Low Frequency Oscillation Suppression Strategy in New Power System Based on Virtual Synchronous Generator

With the blend of massive new energy into power network systems, the inertia and damping features of new power systems are reduced, which is prone to cause low-frequency oscillations (LFO) in the power systems. Virtual synchronous generators (VSG) have received widespread attention by simulating the external characteristics of synchronous generators (SG) to enhance the inertia of new power systems and help suppress low-frequency oscillations. By analyzing the mathematical model of VSG, the control links of each part of VSG are established, the traditional reactive power-voltage (Q-V) of VSG is improved, and the formulas of active voltage control and reactive power control droop coefficient are deduced. Finally, a simulation model of VSG is created by MATLAB/Simulink platform, and new methods for suppressing LFO in power systems are compared and analyzed. The correctness of the formula and the improvement effect of reactive power and voltage control are verified.


Introduction
By a prominent energy supply shortage and environmental pollution, the advantages of new energy power technology have gradually emerged, and the new power system with large-scale new energy has become a trend.New energy instead of the SG weakens inertia and damping in the power system, which is prone to LFO [1][2].LFO is a classical problem of power system stability.When the system lacks damping or even negative damping, it is easy to cause LFO.When LFO occurs, the power and frequency of the line will oscillate from 0.1-2.5 Hz, which will harm system stability [3].Therefore, how to suppress the LFO of the power system has become a major problem in restricting the new energy cluster grid connection [4].
VSG technology has been widely concerned because it can simulate the external characteristics of an SG and increase system inertia [5].How to use VSG technology to solve the oscillation problem caused by the lack of inertia in the new power system has become a research hotspot.In [6], the influence of phase locked loop (PLL) on low frequency oscillation was studied, and it was proposed that the negative damping introduced by PLL is one of the reasons for low frequency oscillation.Reference [7] calculated the generator's active and reactive power reference through the inverter.However, droop control cannot fundamentally solve the problem of low inertia; that is, the constituent system is still a "weak inertia" system.[8,9].To improve the fixity of the power system, VSG control is proposed.However, when the line impedance changes significantly, the traditional VSG reactive power control is prone to circulation problems.The traditional VSG control will have a power coupling phenomenon, affecting the power quality.
Based on this, the droop control method is extended to VSG, and the VSG is improved.This paper analyzes the control principle of VSG through a mathematical model.The VSG Q-V control link is improved, and the calculation formulas of P-f droop coefficient K p and Q-V droop coefficient K q contained in VSG are proposed.Finally, it establishes a simulation model for VSG by using Matlab / Simulink platform.By comparing the droop control and VSG control under the same simulation conditions, it is verified that VSG control can improve the LFO suppression ability of the system.The correctness of the proposed K p and K q formulas is verified through the simulation of droop characteristics.The improved effect of the VSG Q-V control link suggestion in this paper is confirmed, proving that the improved control link can effectively decouple the power and improve the voltage stability.

Mathematical model of VSG
VSG is constructed by emulating the rotor and stator equations of SG, so it is prominent to introduce the mathematical model of the SG [10].In this paper, the VSG is studied by introducing virtual inertia.The reference shaft is taken as the synchronous rotating shaft and the pole number P=1.The rotor mechanical motion equation of SG is: m ( ) where P m is mechanical power, P e is electromagnetic power, T m is mechanical separator torque, T e is electromagnetic torque, m ω rotor angular velocity, n ω is rated angular velocity, J is inertia coefficient, D is damping coefficient.
By simplifying (1), we can get: m ( ) where T m is mechanical separator torque, T e is electromagnetic torque.The stator of the SG transmits voltage to the grid, and the stator voltage equation is: ( ) where m E  is the excitation electromotive force of SG stator, U  is the armature voltage of SG, I  is the armature current, a R is armature resistance, s X is armature reactance.(2) and (3) construct the VSG's mathematical former.According to the two equations, the rotor and stator control links of the SG can be simulated.

Topology of VSG
Figure 1 shows the topology of the VSG.The VSG uses the grid voltage and current as input signals and outputs the PWM signal to control the inverter through the VSG control algorithm.The external characteristics, such as the inertia damping of the SG, are simulated so that the new energy gridconnected operation has a specific inertial response, which can effectively elevate the LFO suppression of the new power systems.

Control strategy of VSG
To reduce the adverse effects caused by the massive new energy grid-connected, such as the low frequency oscillation caused by the lack of inertia and damping, introducing droop control and virtual inertial control in VSG.VSG can enhance the inertial support of large-scale new energy access to new power systems.

Virtual power frequency controller
Power grid load changes, resulting in generator output power will also change.Because the traditional synchronous generator has mechanical inertia, its mechanical power will not change immediately with the load change, which leads to the variation between the P m and the P e .This imbalance will lead to changes in the speed and frequency of the generator, which requires a power frequency controller to improve the active power of the system.The controller shown in Figure 2 can be obtained from the simplified synchronous generator rotor motion (2).Under the background of the continuous expansion of the new power system, the grid requires the inverter to have a particular frequency modulation ability.Therefore, active power-frequency (P-f) droop control is inserted into the VSG's virtual power frequency control link, so the VSG can achieve similar droop characteristics as the traditional synchronous generator.The following P-f droop control equation can be obtained by improving the mechanical power P m input by VSG: where P m is mechanical power, P ref is a given value of active power, and K ω is frequency droop control coefficient.
After adding droop control, the mechanical power input of VSG is shown in Figure 3. Since the damping coefficient D changes the droop characteristics of VSG, K p is defined as the P-f droop coefficient.After the system is disturbed, the frequency is gradually stable, and dω/dt becomes zero.(2) can be simplified to the following equation:

= (
) The frequency change is very small, and the difference between ω n and ω m is almost zero.

Virtual excitation controller
During the power system operation, each part's components may produce voltage drop.When the load fluctuates, the voltage changes more obviously.It is crucial to retain the output stability of voltage and reactive power through the excitation regulator of the SG.Similarly, the VSG should also realize the function of stabilizing the grid voltage.
When the line impedance changes significantly, the traditional reactive power-voltage control, as shown in Figure 4, is prone to circulating current problems [11], affecting power quality.Unlike the traditional Q-V control, as shown in Figure 5, this paper adds a voltage feedback link and PI link to the Q-V control link, which diminishes the degree of power coupling, enhances the system's robustness and improves voltage stability.
When the system is stable: Get Q-V droop control coefficient: where K u is the Q-V droop control coefficient.

Electromagnetic equation
To make the VSG have the same external characteristics as the traditional SG, the VSG also needs to complete the simulation of the stator voltage equation through the electromagnetic equation: where L is the VSG's virtual synchronous inductor, R is the VSG's virtual synchronous resistance, and u abc is the VSG's output voltage.The electromagnetic equation block diagram constructed by ( 6) is shown in Figure 6.

Voltage and current double-loop control
To elevate the waveform and quality of VSG output voltage and current, the symmetrical double PI control shown in Figure 7 is operated to decouple the voltage and current.Through the voltage loop setting, the output voltage of VSG can follow the given value well to ensure stable voltage amplitude.After setting the current loop, the voltage signal under the two-phase rotating coordinate is output, which is input into the SPWM link to control the grid-connected inverter.

Function simulation of VSG
Based on the VSG principle mentioned above and the control system of each link, a VSG is built in MATLAB/Simulink, and an investigation is carried out.The simulation parameters of each part are in Table 1.

Comparison analysis for LFO suppression methods in new power system
Simulation comparison experiments are designed to verify the role of VSG in suppressing the LFO of the new power system.In the main circuit of VSG, the SG is catenated to replace the grid, and the control strategy of the inverter is changed.The influence of the classical droop strategy and VSG strategy on the power system is compared.The initial load is set to 5 kW/2 kvar, and the line load is increased to 8 kW/2 kvar when running to 12 s.The power and frequency changes of the two control strategies are observed in Figure 8.In Figure 8 (a), when VSG adopts the classical droop control strategy, due to insufficient system inertia, oscillation occurs when the load alteration.The power oscillation frequency is about 1 Hz, which belongs to the LFO of power systems.The power oscillation is suppressed after about 7 s.Under the same simulation conditions, when VSG control is used, the oscillation disappears quickly, and the power oscillation is suppressed after about 1 s.In Figure 8 (b), the frequency oscillation suppression time is longer when the classical droop control is adopted, while the frequency oscillation is suppressed after about 1 s when VSG control is adopted.The experimental results verify that VSG can improve the LFO suppression of the new power system by increasing the inertia.

Simulation of droop characteristics of VSG
To validate the availability of the droop control link of the virtual power frequency controller, the initial load of the VSG is set to 2 kW/0 var.When running to 0.5 s, the frequency is reduced to 49.996 Hz.When running to 1 s, the frequency is restored, and the change in the measured active power is shown in Figure 9.  7) that when the frequency is reduced to about 49.996 Hz, the active power increases by about 946 W. The theoretical calculation results are basically in agreement with Figure 9.The results verify the correctness of the formula of the P-f droop coefficient K p , indicating that the virtual power frequency controller can achieve P-f droop control.
To detect the effectiveness of the droop control link of the virtual excitation controller, the initial operating voltage amplitude of VSG is set to 311 V, and the initial load is 2 kW/1 kvar.When running to 0.5 s, E m reduced to 308.6 V; running to 1 s, voltage amplitude recovery and reactive power measurement changes, as shown in Figure 10.9) that Q e increases by about 480 var when E m decreases to 308.6 V.The theoretical calculation results are fundamentally unanimous with the measurement results in the Q-V droop simulation in Figure 10.The results put forward the formula of Q-V droop coefficient K u , which verifies that the virtual excitation controller can realize the function of Q-V droop control.

Improvement effect of reactive power-voltage control
In the last part, two kinds of Q-V control methods are involved in constructing the VSG virtual excitation controller.Simulation experiments are designed to explore the effect of two kinds of Q-V control.Firstly, give the system a step at 0.5 s to suddenly increase the active power rate of the power grid from 2000 W to 3600 W. The contrast between the two control modes is shown in Figure 11 In Figure 11, when the step signal is added in 0.5 s and the excitation controller adopts the traditional reactive power control, the system response is slow, and can remain stable after about 0.4 s.When the ameliorate reactive power control is used, the system can respond quickly, and the active power quickly climbs to 3600 W and remains relatively stable.It is verified that the ameliorated control described above can reduce the degree of power coupling.Secondly, set a load of VSG to 5 kW / 2 kvar, and detect the total harmonic distortion (THD) of VSG parallel node voltage.The detection results are shown in Figure 12.In Figure 12 that when the virtual excitation controller adopts the traditional Q-V control, the THD of the grid-connected voltage is large, and the THD measured at 0.2 s is about 3.93%.When the ameliorated Q-V control is used, the THD of the grid-connected voltage is reduced to 0.43%, which verifies that the improved Q-V control mentioned above can improve voltage stability, reduce harmonic content and improve power quality.

Conclusion
This paper proposes an LFO suppression method based on the virtual synchronous generator, which enhances the stability of the new power systems.The droop characteristics of VSG can be expressed by mathematical derivation of droop coefficients.The VSG-based new energy units can provide virtual inertia and dampness to suppress low-frequency oscillation by simulating SG characteristics.The simulation results show that the time of VSG control suppressing LFO of the system is 6 s shorter than that of droop control.Through the derivation of the VSG control structure, the mathematical expressions of the P-f droop coefficient K p and Q-V droop control coefficient K u are obtained.The simulation results prove the validity of the K p and K u expressions.Furthermore, the THD of the gridconnected voltage is decreased by introducing a voltage feedback link and PI link in Q-V control.In contrast with the traditional reactive power control, the system power coupling is and can respond quickly.Compared with droop control, this method reduces the THD of grid-connected voltage by 3.5%.

Figure 2 .
Figure 2. Virtual power frequency controller

Figure 3 .
Figure 3. Mechanical power with droop control

Figure 7 .
Figure 7. Voltage and current double-loop control

Figure 8 .
Figure 8.(a) Effects of two control strategies on LFO power; (b) Effects of two control strategies on LFO frequency

Figure 9 .
Figure 9. P-f droop characteristics simulation results of VSG It can be calculated from (7) that when the frequency is reduced to about 49.996 Hz, the active power increases by about 946 W. The theoretical calculation results are basically in agreement with Figure9.The results verify the correctness of the formula of the P-f droop coefficient K p , indicating that the virtual power frequency controller can achieve P-f droop control.To detect the effectiveness of the droop control link of the virtual excitation controller, the initial operating voltage amplitude of VSG is set to 311 V, and the initial load is 2 kW/1 kvar.When running to 0.5 s, E m reduced to 308.6 V; running to 1 s, voltage amplitude recovery and reactive power measurement changes, as shown in Figure10.

Figure 10 .
Figure 10.Q-V droop characteristics simulation results of VSG It can be calculated from (9) that Q e increases by about 480 var when E m decreases to 308.6 V.The theoretical calculation results are fundamentally unanimous with the measurement results in the Q-V droop simulation in Figure10.The results put forward the formula of Q-V droop coefficient K u , which verifies that the virtual excitation controller can realize the function of Q-V droop control.

Figure 11 .
Figure 11.Power coupling of the two controls

Fundamental
Figure 12.(a) THD of the grid-connected under the traditional Q-V control; (b) THD of the gridconnected under the improved Q-V control