1. Introduction
Many new energy units are connected to the power system through inverters, and the proportion of power electronic devices in the power system has increased rapidly [
1]. The operation mode and dynamic characteristics of the power grid have changed gradually [
2,
3,
4]. A power system including fewer synchronous generators (SG) and more power electronic devices cannot provide sufficient physical damping and inertia, which is not conducive to the stable operation of the power system [
5].
To solve the above problems, the virtual synchronous generator (VSG) technique is proposed [
6,
7]. The VSG considers the electromechanical and excitation transient characteristics of synchronous generators to provide virtual damping and inertia [
8]. However, although VSG simulates the excellent regulation characteristics of SG, low-frequency oscillation problems will occur and the oscillation mode will be changed [
9,
10]. Therefore, the grid-connected stability of VSG needs to be further analyzed. In this regard, single-VSG and multi-VSG grid-connected stabilities are widely studied.
In the study of single-machine grid connection stability, Reference [
11] developed a double-machine test-bed to analyze the low-frequency oscillation phenomenon after VSG replaces SG, as well as the characteristics and main modes of low-frequency oscillation, and evaluated the role of the power system stabilizer in the VSG grid. In [
12], the internal voltage of the inverter was taken as a parameter rather than a state variable, and the voltage change was introduced into the approximate Lyapunov direct method. The influence of the reactive power voltage control link and different parameters on the stability of VSG was analyzed, and it was pointed out that the reactive power control loop will reduce the stability margin of the VSG power angle. Reference [
13] proposed the concepts of virtual common coupling point and virtual power angle to represent the mathematical model of a variable cross-section vibration generator with virtual damping and analyzed the transient stability of VSG. In [
14], a small-signal model of a VSG-SG interconnected system suitable for studying the low-frequency oscillation damping of the transmission network is proposed. Through this model, the influence of VSG and SG on the power system is compared, and the mechanism of VSG’s influence on damping characteristics is revealed. In [
15], the VSG small-signal model of voltage and current double closed loop and active and reactive power control was established to study the VSG oscillation characteristics. The analysis showed that the reactive power loop and DQ axis voltage control have a great impact on the damping of low-frequency oscillation.
In the research on the stability of multi-machine parallel connection, in [
16], the VSG-based active power frequency loop is equivalent to P/ω. The two-terminal-network model of “admittance” analyzes the three kinds of factors that affect the output power of VSG and the power frequency oscillation characteristics of the three kinds of factors when the parameters change. Reference [
17] defines the deviation of generator voltage angle relative to inertia center angle as a tool to evaluate the stability of a multi-VSG microgrid and optimizes VSG unit parameters through the particle swarm optimization algorithm. Reference [
18] studies a new method to improve the transient stability of a multi-VSG power grid, which suppresses the oscillation between VSG and the inertial frequency center of the power grid during short circuit. Reference [
19] proposes a fully decentralized mutual damping method to solve the problem of power oscillation in parallel with multiple VSGs. By introducing the derivative of local power, the difference between each angular frequency is obtained indirectly, which effectively suppresses power oscillation. In [
20], secondary frequency control of a distributed VSG for low-bandwidth communication is proposed, which suppresses oscillation and restores the frequency to the rated value without changing the virtual inertia provided by VSG.
To summarize, the theory of VSG grid connection stability is gradually maturing, but the extant literature does not discuss the specific impact of the changes in various parameters in VSG on the low-frequency oscillation mode of the power system after VSG grid connection, as well as the dominant factors in the change in oscillation mode. Moreover, nowadays, the stability research on VSG control mostly adopts the damping torque analysis method. Although this method is easy to build a complex global model, its stability criteria are complex and the parameter regions are difficult to identify [
21]. The eigenvalue analysis method in the small-signal analysis method can better analyze the stability of the system when the parameters change. Therefore, we present here a more in-depth study on the grid connection stability of a virtual synchronous generator based on the small-signal model analysis method. The influence of VSG parameters on the stability of a single-machine grid-connected system and a multi-machine grid-connected system is analyzed through system eigenvalue trajectories. The main contributions are as follows:
(1) Based on the topology and algorithm of VSG, small-signal modeling is carried out for a single-machine grid-connected system and a multi-machine parallel grid-connected system.
(2) In the single-machine grid-connected system, the influences of oscillation mode, control parameters of active power loop, and resistance inductance ratio of connecting line on eigenvalues are analyzed.
(3) In the multi-machine parallel connected system, the effects of virtual moment of inertia, damping coefficient, line resistance, and line inductance on the eigenvalues are analyzed. Finally, the conclusions are verified by numerous simulation models.
6. Time Domain Simulation Verification and Result Discussion
6.1. Simulation of Single-VSG Grid-Connected System
To verify the correctness of the analysis of the above variable parameters on the change law of eigenvalue trajectories, a time domain simulation model of a VSG grid-connected system was built, as shown in
Figure 1. The system parameters under the initial operating conditions are shown in
Table 1. When
t = 3 s, the system load is increased by 2 kW.
Under the initial operating conditions, the system parameters are set as the references. The ratios of the virtual inertia J, the virtual damping coefficient D, and the resistance inductance ratio r of the connecting lines to their corresponding references are 0.5, 1, and 1.5, respectively.
Virtual inertia J has a significant influence on the active power and virtual angular frequency of the system. As the virtual inertia gradually increases, the overshoot in active power increases, while the overshoot in virtual angular frequency decreases, and the response time and decay oscillation time of active power and virtual angular frequency are extended.
As the virtual damping coefficient increases, the response times of active power and virtual corner frequency remain the same. However, their overshoot is decreased, the oscillation time becomes shorter, and the decay oscillation time becomes faster.
As the resistive inductance ratio r increases, the response times of active power and virtual angular velocity increase, and the decay oscillation time decreases. The overshoot of active power is decreased, but the overshoot of virtual angular frequency is increased.
6.2. Simulation of Multi-VSG Grid-Connected System
The time domain simulation model of the two-VSG grid-connected system is built to verify the correctness of the analysis of the influence of the above variable parameters (
J,
D,
Rc,
Lc) on the system stability. With the same other parameters (as shown in
Table 4), when the power is disturbed, the response simulation waveforms under different virtual moments of inertia, virtual damping coefficients, line resistances, and line inductances are shown in
Figure 14,
Figure 15,
Figure 16 and
Figure 17, respectively.
As can be seen from
Figure 14 and
Figure 15, increasing the virtual inertia
J or decreasing the virtual damping coefficient
D will make the system unstable under a power disturbance. Increasing the virtual inertia
J influences the number of oscillations of active power and frequency under power disturbance, increasing the regulation time of the system. Increasing the virtual damping coefficient
D reduces the amplitude of oscillations of active power and frequency and shortens the time for the system to reach stability.
In
Figure 16 and
Figure 17, reducing the line resistance
Rc or increasing the line inductance
Lc will deteriorate the system stability. Reducing the line resistance
Rc will increase the overshoot of active power, and the adjustment time of active power and frequency will be increased. Increasing the line inductance
Lc will enlarge the overshoot of active power and reduce the overshoot of frequency.
7. Conclusions
We studied the stability of single-VSG and multi-VSG systems. The influence mechanisms of various parameters on system stability were verified by small-signal models and numerous simulation models. The conclusions are as follows.
(1) In the single-VSG grid-connected system, increasing the virtual moment of inertia will rapidly reduce the damping ratio of the corresponding oscillation attenuation mode and deteriorate the system stability. Increasing the virtual damping coefficient and the resistance inductance ratio of the connecting line will increase the damping ratio and improve the system stability.
(2) In the multi-VSG system, increasing the damping coefficient and line resistance will increase the system damping and improve the system stability. Increasing the virtual moment of inertia and line inductance will reduce the system damping, which is not conducive to the system stability.
We achieved some research results that provide a theoretical reference for the matching and selection of various parameters in VSG single-machine grid-connected systems and multi-VSG parallel grid-connected systems. However, further in-depth research and discussion are still needed:
(1) The influence of grid voltage fluctuation is not considered in the small-signal stability analysis of VSG single-machine and multi-machine parallel systems. When the voltage fluctuates, the transient stability of VSG needs further study.
(2) This paper mainly verifies the theoretical analysis through time domain simulation, and a semi-physical test platform based on theory and simulation is necessary to further prove the effectiveness of the results.