The Strategy of Active Grid Frequency Support for Virtual Synchronous Generator

: Virtual synchronous generator (VSG) control is a promising control approach for voltage source converters as an interface between new energy sources and the power grid. VSG is a grid-friendly control scheme, which can imitate the mechanical inertia of the synchronous generator (SG) and the power droop characteristics. Yet, the droop characteristics imitation of SG induces the frequency variation of the grid-connected inverter along with the droop characteristic curve, which will deteriorate the performance of the grid frequency support during the transient process. In this paper, a control scheme, which shapes the droop curve during the disturbance, is proposed for active grid frequency support. First, a load disturbance extraction strategy with a high-pass ﬁlter is applied in the proposed method, and the disturbance component is effectively extracted to compensate for the frequency reference variation in traditional VSG control. The grid frequency is actively supported by shaping the droop curve of active power to the frequency of VSG during the disturbance. Afterward, H ∞ and H 2 norms are used as the objective function to quantify the control performance of the proposed method, and the particle swarm optimization (PSO) algorithm is applied to optimize the control parameters of the proposed method. With a well-optimized high-pass ﬁlter, the active support performance is further improved. Finally, the simulation results and hardware in the loop (HIL) tests verify the effectiveness of the proposed method.


Introduction
The grid-connected inverter has been widely applied in the power grid with the increase of the penetration rate of renewable energy. The grid-friendly control scheme is mainly concerned for improving the interaction performance between the grid and the inverter. Traditionally, the control schemes for grid-connected inverter include gridfollowing control and grid-forming control [1]. The former, which includes constant current control, constant power control [2,3], cannot support the power grid during the transient process. Therefore, a large number of inverters with grid-following control connected to the grid will reduce the system inertia, increase the frequency fluctuations, which is a serious challenge for the safe and stable operation of the power system [4][5][6][7][8][9].
To mitigate the negative effect caused by the inverters on the power grid, smart inverters (SIs) are designed and have been applied in several locations. SIs are inverters with advanced functions, which can improve the disturbance rejection ability and support the frequency and voltage of the power grid during the load disturbance [10,11]. However, the increase of total inertia is limited with SIs [12]. To solve the low inertia issue and overcome the frequency fluctuation more reliably, as the representative grid-forming control, the virtual synchronous generator (VSG) control has been widely studied in recent years [13][14][15][16]. VSG has similar natures to the synchronous generator, and it can simulate 1. In the VSG-SG coupling system, the closed-loop transfer function between the load disturbance input and the SG angular frequency output is built. The frequency dynamic of the VSG-SG coupling system is revealed by this closed-loop transfer function.

2.
An active grid frequency support strategy is proposed, which enables VSG to compensate for the power balance and effectively realize the active support of the grid frequency by a high-pass filter. 3.
To further improve the frequency support performance of the power grid, the particle swarm optimization (PSO) algorithm is used to optimize the parameters of the proposed strategy.
The paper is organized as follows. The basic operation principle and frequency characteristics of the VSG-SG coupling system are introduced in Section 2. In Section 3, the active grid frequency support strategy is presented, the theory of PSO algorithm and H ∞ and H 2 norms are also elaborated. Then, simulation and hardware in the loop (HIL) test results are given in Section 4. The main conclusions are summarized in Section 5.

Frequency Characteristics of VSG-SG Coupling System
The simplified block diagram of the VSG-SG coupling system is shown in Figure 1, where three-phase voltage-source inverter and synchronous generator are connected to the load at the common coupling point (PCC). U dc represents the VSG's DC voltage. u oabc and i oabc are the output voltage and current of the inverter, respectively. L f and C f are the filter inductor and capacitor, respectively. L 1 and L 2 are the line inductance of VSG and SG, respectively. x t1 and x t2 are the leakage reactance of SG export step-up transformer and step-down transformer, respectively. namic of the VSG-SG coupling system is revealed by this closed-loop tran tion.
2. An active grid frequency support strategy is proposed, which enables VS pensate for the power balance and effectively realize the active support o frequency by a high-pass filter. 3. To further improve the frequency support performance of the power grid cle swarm optimization (PSO) algorithm is used to optimize the parame proposed strategy.
The paper is organized as follows. The basic operation principle and frequ acteristics of the VSG-SG coupling system are introduced in Section 2. In Sec active grid frequency support strategy is presented, the theory of PSO algorith and H2 norms are also elaborated. Then, simulation and hardware in the loop results are given in Section 4. The main conclusions are summarized in Section

Frequency Characteristics of VSG-SG Coupling System
The simplified block diagram of the VSG-SG coupling system is shown in where three-phase voltage-source inverter and synchronous generator are con the load at the common coupling point (PCC). Udc represents the VSG's DC vo and ioabc are the output voltage and current of the inverter, respectively. Lf and filter inductor and capacitor, respectively. L1 and L2 are the line inductance of SG, respectively. xt1 and xt2 are the leakage reactance of SG export step-up transf step-down transformer, respectively. v oabc i oabc g 1- Figure 2 shows the block diagram of the VSG control, where Eref and θ are tude and the phase angle of the voltage reference, respectively. En represents voltage. Qset and Q1 are the reactive power reference and output reactive pow tively. kq1 represents the voltage-drooping coefficient. The reactive power con lates the excitation regulator, while the active power control emulates the rot equation and the governor of the synchronous generator.  Figure 2 shows the block diagram of the VSG control, where E ref and θ are the amplitude and the phase angle of the voltage reference, respectively. E n represents the rated voltage. Q set and Q 1 are the reactive power reference and output reactive power, respectively. k q1 represents the voltage-drooping coefficient. The reactive power control emulates the excitation regulator, while the active power control emulates the rotor motion equation and the governor of the synchronous generator.

Control and Mathematical Model of VSG
Reactive power control Active power control According to Figure 2, the rotor motion equation can be expressed as ( ) where ωn represents the rated angular frequency. ω1 is the virtual angular frequen VSG. Pm1 and P1 are the virtual mechanical active power and output active power, res tively. J1 represents the virtual inertia, and D1 is the damping coefficient. The virtual governor reflects the primary frequency characteristics of the sync nous generator, which can be represented as where Pref is the active power reference. kp1 is the droop coefficient. Substituting Equation (2) into Equation (1), and Equation (3) can be derived by small-signal linearization method.

Control and Mathematical Model of SG
The control system of the synchronous generator consists of an excitation regu and governor. Figure 3 shows the governor control block diagram. where ω2* represents the angular frequency of SG. kp2 and T2 represent the proport coefficient and time-delay constant of the governor, respectively. Superscript "*" indi the nominal value. According to Figure 2, the rotor motion equation can be expressed as where ω n represents the rated angular frequency. ω 1 is the virtual angular frequency of VSG. P m1 and P 1 are the virtual mechanical active power and output active power, respectively. J 1 represents the virtual inertia, and D 1 is the damping coefficient. The virtual governor reflects the primary frequency characteristics of the synchronous generator, which can be represented as where P ref is the active power reference. k p1 is the droop coefficient. Substituting Equation (2) into Equation (1), and Equation (3) can be derived by the small-signal linearization method.

Control and Mathematical Model of SG
The control system of the synchronous generator consists of an excitation regulator and governor. Figure 3 shows the governor control block diagram.
Reactive power control According to Figure 2, the rotor motion equation can be expressed as ( ) where ωn represents the rated angular frequency. ω1 is the virtual angular fre VSG. Pm1 and P1 are the virtual mechanical active power and output active pow tively. J1 represents the virtual inertia, and D1 is the damping coefficient. The virtual governor reflects the primary frequency characteristics of th nous generator, which can be represented as where Pref is the active power reference. kp1 is the droop coefficient. Substituting Equation (2) into Equation (1), and Equation (3) can be deri small-signal linearization method.

Control and Mathematical Model of SG
The control system of the synchronous generator consists of an excitation and governor. Figure 3 shows the governor control block diagram. where ω2* represents the angular frequency of SG. kp2 and T2 represent the pr coefficient and time-delay constant of the governor, respectively. Superscript "* the nominal value.
The rotor motion equation of SG can be expressed as According to Figure 3, the mechanical active power P m2 * of SG satisfies where ω 2 * represents the angular frequency of SG. k p2 and T 2 represent the proportional coefficient and time-delay constant of the governor, respectively. Superscript "*" indicates the nominal value. The rotor motion equation of SG can be expressed as where T j is the inertial constant. Combining with Equations (4) and (5), the relation between ∆ω 2 and ∆P 2 can be written as Equation (6) by the small-signal linearization method.
where S base is the power reference value.

Model of VSG-SG Coupling System
The VSG and SG are equivalent to the ideal voltage source with an output impedance, as shown in Figure 4, E 1 and E 2 are the root mean square values of VSG and SG output voltages, respectively. θ 1 and θ 2 are the output voltage phase of VSG and SG, respectively. V pcc and θ pcc represent the root mean square value and phase of the PCC voltage, respectively. X 1 and X 2 represent the equivalent reactance of VSG and SG, respectively. P load is the load active power.
Combining with Equations (4) and (5), the relation between Δω ten as Equation (6) by the small-signal linearization method. where Sbase is the power reference value.

Model of VSG-SG Coupling System
The VSG and SG are equivalent to the ideal voltage source w ance, as shown in Figure 4, E1 and E2 are the root mean square v output voltages, respectively. θ1 and θ2 are the output voltage pha spectively. Vpcc and θpcc represent the root mean square value and p age, respectively. X1 and X2 represent the equivalent reactance of tively. Pload is the load active power.
where δ1 and δ2 are the phase angle difference of VSG and SG out PCC voltage, respectively. The relation between the phase angles c The Equation (9) can be derived by linearizing Equation (7) an According to Figure 4, the expressions of output active power of VSG and SG can be written as where δ 1 and δ 2 are the phase angle difference of VSG and SG output voltage relative to PCC voltage, respectively. The relation between the phase angles can be expressed as The Equation (9) can be derived by linearizing Equation (7) and (8).
Based on the power conservation relationship, the load disturbance power can be written as Substituting Equation (6) into (10), the angular frequency of PCC can be expressed as Substituting Equations (12) and (13) into (9), The relation between active power ∆P 1 and ∆P 2 can be expressed as In VSG and SG coupling system, we focus on the SG frequency rather than the VSG frequency because the former is considered as the main reliable energy source.
Combining with Equations (6), (11) and (13), the closed-loop transfer function between the load disturbance input and the SG frequency output can be obtained.
where the coefficients a 0 -a 4 , b 0 -b 3 are presented in Appendix A.

Frequency Characteristics of VSG-SG Coupling System Based on Active Grid Frequency Support Strategy
This paper proposes a load power extraction strategy based on the first-order highpass filter to provide active frequency support. The structure of the proposed control strategy is shown in Figure 5. Under the proposed control scheme, the load disturbance component is introduced into the active power control of the virtual synchronous generator without detecting other variables. Simultaneously, the control structure is relatively simple, and the VSG can detect the change of active power directly under load disturbance. In other words, the proposed control strategy can actively provide additional power to improve the frequency stability of the synchronous generator. and ΔP2 can be expressed as ( ) ( ) In VSG and SG coupling system, we focus on the SG frequency rather than the V frequency because the former is considered as the main reliable energy source.
Combining with Equations (6), (11) and (13), the closed-loop transfer function tween the load disturbance input and the SG frequency output can be obtained.

Frequency Characteristics of VSG-SG Coupling System based on Active Grid Frequency Support Strategy
This paper proposes a load power extraction strategy based on the first-order hi pass filter to provide active frequency support. The structure of the proposed control st egy is shown in Figure 5. Under the proposed control scheme, the load disturbance co ponent is introduced into the active power control of the virtual synchronous genera without detecting other variables. Simultaneously, the control structure is relatively s ple, and the VSG can detect the change of active power directly under load disturban In other words, the proposed control strategy can actively provide additional powe improve the frequency stability of the synchronous generator. According to Figure 5, the active loop control equation of the VSG after introduc the high-pass filter can be written as According to Figure 5, the active loop control equation of the VSG after introducing the high-pass filter can be written as where K and T are the proportional coefficient and time constant of the high-pass filter, respectively. Combining with Equations (6), (9), (10) and (16), the closed-loop transfer function between load disturbance input and SG frequency output can be obtained as where the coefficients a 0 -a 5 , b 0 -b 5 are presented in Appendix A. Figure 6 shows the frequency output characteristics of the traditional P-f droop control and the active frequency support strategy proposed in this paper. As the load increases, the operating points of the VSG in the two modes move from point A to point B along the blue and red curves, respectively. It can be observed that the active frequency support strategy changes the VSG frequency output characteristic during the transient process, and then provides active support for the grid frequency.
Combining with Equation (6), (9)-(10), and (16), the closed-loop tra tween load disturbance input and SG frequency output can be obtained where the coefficients a0-a5, b0-b5 are presented in Appendix A. Figure 6 shows the frequency output characteristics of the traditio trol and the active frequency support strategy proposed in this pape creases, the operating points of the VSG in the two modes move from p along the blue and red curves, respectively. It can be observed that the support strategy changes the VSG frequency output characteristic du process, and then provides active support for the grid frequency.
The droop curve of the proposed control strategy Traditional P-f droop control

Optimization of High-Pass Filter Parameters
By taking the first-order high-pass filter into the active power co active power support for the system can be provided. Meanwhile, the f tion can be reduced after a load disturbance. However, the control perfo to the parameters K and T of the high-pass filter, where the duration depends on the time constant of the high-pass filter. The value of power on the proportional coefficient. Therefore, the optimization design of pa is necessary to further improve the frequency support performance.

H∞ and H2 Norms
To analyze the effect of the high-pass filter on the disturbance sup the SG frequency quantitatively, the H∞ and H2 norms of the transfer fu in the Equation (17) can be utilized as a performance indicator. The H the maximum gain of the closed-loop system in the frequency domai disturbance suppression ability at the resonance frequency, which is m damping characteristics. The H2 norm reflects the system's control perfo tire frequency band, which is related to the overshoot [34]. The smaller the stronger the disturbance rejection ability of the system. In other word

Optimization of High-Pass Filter Parameters
By taking the first-order high-pass filter into the active power control of VSG, the active power support for the system can be provided. Meanwhile, the frequency fluctuation can be reduced after a load disturbance. However, the control performance is related to the parameters K and T of the high-pass filter, where the duration of power support depends on the time constant of the high-pass filter. The value of power support depends on the proportional coefficient. Therefore, the optimization design of parameters K and T is necessary to further improve the frequency support performance.

H ∞ and H 2 Norms
To analyze the effect of the high-pass filter on the disturbance suppression ability of the SG frequency quantitatively, the H ∞ and H 2 norms of the transfer function G(s) shown in the Equation (17) can be utilized as a performance indicator. The H ∞ norm represents the maximum gain of the closed-loop system in the frequency domain. It indicates the disturbance suppression ability at the resonance frequency, which is more related to the damping characteristics. The H 2 norm reflects the system's control performance in the entire frequency band, which is related to the overshoot [34]. The smaller H ∞ and H 2 norms, the stronger the disturbance rejection ability of the system. In other words, the disturbance suppression ability is improved with the decrease of H ∞ and H 2 norms.
The H ∞ and H 2 norms of the transfer function G(s) are defined as [35]  where σ[G(jω)] represents the largest singular value of G(jω). G H is the conjugate transpose of G and trace(G) represents the trace of G.

Particle Swarm Optimization Algorithm
Although the H ∞ and H 2 norms can effectively reflect the impact of disturbance input on output, the analytic expression of the Equation (18) is extremely complicated. After substituting the transfer function G(s) into the Equation (18), the analytic expression of the optimal solution of parameters K and T cannot be obtained directly. Thus, optimal algorithmic techniques need to be carried out to search optimal parameters K and T, such as butterfly algorithmic (BOA) [36], genetic algorithm (GA) [37]. The particle swarm optimization algorithm (PSO) is considered in this paper due to its higher convergence characteristic with lesser elapsed time [38].
The PSO algorithm is a random optimization algorithm based on swarm intelligence [39]. The position in the search space represents a potential solution to the optimization problem. Each particle's characteristic can be represented by indicators, such as the particle's position, velocity, and fitness value, where the fitness value determines the quality of the particle. Particles are updated by following two factors: one is the individual's best position ever found (P id ); the other is the group's best position (P gd ). In every iteration, the particle updates its position and velocity with Equation (19).
where w is the inertia weight. k represents the iteration number. c 1 and c 2 are learning factors, respectively. r 1 and r 2 are random numbers between 0 and 1. V id and X id are the velocity and position of i-th particle, respectively. To improve the search performance of the PSO algorithm, a method of dynamic inertia weight is considered, and the dynamic inertia weight coefficient can be given as (20) where T max represents the maximum number of iterations. Generally, the algorithm performance is the best when w start is 0.9 and w end is 0.4 [40].
The H ∞ and H 2 norms are utilized as an index to describe the frequency response characteristics of the system, which can reflect the system's performance to suppress disturbances. Therefore, this paper chooses the weight of H ∞ and H 2 norms as the objective function where G(s) represents the transfer function shown in the Equation (17). α is the weight coefficient in the range [0, 1], which represents the proportion of the H ∞ norm in the objective function. Figure 7 shows the three-dimensional graph, which reflects the relation between objective function J and parameters K and T of the high-pass filter under different weight coefficients. It can be observed that the objective function in Figure 7a,b has a minimum value, and the optimal results under different weight coefficients are different; whereas, the optimal results with different weight coefficients are not comparable since the weight coefficients are selected according to design requirements. When α is set to be smaller than 0.5, better performance of H 2 norm is obtained. When α is set to be larger than 0.5, better performance of H ∞ norm is obtained. In this paper, the value of α is chosen as 0.7.
Electronics 2021, 10, x FOR PEER REVIEW 9 of 20 coefficients are selected according to design requirements. When α is set to be smaller than 0.5, better performance of H2 norm is obtained. When α is set to be larger than 0.5, better performance of H∞ norm is obtained. In this paper, the value of α is chosen as 0.7.
Objective Function

Verification of Proposed Strategy
The effectiveness of the proposed active grid frequency support strategy is first verified by the simulation for a VSG-SG coupling system shown in Figure 1 in MATLAB/SIM-ULINK, and the system parameters are listed in Table 1. The switching frequency is 10 kHz. At the initial operating point of the system, the load is a constant power load with 15 kW. A 10% load disturbance is increased suddenly at 2 s.

Verification of Proposed Strategy
The effectiveness of the proposed active grid frequency support strategy is first verified by the simulation for a VSG-SG coupling system shown in Figure 1 in MAT-LAB/SIMULINK, and the system parameters are listed in Table 1. The switching frequency is 10 kHz. At the initial operating point of the system, the load is a constant power load with 15 kW. A 10% load disturbance is increased suddenly at 2 s. According to Equations (15) and (17), the frequency response of the SG during a load disturbance can be obtained. Additionally, the comparison between theoretical analysis and simulation results is shown in Figure 8. It can be seen in Figure 8 that theoretical results obtained by the small-signal model can accurately represent the dynamics of the system, which verifies the correctness of the small-signal model. (15) and (17), the frequency response of the SG during a load disturbance can be obtained. Additionally, the comparison between theoretical analysis and simulation results is shown in Figure 8. It can be seen in Figure 8 that theoretical results obtained by the small-signal model can accurately represent the dynamics of the system, which verifies the correctness of the small-signal model.

Simulation Results with Constant Power Load
The PSO parameters are chosen as c1 = c2 = 1.425 and Tmax = 100. The original parameters K and T of the high-pass filter are set as 2000 and 0.07, respectively. The high-pass filter parameters can be optimized as K = 1658.2 and T = 0.1.
To verify the effectiveness of the strategy quantitatively, the H∞ and H2 norms are calculated and presented in Table 2.  Table 2 shows that when the high-pass filter is added to the active power loop of the VSG, the H∞ and H2 norms are reduced. Moreover, H∞ and H2 norms with optimized parameters are further reduced, which indicates that the disturbance rejection ability of SG is gradually increasing, and the frequency fluctuation is decreasing.

Simulation Results with Constant Power Load
The PSO parameters are chosen as c 1 = c 2 = 1.425 and T max = 100. The original parameters K and T of the high-pass filter are set as 2000 and 0.07, respectively. The high-pass filter parameters can be optimized as K = 1658.2 and T = 0.1.
To verify the effectiveness of the strategy quantitatively, the H ∞ and H 2 norms are calculated and presented in Table 2.  Table 2 shows that when the high-pass filter is added to the active power loop of the VSG, the H ∞ and H 2 norms are reduced. Moreover, H ∞ and H 2 norms with optimized parameters are further reduced, which indicates that the disturbance rejection ability of SG is gradually increasing, and the frequency fluctuation is decreasing. Figure 9 shows the angular frequency of VSG under three cases. In case 1, a high-pass filter for load disturbance extraction is not used in VSG control, and in case 2, the high-pass filter is introduced in VSG control without optimized parameters. In the last case, the control parameters of the proposed method are optimized. Figure 9 shows the angular frequency of VSG under three cases. In case 1, a highpass filter for load disturbance extraction is not used in VSG control, and in case 2, the high-pass filter is introduced in VSG control without optimized parameters. In the last case, the control parameters of the proposed method are optimized.
Angular Frequency(rad/s) Figure 9. The simulation result of VSG angular frequency in three cases under the condition of load sudden increase.
In Figure 9, the frequency of the VSG without the high-pass filter directly drops due to the droop characteristic under the increase of load power. On the contrary, when adopting the VSG control strategy proposed in this paper, the frequency increases first during the transient process, which demonstrates that the VSG control strategy based on the highpass filter is an active frequency support strategy. Figures 10 and 12 show the angular frequency of SG and PCC point under three cases, respectively. The active power comparison of SG and VSG is shown in Figure 11.  In Figure 9, the frequency of the VSG without the high-pass filter directly drops due to the droop characteristic under the increase of load power. On the contrary, when adopting the VSG control strategy proposed in this paper, the frequency increases first during the transient process, which demonstrates that the VSG control strategy based on the high-pass filter is an active frequency support strategy. Figure 10 and Figure 12 show the angular frequency of SG and PCC point under three cases, respectively. The active power comparison of SG and VSG is shown in Figure 11. Figure 9 shows the angular frequency of VSG under three cases. In case 1, a highpass filter for load disturbance extraction is not used in VSG control, and in case 2, the high-pass filter is introduced in VSG control without optimized parameters. In the last case, the control parameters of the proposed method are optimized.
Angular Frequency(rad/s) Figure 9. The simulation result of VSG angular frequency in three cases under the condition of load sudden increase.
In Figure 9, the frequency of the VSG without the high-pass filter directly drops due to the droop characteristic under the increase of load power. On the contrary, when adopting the VSG control strategy proposed in this paper, the frequency increases first during the transient process, which demonstrates that the VSG control strategy based on the highpass filter is an active frequency support strategy. Figures 10 and 12 show the angular frequency of SG and PCC point under three cases, respectively. The active power comparison of SG and VSG is shown in Figure 11.    From Figures 10 and 11, it can be seen that the conventional VSG control strategy without a high-pass filter shows the most serious oscillation. In comparison, with the proposed strategy, the VSG actively shares more active power during the load disturbance From Figures 10 and 11, it can be seen that the conventional VSG control strategy without a high-pass filter shows the most serious oscillation. In comparison, with the proposed strategy, the VSG actively shares more active power during the load disturbance and extends the supporting time of the active power. The SG frequency nadir is increased from 313.1556 to 313.2305 rad/s, and the slope of frequency is reduced. After adopting the high-pass filter with optimized parameters based on the PSO algorithm, the angular frequency performance of SG is the best compared with other cases. Furthermore, since the VSG provides more additional power and extends the duration of power support, the damping of the system becomes larger, which attenuates the frequency oscillations.
As shown in Figure 12, the frequency response of the PCC point in different cases also demonstrates that the proposed strategy has the ability of active frequency support. P vsg /with the high-pass filter/parameters optimized P sg /with the high-pass filter/parameters optimized Figure 11. The simulation result of active power in three cases under the condition of load sudden increase.
From Figures 10 and 11, it can be seen that the conventional VSG control strategy without a high-pass filter shows the most serious oscillation. In comparison, with the proposed strategy, the VSG actively shares more active power during the load disturbance and extends the supporting time of the active power. The SG frequency nadir is increased from 313.1556 to 313.2305 rad/s, and the slope of frequency is reduced. After adopting the high-pass filter with optimized parameters based on the PSO algorithm, the angular frequency performance of SG is the best compared with other cases. Furthermore, since the VSG provides more additional power and extends the duration of power support, the damping of the system becomes larger, which attenuates the frequency oscillations.
As shown in Figure 12, the frequency response of the PCC point in different cases also demonstrates that the proposed strategy has the ability of active frequency support.

Simulations Results with Full Load
Asynchronous motors are a common type of load in the actual power system. Therefore, to show the effectiveness of the proposed method with different load types, the asynchronous motor is considered here instead of constant power load. The simulation results in different cases, i.e., without the high-pass filter, with the high-pass filter, and with the parameters optimized high-pass filter, are displayed in Figures 13 and 14. Figure 13 shows the simulation result of VSG angular frequency in three cases. It can be seen in Figure 13 that the VSG angular frequency increases first during the transient

Simulations Results with Full Load
Asynchronous motors are a common type of load in the actual power system. Therefore, to show the effectiveness of the proposed method with different load types, the asynchronous motor is considered here instead of constant power load. The simulation results in different cases, i.e., without the high-pass filter, with the high-pass filter, and with the parameters optimized high-pass filter, are displayed in Figures 13 and 14.
Electronics 2021, 10, x FOR PEER REVIEW 13 o process, while the frequency of conventional VSG control without the high-pass filter creases directly due to the droop characteristic. Thus, it can be found that the VSG con strategy based on the high-pass filter is an active frequency support strategy.    The simulation result of SG angular frequency with the asynchronous motor shown in Figure 14. The frequency curves in the three cases depict that the pro method with the optimized high-pass filter is superior to the other methods, and th posed method has lower frequency deviation and smaller frequency oscillation. Th ulation results show the effectiveness of the proposed control strategy and the PSO rithm once again.

Comparison with Other Control Method
To show the superiority of the active grid frequency support strategy, the met increasing virtual inertia J in [21] and bang-bang-control in [22] are compared, and two approaches are the typical frequency improvement scheme of VSG. The comp performances of different methods are displayed in Figures 15 and 16, respectively According to the VSG angular frequency of Figure 15, it can be seen clearly t VSG angular frequency increases first when the load increases, which is quite di from the other two methods. Therefore, it can be proved that the active support c teristics can only be implemented by the proposed method.  Figure 13 shows the simulation result of VSG angular frequency in three cases. It can be seen in Figure 13 that the VSG angular frequency increases first during the transient process, while the frequency of conventional VSG control without the high-pass filter decreases directly due to the droop characteristic. Thus, it can be found that the VSG control strategy based on the high-pass filter is an active frequency support strategy.
The simulation result of SG angular frequency with the asynchronous motor load is shown in Figure 14. The frequency curves in the three cases depict that the proposed method with the optimized high-pass filter is superior to the other methods, and the proposed method has lower frequency deviation and smaller frequency oscillation. The simulation results show the effectiveness of the proposed control strategy and the PSO algorithm once again.

Comparison with Other Control Method
To show the superiority of the active grid frequency support strategy, the method of increasing virtual inertia J in [21] and bang-bang-control in [22] are compared, and these two approaches are the typical frequency improvement scheme of VSG. The comparative performances of different methods are displayed in Figures 15 and 16 Figure 16 shows the comparison of SG angular frequency. It can be observed that these three methods can improve frequency response effectively. A better frequency performance can be obtained by bang-bang control compared with the method of increasing J. When the proposed approach, i.e., active frequency support strategy is employed, the enhancement effect on SG angular frequency is more obvious, and the simulation results show the superiority of the proposed method.

Hardware in the Loop Experimental Test
To further verify the active grid frequency support strategy, a HIL experimental platform is established, as shown in Figure 17. The experimental platform consists of HIL realtime simulator and rapid control prototyping (RCP), host computer, and oscilloscope. The HIL has CPU and FPGA resources for real-time calculations, which simulates the VSG-SG coupling system. Meanwhile, the VSG control strategy is implemented in RCP. Here the HIL simulator and RCP are connected to exchange voltage signals, current signals, and PWM signals through the physical IO interface. The experimental parameters are consistent with the simulation, and the disturbance is simulated by switching the load. According to the VSG angular frequency of Figure 15, it can be seen clearly that the VSG angular frequency increases first when the load increases, which is quite different from the other two methods. Therefore, it can be proved that the active support characteristics can only be implemented by the proposed method. Figure 16 shows the comparison of SG angular frequency. It can be observed that these three methods can improve frequency response effectively. A better frequency performance can be obtained by bang-bang control compared with the method of increasing J. When the proposed approach, i.e., active frequency support strategy is employed, the enhancement effect on SG angular frequency is more obvious, and the simulation results show the superiority of the proposed method.

Hardware in the Loop Experimental Test
To further verify the active grid frequency support strategy, a HIL experimental platform is established, as shown in Figure 17. The experimental platform consists of HIL real-time simulator and rapid control prototyping (RCP), host computer, and oscilloscope. The HIL has CPU and FPGA resources for real-time calculations, which simulates the VSG-SG coupling system. Meanwhile, the VSG control strategy is implemented in RCP. Here the HIL simulator and RCP are connected to exchange voltage signals, current signals, and PWM signals through the physical IO interface. The experimental parameters are consistent with the simulation, and the disturbance is simulated by switching the load.   Figure 18 shows the waveform of the SG angular frequency. From Figure 18a,b, it can be observed that the system with conventional VSG control will endure a larger frequency deviation, where the overshoot is 0.5432 rad/s. In the proposed method, the overshoot is reduced to 0.471 rad/s. Compared with the original parameters of the high-pass filter, the frequency deviation, which is less than 25.9%, has a significant improvement as Figure  18c.  Figure 18 shows the waveform of the SG angular frequency. From Figure 18a,b, it can be observed that the system with conventional VSG control will endure a larger frequency deviation, where the overshoot is 0.5432 rad/s. In the proposed method, the overshoot is reduced to 0.471 rad/s. Compared with the original parameters of the high-pass filter, the frequency deviation, which is less than 25.9%, has a significant improvement as Figure 18c.  Figure 18 shows the waveform of the SG angular frequency. From Figure 18a,b, it can be observed that the system with conventional VSG control will endure a larger frequency deviation, where the overshoot is 0.5432 rad/s. In the proposed method, the overshoot is reduced to 0.471 rad/s. Compared with the original parameters of the high-pass filter, the frequency deviation, which is less than 25.9%, has a significant improvement as Figure  18c.     Figure 19 shows the waveform of the output active power. As shown in Figure 19c, the proposed strategy with the optimized parameter can provide more active power support compared to the cases with and without the proposed control shown in Figure 19a,b, respectively. Thus, the frequency deviation and oscillation are significantly reduced. It is concluded that the active grid frequency support strategy can effectively improve the system frequency response characteristics. Meanwhile, these experimental results are in good accordance with the simulation results.  Figure 19 shows the waveform of the output active power. As shown in Figure 19c, the proposed strategy with the optimized parameter can provide more active power support compared to the cases with and without the proposed control shown in Figure 19a,b, respectively. Thus, the frequency deviation and oscillation are significantly reduced. It is concluded that the active grid frequency support strategy can effectively improve the system frequency response characteristics. Meanwhile, these experimental results are in good accordance with the simulation results.

Conclusions
For breaking the limitation of the virtual synchronous generator to support the grid frequency, an active grid frequency support strategy for the VSG-SG coupling system is proposed in this paper. In this method, a high-pass filter is applied to extract the load disturbance component, which is superimposed to the active power loop of the VSG, and then the extra power support for SG can be provided. The effectiveness of the proposed method is verified by the simulations in MATLAB/SIMULINK and HIL experimental tests. Compared to the traditional VSG, the grid-connected inverter with the proposed method can provide additional active power support, which alleviates the power imbalance of SG greatly, and the proposed method thereby presents a better frequency regulation performance under the disturbance. The frequency deviation and the slope of grid frequency are both decreased with the active grid frequency support strategy. Meanwhile, the H∞ and H2 norms are used to quantitatively describe the impact of the proposed method on the frequency response. Combined with the particle swarm optimization algorithm, the optimal parameters of the high-pass filter are obtained, and the performance of the proposed active grid frequency support strategy is further improved.

Conflicts of Interest:
The authors declare no conflict of interest.