Improving the Synchronous Stability Control Strategy of Virtual Synchronous Generators

The microgrid dominated by new energy has small inertia and weak damping, while a virtual synchronous generator (VSG) is an effective means to enhance inertia and damping to improve the stability of the microgrid. However, it also introduces power angle oscillation problems similar to that of synchronous machines. This paper is based on the current inner loop and voltage outer loop control of the three-phase LCL inverter. It introduces the virtual inertia and damping coefficient of the virtual synchronous generator, achieving a good grid connection effect. While a significant change in active power occurs, the system can lose synchronization and stability. Therefore, the paper proposes an improved synchronization stability control strategy for virtual synchronous generators by introducing a frequency-proportional integral feed-forward link in the reactive power loop to suppress power angle oscillation and improve system synchronization stability. Theoretical analysis was conducted on the synchronous stability of the improved control strategy in case of sudden changes in active power load. The effectiveness of the strategy was verified through simulation.


Introduction
Under the target of carbon peaking and carbon neutrality, the microgrid with wind and solar energy as the main energy sources has become one of the focuses of attention.The operation of microgrids composed of new energy leads to small inertia and weak damping characteristics [1].The virtual synchronous generator control that simulates the characteristics of synchronous machines has damping and inertia characteristics, which is an important measure to improve the stability of microgrids.However, the introduction of the rotor motion characteristics of synchronous generators into inverter control [2] leads to synchronization stability issues similar to power angle oscillation in synchronous generators.Therefore, how to improve synchronization stability has become a technical challenge for virtual synchronous generator control.
A lot of research work focuses on small signal stability analysis, and the introduction of inertia and damping coefficient plays an important role in the stability control of virtual synchronous generators [3][4].Moreover, the control strategy of fixed rotational inertia J and damping D is developing towards adaptive adjustment of virtual parameters in order to improve the power response dynamic performance of VSG and enhance the stability of the microgrid.In [5], a microgrid VSG control was proposed based on frequency deviation adjustment of virtual inertia size based on power angle characteristics to suppress power oscillation.In [6], a virtual moment of inertia-based fuzzy controller was added to the VSG control of microgrids to improve the dynamic response characteristics of VSG power and enhance the stability of microgrids.In [7], a state feedback damping term was added, and the results showed that increasing damping is beneficial for improving small disturbance stability.Lin et al.'s study [8] was beneficial for online optimization algorithms to adjust damping and moment of inertia to reduce electromagnetic energy consumption and improve small disturbance stability of VSG control.Wang [9] proposed a dual adaptive VSG control strategy to alleviate the contradiction between active power response and frequency response in the VSG control strategy and enhance the small disturbance stability of VSG control.
When the active load of the grid suddenly changes, the synchronous stability of VSG is an important issue in maintaining the stable operation of the power system.A low-pass filter (LPF) with a sufficiently low cutoff frequency in the reactive power control loop (RPCL) can improve transient synchronization stability.So, the frequency difference between VSG and the power grid is fed back to RPCL, and the frequency response is obtained through a combination of linearization and nonlinear models.The results show that the frequency feedforward method can enhance frequency stability [9][10].However, frequency response, as a key indicator of VSG and important synchronization stability, has been rarely studied, Therefore, this paper proposes a new frequency feedforward method based on a combination of linear and nonlinear models [11], which feeds the frequency difference in the VSG active loop into the reactive loop through a PI (proportional integration) link to improve system stability.The effectiveness of this method is verified through theoretical analysis and simulation.

Structure and principle of virtual synchronous generator
Figure 1 shows the complete VSG structure topology diagram.The LC-type filter is composed of resistor R, inductance L, and filtering capacitor C f .i f is the filtering current.The grid is modeled as an infinite voltage in series with an inductance L g .v g and i g represent the grid voltage and current, respectively, and v pcc represents the PCC (point of common coupling) voltage.The DC voltage source V DC is the ideal voltage source.The active power loop and reactive power loop jointly simulate the operating characteristics of synchronous generators in Figure 1.The active loop simulates the inertia and primary frequency regulation characteristics of a synchronous generator, while the reactive loop simulates the primary voltage regulation characteristics of a synchronous generator.The mathematical equations for active and reactive power loops are given in Equation (1).

(
) where P set and Q set represent the given active power and reactive power, respectively, P e is output active power; Q e is output reactive power, T set is the given torque, T e is the electromagnetic torque, D p is the active frequency droop coefficient, K q is the reactive power voltage droop coefficient, ω is the angular frequency of VSG, ω n is the rated angular frequency, ∆ω is the difference in electrical angular velocity, θ is the electrical angle, V 0 is the command voltage, J is the virtual moment of inertia, V mref is output voltage amplitude.
According to Figure 1, the output active power and output reactive power can be derived as Equations ( 2) and (3), respectively.
pcc g e g sin 3 According to the reactive power voltage droop characteristics, i.e., ( ) And assuming V mref is equal to V pcc , the function of V pcc corresponding to the power angle can be obtained as Equation ( 4).
( ) ( ) 2 q g g g q g q g 0 q set pcc q 3 cos 3 cos 12 () 6 According to conventional stability methods, the parameter design is shown in Table 1

Virtual synchronous generator control grid connection situation
At the initial moment, the system is in an unloaded state.At the time of t =1 s, it is connected to the grid, and its output active power is set to 2 kW (P set =2 kW).The simulation results during the 0-5 s process are shown in Figure 2.
From Figures 2 (a) and (b), it can be observed that the inverter undergoes a surge from no-load to grid connection, and the voltage and current have reached stability after 2 seconds.The output waveform is a good sine wave.From Figures 2 (c) and (d), it can be seen that after the inverter is connected to the grid, the output active power is 2 kW, which is consistent with the set value, and the reactive power output is 0.83 kVar.From Figure 2 (d), the power angle of the system stabilizes at 0.27 rad, so the connected-grid inverter has synchronous stability.

Simulation of sudden changes in active power load with VSG
At the time of 6 s, the output active power of the inverter suddenly increases to 4 kW.The simulation waveform results during the 5-10 s process are shown in Figure 3.
After a sudden change in active power, the output voltage and current amplitudes in Figures 3 (a) and (b) oscillate periodically.From Figure 3 (c) and (d), the waveform of active and reactive power output from the inverter also oscillates, which cannot achieve stable output power.From Figure 3 (e), it can be seen that the power angle undergoes periodic oscillations and cannot be synchronized and stable.That is to say, the grid-connected inverter loses synchronization stability when the active power output steps from 2 kW to 4 kW.

Frequency PI feedforward to reactive power loop
When the active load undergoes a sudden change, in order to maintain system synchronization stability, The article proposes an improved synchronous stability control strategy for virtual synchronous generators.It introduces the frequency difference between the VSG active loop and the grid into reactive power control through the PI link, as shown in Figure 4.The PI link is set to  1 +  2 /s.Due to being in a steady-state state ω = ω n , the introduction of the loop does not affect steady-state characteristics.According to Figure 4, the improved reactive power control equation is derived as Equation ( 5).
( ) ( ) 2 g q g q g 0 q set q 1 q 2 q g g pcc q 1.5 cos 6 1.5 cos ( , ) 3 According to  e = 3 g sin  g  pcc , so, ( ) ( ) , sin , according to the dynamic second-order state equation of the system (8).

(
) If the differential term in the equation is zero, the equilibrium point can be obtained as  e = [ e , ∆ e ] T .The nonlinear system is linearized at x e, and the Jacobian matrix is obtained as Equation (10).
where  21 = − ( ) ( ) Solving the characteristic equation, i.e., det[ − (  )] = 0, the eigenvalues are calculated as Equation (13).The root trajectory diagram of the K 1 eigenvalues of the PI link in the second-order system is drawn, increasing from 0 p.u. to 785.40 p.u., as shown in Figure 5.
The blue and orange curves in Figure 5 represent the two roots of the characteristic equation, and their motion trajectories on the coordinate axis are plotted with the transformation of the K 1 value.During the process of increasing the K 1 value from 0 p.u. to 785.40 p.u., the two roots of the characteristic equation change from a pair of complex conjugate roots to two equal negative real roots and then to two unequal negative real roots.

Analysis and simulation of the stability of improved active power load sudden changes
Similarly, at 6 s, the output active power increases from 2 kW to 4 kW.The integral link parameter K 2 in the PI link is set to 10, and the impact of the proportional link parameter K 1 in the PI link on system stability is discussed.The values of K 1 are K 11 =0, K 12 =100, K 13 =300, and K 14 =500, respectively.The simulation results are shown in Figure 6.   Figure 6 shows: (1) When the value of K is 0, that is, K 11 is 0, the frequency feedforward PI loop introduced is equivalent to an integral loop with K being 10.When the active power increases from 2 kW to 4 kW, VSG can achieve synchronous stability by only introducing an integration link.(2) As the value of K increases, the overshoot of power angle δp decreases, and ultimately the power angle δ tends to stabilize at 0.82; the overshoot of the active power waveform decreases and the time to stabilize decreases.(3) When changing the value of proportional link K 1 from 0 to 100, the reactive power overshoot decreases; when increasing from 300 to 500, the reactive power overshoot increases.

Conclusion
Based on the current inner loop and voltage outer loop of the three-phase LCL inverter, the virtual inertia and damping coefficient of the virtual synchronous generator are introduced to achieve a good grid connection effect.However, when there is a sudden change in active power, the oscillation loses synchronization and stability.Therefore, this article adopts an improved control method for virtual synchronous generators by introducing a frequency-proportional integral feedforward link in the reactive power loop and theoretically analyzes that adding a frequency feedforward PI link can improve system synchronization stability.Through simulation, it is shown that during the process of active load mutation, the introduction of frequency feedforward PI link increases synchronous stability, and the reasonable, proportional coefficient dynamic response is better, thereby proving the effectiveness and correctness of the frequency feedforward proportional integration link of the paper.

Figure 2 .
Figure 2. Waveform diagram of virtual synchronous generator connected with grid

Figure 3 . 4 .
Figure 3. Waveform of active output step change in virtual synchronous with the grid

Figure 4 .
Figure 4. Control strategy for improving synchronous stability with frequency PI feedforward.

Figure 5 .
Figure 5. Root trajectories of K 1 eigenvalues in second-order systems increasing from 0 to 785.40 p. u.
Frequency-power angle curve Figure6.Waveform diagram of improved active power load step mutation.