With the increasing integration of new energy generation into the power system and the massive withdrawal of traditional fossil fuel generation, the power system is faced with a large number of stability problems. The phenomenon of low-frequency oscillation caused by lack of damping and moment of inertia is worth studying. In recent years, virtual synchronous generator (VSG) technique has been developed rapidly because it can provide considerable damping and moment of inertia. While improving the stability of the system, it also inevitably causes the problem of active power oscillation, especially the low mutual damping between the VSG and the power grid will make the oscillation more severe. The traditional time-domain state-space method cannot reflect the interaction among state variables and study the interaction between different nodes and branches of the power grid. In this paper, a frequency-domain method for analyzing low-frequency oscillations considering VSG parameter coupling is proposed. First, based on the rotor motion equation of the synchronous generator (SG), a second-order VSG model and linearized power-frequency control loop model are established. Then, the differences and connections between the coupling of key VSG parameters and low-frequency oscillation characteristics are studied through frequency domain analysis. The path and influence mechanism of a VSG during low-frequency power grid oscillations are illustrated. Finally, the correctness of the theoretical analysis model is verified by simulation.

With the development of distributed energy technology, power systems have been equipped with a large number of power electronic inverters. Unlike the traditional synchronous generator (SG), the inverter power supply cannot provide inherent inertia to respond to changes in grid frequency, thus providing insufficient inertia and weak frequency regulation of the power system [

Power systems with insufficient damping caused by the interaction between the SG and the power grid often suffer from low-frequency oscillation, a classic small-disturbance stability problem [

Focusing on the factors influencing the low-frequency oscillation of a grid-connected VSG system, this study considers an inverter power supply based on virtual inertia control as the research object. Based on an analysis of the expansion structure and power-frequency control loop of the VSG circuit, the frequency-domain analysis method is adopted to simplify the model into a second-order form. The possible factors influencing the VSG connection and the key parameters causing low-frequency oscillation are systematically analyzed through the damping ratio and natural frequency. Finally, the simulation is used to verify the accuracy of the model analysis results.

The classical Phillips-Heffron model of a synchronous generator describes the inertia, damping, and synchronization characteristics of the generator through a linearized rotor motion equation [_{m}_{e}_{0} is the rated angular frequency; _{g}_{g}_{a}_{t}

The control block diagram of the inverter based on VSG is shown in _{dc}_{f}_{f}_{abc}_{abc}_{g}

The active and reactive power controllers of the VSG simulate the droop characteristics of the traditional synchronous generator governor and exciter, respectively, such that the inverter can perform frequency and voltage regulation [_{ref}_{ref}_{e}_{p}_{q}_{0}

The VSG output voltage _{abc}_{abc}

To analyze the influence of the key VSG parameters on low-frequency oscillation, the grid-connected VSG is equivalent to a steady-state circuit, as shown in _{g}_{L}

According to _{g}

According to frequency-domain analysis theory, the voltage and current inner loop are more sensitive in the high-frequency region, whereas the power outer loop is more sensitive in the low-frequency region, and the response speed of the inner loop is much faster than that of the outer loop [

To enable the VSG to support the power grid frequency, part of the voltage synchronization was added to the active power control loop in

The active power-frequency model in the frequency domain can be obtained from

According to the final value theorem of the Laplace transform, when

The effect of the grid frequency deviation on the VSG output power is shown in

According to

By comparing _{n}_{n}

The essence of the system oscillation is the power-angle oscillation between the VSG and the power grid, as shown in

To verify the validity of the proposed model and the relevant conclusions, a simulation model was built as shown in

Parameter/Unit | Value | Parameter/Unit | Value |
---|---|---|---|

_{dc} |
800 | 15 | |

_{g} |
310 | 5 | |

310 | 1 | ||

_{ref} |
10 | _{f} |
5 |

_{p} |
1 | _{f} |
300 |

_{0} |
50 | _{0} |
314 |

When these parameters change, the VSG generates an amplitude-frequency gain peak in the low-frequency region. The changes in the amplitude-frequency gain peak’s peak value corresponding to the oscillation frequency changes in the time-domain waveform. The changes in the amplitude-frequency response bandwidth and amplitude correspond to the changes in the oscillation dynamic response time and amplitude in the time-domain waveform.

Based on the parameters in

As shown in

As shown in _{p}

In the low-frequency oscillation simulation verification of the grid-connected virtual synchronous generator, the operating condition is a single VSG connected to an infinite grid with load, and the parameters of the system are shown in _{p}

Scenario 1: Only the transmission reactance is changed. The VSG’s active power and frequency responses with different transmission reactance values are shown in

Scenario 2: Only the active droop coefficient is changed. The active power and frequency responses of the VSG with different active droop coefficients are shown in _{p}_{p}_{p}_{p}_{p}_{p}_{p}_{p}

Scenario 3: Only the virtual inertia coefficient is changed. The active power and frequency responses of the VSG with different virtual inertia coefficients are shown in

Scenario 4: Only the damping coefficient is changed. The simulation results for the VSG output active power oscillation under different gains of

The damping coefficient was set to 100 and the operation reached a stable state when t < 3 s. The active power step from 10 to 12 kW generates instruction disturbance when t = 3 s, and

In this study, a small-signal model of a single VSG connected to an infinite power grid was established, and the mechanism of VSG participating in the low-frequency oscillation of the power grid was studied using the frequency-domain analysis method. In this way, the frequency-domain characteristics of the closed-loop transfer function of the VSG power-frequency small-signal were used to analyze the influence mechanism of the transmission reactance, active droop coefficient, virtual inertia coefficient, and damping coefficient on the frequency and amplitude of low-frequency oscillation. Furthermore, these results provide technical theoretical support for the application of VSG in energy grids.