size and type of ESS by considering the economy, stability and reliability in a complete context, which is important for practical implementation of VSG. In addition, a power curtailment strategy deviating the operation power away from the maximum power point of RES during the transient state, which can use the power reserve to provide virtual inertia, may also be an interesting direction for further investigation.
Like traditional power systems with multiple SGs, the coordination of multi-VSG in one system is of vital importance for the stable and reliable operation of power systems. A consensus-based control of VSG is proposed in [
It is evident that some literatures have started to investigate multi-VSGs rather than single VSG. As in a power supply case, multi-VSG system has the same problems such as power sharing and power oscillation as the traditional paralleled inverters. Moreover, due to its special functions of inertia and damping provision, the size, placement, and design of parameters of multi-VSGs need to be further evaluated in order to achieve stable, reliable, and optimal operation.
This paper has presented a comprehensive review of VSG emulation including the modelling development and the important application in power systems such as RES integration, microgrids, and VSC-HVDC. As a promising technology for more power electronic based power systems in the future, the basic modelling, analysis, and design methods of VSGs have been studied in the literature. However, to achieve a practical application, further investigations on the stability analysis and ESS controlling, sizing, and optimization are still necessary. In particular, in terms of a system with high penetration of RES, multi-VSGs system has drawn more attention in recent years, which can be one of the most important issues for future power systems.
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