Adaptive Inertia and Damping Coordination (AIDC) Control for Grid-Forming VSG to Improve Transient Stability

Abstract

Different from the conventional synchronous generator, the virtual inertia and damping control parameters for the inverter-based virtual synchronous generator (VSG) provide more flexibility for stable operation and dynamic performance optimization. However, the operation control principle is still unclear regarding how to coordinate virtual inertia and damping considering both frequency stability and transient synchronization stability. In this paper, an Adaptive Inertia and Damping Coordination (AIDC) control strategy is proposed for grid-forming VSGs to improve transient stability. The proposed AIDC strategy adaptively adjusts the virtual inertia and damping coefficients based on real-time conditions of operation frequency deviation and its rate of change of frequency (RoCoF). The virtual inertia is designed to dynamically increase in the accelerated area and decrease in the decelerated are, and the virtual damping coefficient is designed to increase and enlarge the positive virtual damping effect during the whole accelerated/decelerated transient process. In addition, the proposed AIDC strategy is realized through the practical arctan-function control method with limited boundaries, which can assist engineers. The effectiveness of the proposed AIDC strategy is validated through hardware-in-the-loop experiments.

1. Introduction

With the increasing penetration of renewable generations, synchronous generators have been gradually replaced by inverter-based distributed generations (IBGs), such as photovoltaic and wind renewable power generation. In addition, the dynamic stability behavior of power systems has gradually changed. On the one hand, the IBGs provide more control flexibility. On the other hand, the device fragility of the converter must be considered under large disturbances. Therefore, how to flexibly configure available IBG control resources is still an open problem [1].

Traditional IBGs synchronize with the grid through the phase-locked loop (PLL) and tend to operate in grid-following mode [2]. This kind of grid-following (GFL) converter can be equivalent to a controlled current source, and its normal operation depends on the presence of a voltage source in the system to build a voltage reference. However, the stable operation of the GFL converters will be restricted by the gradual decrease in the proportion of SGs, resulting in a lack of voltage support.

To face this challenge, the grid-forming (GFM) control for converters, which has a duality with GFL control, has been proposed and widely discussed to have the ability to form the grid [3,4]. Among various GFM control schemes, droop control [5,6] and virtual synchronous generator (VSG) control [7,8] are the two typical GFM control methods. The inspiration of droop control is to make the converters have the ability to flexibly adjust the output active power and reactive power as the droop relationship of active power frequency (P-ω) and the reactive power voltage (Q-V), which is similar to the traditional synchronous generators (SGs). However, the inertia-less characteristics of a droop control-based converter brings frequency stability issues to converter-dominant power systems, such as an overlarge Rate of Change of Frequency (RoCoF) issue and overlimit frequency nadir issue. On the basis of droop control, VSG deploys the swing equation of SG to mimic both dynamic and steady-state characteristics. The virtual inertia coefficient and the virtual damping coefficient are the key control parameters for VSG control. The virtual inertia item of VSG provides the inertia support for dealing with frequency disturbance events, while the virtual damping item helps frequency regulation and transient power oscillation damping. To further facilitate the understandings and practical applications of these two control schemes, the relationships and similarities between droop control and VSG control have been discussed, and it is pointed out in [9] that there is the form equivalence between droop control and VSG control owing to the active power low-pass filter of droop control. In short, VSG control can be regarded as the improved droop control scheme with more powerful virtual inertia support and dynamic frequency performance optimization [7,8,9].

One advantage of VSG control is its flexibility in adjusting control parameters. For example, virtual inertia can be adjusted within a certain range according to the real-time status of system operation, which provides more possibilities for dynamic performance optimization and frequency stability enhancement. This flexibility allows for frequency stability improvement through techniques such as self-adaptive inertia [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Recently, the design ideas and principles of adaptive inertia control have been rapidly discussed. The benefits of different values of virtual inertia were discussed in [10]. In [11], the authors modified the droop gain as a function of the frequency derivative term to reduce frequency deviation under disturbances. However, this method only focused on the frequency deviation as the feedback to adjust the droop gain. In [12], the dynamic frequency deviation and RoCoF are combined as the reference for adaptive virtual inertia design. The combination of dynamic frequency deviation and RoCoF can help determine the dynamic operation state of VSG, which have been widely used in the following studies. However, only two values of virtual inertia can be adjusted in [12], which can be viewed as a bang-bang virtual inertia control. To further develop this technology, more finely detailed adaptive virtual inertia algorithms were studied in [13,14,15,16,17,18,19,20,21,22,23,24], and the design for adaptive virtual damping is also considered to realize a better dynamic performance. These kinds of adaptive virtual inertia methods have been gradually applied in Energy Storage Systems [25], multi-area microgrids [23,24], MMC-MTDC transmission systems [26], and VSC-HVDC transmission systems [27,28]. However, these works only focused on the impact of variable control parameters on dynamic performance optimization and frequency stability. Clearly, the potentialities of the variable virtual inertia and virtual damping for transient synchronization stability enhancement still remain to be explored, which is also crucial to the VSG stable operation.

The transient synchronization stability of VSG refers to the ability that the VSG can realize synchronization with the grid under large disturbances such as severe grid voltage sags and short-circuit faults [29]. The transient stability of virtual synchronous generators (VSGs) is highly affected by virtual inertia and damping coefficient. As is pointed out in [30], small virtual inertia improves transient synchronization stability but harms frequency stability. Increasing the virtual damping coefficient can enlarge the positive virtual damping effect and enhance transient stability. However, the value of the virtual damping coefficient is often designed fixed and restricted by the frequency regulation requirement of the grid code [31]. It is also reported in [32] that droop control performs better than VSG control in transient stability enhancement for the hybrid power system. Furthermore, methods to improve transient stability have been proposed, including transient damping [33,34,35], co-design for virtual inertia and damping coefficient [36], and mode-adaptive switching [37,38]. Although various modified methods have been designed, it is still unknown how to dynamically coordinate virtual inertia and damping in a unified framework to enhance the transient synchronization stability of VSG.

To fill this gap, an Adaptive Inertia and Damping Coordination (AIDC) strategy is proposed for grid-forming VSG to enhance transient stability. The advantages of the AIDC control are summarized as follows:

(1)

The design principle of the adaptive virtual inertia and damping is given considering not only frequency stability but also transient synchronization stability. The virtual inertia is designed to adaptively increase in the accelerated area and decrease in the decelerated area. Meanwhile, the virtual damping coefficient is designed to increase and enlarge the positive virtual damping effect during the transient process. Compared with the studies in [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], the benefits of adaptive virtual inertia and virtual damping on transient synchronization stability is fully discussed. The comparisons are summarized in

Table 1. Comparisons among existing methods [13,14,15,16,17,18,19,20,21,22,23,24] and the proposed AIDC control.

Types	Adaptive Virtual Inertia	Adaptive Virtual Damping	Characteristics	Optimization Objectives
[13,19,20]	$J=\left\{\begin{array}{l}{J}_0+k_J\left|\mathrm{d}\omega /\mathrm{d}t\right|,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)>0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_J\\ 0,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\le 0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_J\\ J_0,\left|\mathrm{d}\omega /\mathrm{d}t\right|\le M_J\end{array}\right.$	$D=\left\{\begin{array}{l}{D}_0,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\ge 0\\ D_0+k_D|\Delta \omega |,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)<0\\ \cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_d\\ D_0,\left|\mathrm{d}\omega /\mathrm{d}t\right|\le M_d\end{array}\right.$	Thresholds to avoid frequent switching. In the form of piecewise function.	Dynamic performance optimization.
[14]	$J=\left\{\begin{array}{l}{J}_0+k_J\left|\mathrm{d}\omega /\mathrm{d}t\right|,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)>0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_J\\ 0,\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\le 0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_J\\ J_0,\left|\mathrm{d}\omega /\mathrm{d}t\right|\le M_J\end{array}\right.$	$D=\left\{\begin{array}{l}{D}_0+k_D|\Delta \omega |,\left|\mathrm{d}\omega /\mathrm{d}t\right|>M_d\\ D_0,\left|\mathrm{d}\omega /\mathrm{d}t\right|\le M_d\end{array}\right.$	Minimum virtual inertia is zero. In the form of piecewise-function.	Dynamic performance optimization.
[15]	$J=\left\{\begin{array}{l}{J}_{\max },\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)>0\\ J_{\min },\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\le 0\end{array}\right.$	$D=\left\{\begin{array}{l}{D}_{\max },\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)>0\\ D_{\min },\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\le 0\end{array}\right.$	Bang-bang-based adaptive control. The ratio D/J is fixed.	Dynamic performance optimization.
[16]	$J=a_J{e}^{-b_J(\frac{\Delta \omega }{2\pi }+c_J)}+J_{\min }$	$D=D_0+k_D|\Delta \omega |,D_0=f(SoC,\Delta \omega )$	State of Charge (SoC) and power limit are considered.	Frequency stability improvement.
[17]	$J=J_0+k_J|P_{ref}-P|$	Fixed virtual damping	Adaptive virtual inertia is determined by power feedback.	Frequency stability improvement.
[18]	$J=\left\{\begin{array}{l}{J}_0,|\Delta \omega |\le M_{J0}\\ J_0+k_{J1}\frac{|\mathrm{d}\omega /\mathrm{d}t|}{T_{1}s+1},\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)>0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_{J1}\\ J_0+k_{J2}\frac{|\mathrm{d}\omega /\mathrm{d}t|}{T_{2}s+1},\Delta \omega (\mathrm{d}\omega /\mathrm{d}t)\le 0\cap \left|\mathrm{d}\omega /\mathrm{d}t\right|>M_{J1}\\ J_0,|\Delta \omega |>M_{J0}\cup \left|\mathrm{d}\omega /\mathrm{d}t\right|\le M_J\end{array}\right.$	$D=\left\{\begin{array}{l}{D}_0,|\Delta \omega |\le M_D\\ D_0+k_{D1}|\Delta \omega |,(\mathrm{d}\omega /\mathrm{d}t)>0\\ \cup |\Delta \omega |\ge M_D\\ D_0+k_{D2}\left|\mathrm{d}\omega /\mathrm{d}t\right|+e|\Delta \omega |,\\ (\mathrm{d}\omega /\mathrm{d}t)\le 0\end{array}\right.$	Fast change of virtual inertia is avoided. Virtual damping is also adaptively changed with |dω/dt|.	Dynamic performance optimization.
[21]	$\begin{array}{l}J=J_0+k_J\Delta \omega \left|\mathrm{d}\omega /\mathrm{d}t\right|\\ \mathrm{VSG} \mathrm{Control} \mathrm{law}: \downarrow \\ \frac{d\omega }{dt}=\frac{-2[D(\omega -{\omega }^{*})-P^{*}-P]}{J_0+\sqrt{J_0^2-4k_J(\omega -{\omega }^{*})[D(\omega -{\omega }^{*})-P^{*}-P]}}\end{array}$	Fixed virtual damping	VSG control law is re-expressed to avoid the measurement noise in frequency derivation.	Dynamic performance optimization.
[22]	$J=J_0+\frac{2k_J}{\pi }\arctan (\Delta \omega \cdot \Delta P)$	Fixed virtual damping	Arctan-function-based adaptive virtual inertia.	Frequency oscillation suppression.
[23]	Adaptive virtual inertia coefficient with Jaya-based-BE (balloon effect) algorithm.	Adaptive virtual damping coefficient with Jaya-based-BE (balloon effect) algorithm.	Suitable for multi-area microgrids. Load frequency control issues in islanded systems are considered. Intelligent algorithm.	Dynamic performance optimization.
[24]	Adaptive virtual inertia coefficient with HHO (Harris hawks optimization) optimizer.	Adaptive virtual damping coefficient with HHO optimizer.	High speed convergence. Suitable for large power system.	Dynamic performance optimization.
This study	$J=J_0+k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})$	$D=D_0+k_D{\arctan }^2(\frac{\mathrm{d}\omega }{\mathrm{d}t})$	Arctan-function-based adaptive virtual inertia and virtual damping. Adaptively change in accelerated area and decelerated area to ride through fault.	Transient synchronization enhancement and frequency stability improvement.

.

(2)

A practical arctan-function-based control realization of adaptive virtual inertia and damping with limited boundaries is proposed. The mathematical function ∆J = arctan(∆ω∙dω/dt) guarantees the boundaries for the adaptive virtual inertia, and ∆D_m = arctan²(dω/dt) provides an upper limit and guarantees ∆D remains positive during the whole accelerated/decelerated transient process, which facilitates engineers’ design.

(3)

The effectiveness of the proposed AIDC control is verified through large-signal attraction area analysis and time-domain experimental results. By coordinating the design for virtual inertia and damping, the system attraction area, dynamic performance, and transient stability have been significantly improved.

2. Proposed AIDC Control Method of VSG

2.1. Classical VSG System Configuration

Figure 1 shows the typical VSG control diagram. The power control loop of VSG can be expressed as [8]:

$$J\frac{\mathrm{d}\omega }{\mathrm{d}t}=P^{*}-P-D(\omega -{\omega }^{*})$$

(1)

$$V_{vref}=V^{*}-n(Q^{*}-Q)$$

(2)

where (1) and (2) represent the P-ω loop and Q-V loop, respectively. P* and Q* are the reference of active power and reactive power reference, respectively. P and Q are the output power of active power and reactive power at the PCC. The virtual inertia coefficient and virtual damping coefficient are expressed as J and D, respectively. The Q-V loop droop coefficient is expressed as n. V is the VSG output voltage at PCC. ω* and V* are the angular speed reference and the amplitude reference voltage. ω and V are the angular speed and amplitude of the VSG output voltage.

The active power transmitted from VSG to the grid is expressed as [5]:

$$P=\frac{3V{V}_g}{2X_g}\sin \delta$$

(3)

where V_g is the grid voltage amplitude and δ represents the power angle between VSG and the grid. X_g represents the line impedance, and the line resistance is ignored in the highly inductive transmission line.

2.2. Proposed Universal AIDC Control Principle Oriented to Transient Stability

As is shown in Figure 2a, the maximum deceleration area should be larger than the maximum acceleration area to remain in synchronization with the grid under large distances according to the equal area criterion (EAC) [39]. Figure 2b shows the time-domain response of power angle/frequency. It can be mainly divided into four segments. The grid fault occurs at point B and time t₁. During the first segment from point B to point C (from t₁ to t₂), the frequency will accelerate, and the transient power angle is increased. This area is called the accelerated area. At this moment, a large virtual inertia is needed to slow down the deviation trend and reduce the maximum frequency deviation. At point C, the fault is cleared. During the second segment from point C to point D (from t₂ to t₃), the frequency will decelerate, but ∆ω is greater than zero, and then the power angle is still increased. This area is called the decelerated area. In this process, small inertia is needed to make VSG return to the nominal frequency quickly. For example, if the virtual inertia is changed to 0 at point C, the frequency can return to the nominal frequency instantaneously. Then, the power angle of VSG will reduce, return back to point A, and remain stable in the steady state. The decelerated area for transient stability is no longer needed, which is totally different from the SG.

Therefore, a large amount of inertia is needed in the accelerated area, and a small amount of inertia is needed in the decelerated area. So, ∆J should be positive during the segments of t₁–t₂ and t₃–t₄, and it should be negative during the segments of t₂–t₃ and t₄–t₅. For the virtual damping control, the virtual damping coefficient D should be always greater than 0 during all segments. In addition, the dynamic adaptive compensation should only affect the dynamic response (∆J = 0, ∆D = 0 in steady-state), and ∆J and ∆D should be designed by sampling available signals. The corresponding design guidelines are summarized in

Table 2. Design Principles of Virtual Inertia and Damping Coefficient Oriented to Transient Synchronization Stability at Different Operation States.

Segment	Δω	dω/dt	ω State	Power Angle Operation Area	ΔJ	ΔD
t1–t2	>0	>0	Deviation	Accelerated Aera	>0	>0
t2–t3	>0	<0	Return	Decelerated Aera	<0	>0
t3–t4	<0	<0	Deviation	Accelerated Aera	>0	>0
t4–t5	<0	>0	Return	Decelerated Aera	<0	>0

.

2.3. Proposed Arctan-Function-Based AIDC Control Method

The proposed AIDC control method can be expressed as:

$$(J_0+\Delta J)\frac{\mathrm{d}\omega }{\mathrm{d}t}=P^{*}-P-(D_0+\Delta D)(\omega -{\omega }^{*})$$

(4)

where J₀ and D₀ represent the static control variables for the virtual inertia constant and damping coefficient, while ∆J and ∆D represent the designed dynamic control variables. According to the design guidelines, the adaptive inertia and damping control items of AIDC can be designed based on real-time conditions of operation frequency deviation and its rate of change of frequency (RoCoF):

$$\left\{\begin{array}{l}\Delta J=k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})\\ \Delta D=k_D{\arctan }^2(\frac{\mathrm{d}\omega }{\mathrm{d}t})\end{array}\right.$$

(5)

where k_J and k_D represent the adaptive constants of virtual inertia and the damping constant, respectively.

The proposed method contains two adaptive items, which can be seen in Figure 3.

2.3.1. The Adaptive Virtual Inertia according to ∆ω and dω/dt

The virtual inertia coefficient (J₀ + ∆J) is required to increase during the accelerated area and decrease in the decelerated area. It can adaptively change according to the combination of ∆ω and dω/dt. The adaptive virtual inertia is also required to have the upper and lower boundaries. The maximum virtual inertia J_max is relevant to the instantaneous power capacity limitation of the inverter [16], and the minimum virtual inertia J_min is required to satisfy the minimum frequency stability requirement. Therefore, the upper and the lower limits of virtual inertia can be designed as [16,17,18]:

$$\left\{\begin{array}{l}PO(J_{\max })\Delta {\omega }_{\max }\le P_{\max }-P^{*}\\ J_{\min }>\frac{\Delta P_{dis}}{{|\mathrm{d}\omega /\mathrm{d}t|}_{\max }}\end{array}\right.$$

(6)

where PO(J_max) represents the VSG output power overshoot with J_max caused by a step disturbance in ∆ω. P_max represents the instantaneous power capacity limitation of the inverter, and P^* represents the rated power. ∆P_dis represents the output power change due to disturbance, and |dω/dt|_max is the required maximum frequency change according to the grid code. To realize the required virtual inertia control, the mathematical function ∆J = arctan(∆ω∙dω/dt) is introduced in this paper. The adaptive virtual inertia curve is shown in Figure 4a. Then, the reasonable value of the coefficient k_J can also be determined as shown in Equations (7) and (8). It guarantees the boundaries for the adaptive virtual inertia, which is easy for engineers to design.

$$\left\{\begin{array}{l}J=J_0+\Delta J=J_0+k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})\\ J_{\min }\le J_0+k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})\le J_{\max }\end{array}\right.$$

(7)

As the boundary of the arctan function is [−π/2, π/2], the adaptive inertia control coefficient k_J should meet the following equation.

$$0\le k_J\le min\left\{\frac{2}{\pi }(J_{\max }-J_0), \frac{2}{\pi }(J_0-J_{\min })\right\}$$

(8)

2.3.2. The Adaptive Virtual Damping according to dω/dt

The increase in the virtual damping coefficient can increase the system positive damping effect for transient synchronization stability enhancement. Therefore, the virtual damping coefficient (D₀ + ∆D) is designed to be adaptively increased according to (dω/dt) under disturbance. ∆D can also be understood as the transient damping coefficient, which is positive during transient stability issues and returns to zero in the steady state. Since large transient virtual damping may cause a large power fluctuation when the grid frequency disturbances occur, the upper limit of the virtual damping coefficient can be designed as [18]:

$$D_{\max }\le \frac{P_{\max }-P^{*}}{|\Delta \omega |}$$

(9)

In addition, the mathematical function ∆D = arctan²(dω/dt) provides an upper limit and guarantees that ∆D remains positive during the whole accelerated/decelerated transient process. The adaptive virtual damping curve is shown in Figure 4b. According to Equations (10) and (11), a reasonable value of the coefficient k_D can also be determined. The arctan function facilitates the parameters design.

$$\left\{\begin{array}{l}D=D_0+\Delta D=D_0+k_D{\arctan }^2(\frac{\mathrm{d}\omega }{\mathrm{d}t})\\ D_{\min }\le D_0+k_D{\arctan }^2(\frac{\mathrm{d}\omega }{\mathrm{d}t})\le D_{\max }\end{array}\right.$$

(10)

As the boundary of the arctan function is [−π/2, π/2], the adaptive virtual damping control coefficient k_D should meet the following equation.

$$\frac{4}{{\pi }^2}(D_{\min }-D_0)\le k_D\le \frac{4}{{\pi }^2}(D_{\max }-D_0)$$

(11)

3. Transient Stability Analysis of the Proposed AIDC Control

Before analyzing the transient synchronization stability of the proposed AIDC control, some assumptions are made: (1) Due to the fast inner voltage/current control loop, the transient stability is mainly determined by the outer power control loop. (2) The influence of the Q-V loop is approximately neglected. (3) The line impedance is highly inductive and the dynamics of line impedance is ignored. Therefore, the power angle swing equation of the VSG can be expressed as:

$$\left\{\begin{array}{l}\stackrel{·}{\delta }=\omega \\ \stackrel{··}{\delta }=\frac{1}{J}{P}^{*}-\frac{3V{V}_g}{2J{X}_g}\sin \delta -\frac{D}{J}\stackrel{·}{\delta }\end{array}\right.$$

(12)

where J = J₀ + ∆J, and D = D₀ + ∆D. To facilitate transient stability analysis, this paper focuses on faults that will not trigger current limitation protection.

The attraction region analysis can represent the transient synchronization stability margin. According to the equivalent dynamic Equation (12), the attraction regions among the traditional VSG control (k_J = 0, k_D = 0; → ∆J = 0, ∆D = 0), adaptive virtual inertia control (k_D = 0; → ∆D = 0), and the proposed AIDC control method can be drawn and seen in Figure 5. Through the comparison of the above attraction regions, the proposed AIDC method has a broader attraction region. Therefore, transient synchronization stability under AIDC control is greatly enhanced.

To further verify the effectiveness of the proposed adaptive inertia and damping coordination (AIDC) control, a comparison on transient performances of VSG without/with dynamic items is shown in Figure 6. In this comparison, the second transient stability issue is considered, where the system has no equilibrium point under the severe disturbance. This kind of disturbance is required to be cleared within the Critical Clear Time (CCT) to make the system recover to stable. In this case, the CCT and Critical Clear Angle (CCA) are used as indicators to represent the strength of transient synchronization stability with larger values indicating stronger stability. To obtain a more accurate CCT and less conservative transient stability boundary, the inverse time integral-based approach is employed here [21].

As shown in Figure 6, the power oscillation under the proposed Adaptive Inertia and Damping Coordination (AIDC) control is greatly suppressed during the transient process, and the settling time is reduced from 19.249 to 3.288 s, indicating a faster dynamic response speed. The CCA is increased from 2.23 to 2.65 rad, while the CCT is increased from 1.219 to 1.936 s. Thus, we can see that AIDC control items can improve both transient stability and dynamic performance.

4. Control-Hardware-In-Loop (CHIL) Tests

CHIL tests are carried out to further verify the feasibility of the proposed Adaptive Inertia and Damping Coordination (AIDC) control in transient synchronization stability enhancement. As shown in Figure 7, the HIL system consists of two parts: the hardware circuits in the loop and the controller outside. The hardware physical circuits in the loop are simulated by the OP5600 real-time simulator with a time-step of 20 µs to accurately simulate the dynamic characteristics, which includes the inverter switches, gate-driven circuit, LC filters, line impedance, and the utility grid. The dSPACE 1202 Microlab-Box device is applied as the system controller with a practical sampling frequency of 20 kHz, and the detailed proposed control algorithm is shown in Figure 3.

4.1. Transient Synchronization Stability Enhancement Verifications

Figure 8 shows the model of the proposed adaptive inertia and damping coordination (AIDC) control-based DGs, which includes the average power calculation, the proposed AIDC control, the dual voltage–current closed loops, and Pulse Width Modulation (PWM). The CHIL parameters are listed in

Table 3. Control-Hardware-In-Loop (CHIL) Test Parameters.

Parameter	Symbol	Value
System Parameters
Nominal frequency	f*	50 Hz
Nominal voltage	V*	311 V
Rated active power	P*	20 kW
Rated reactive power	Q*	0 kvar
Control Parameters
Power filter time constant	τ	1/60
Q-V droop coefficient	n	1 p.u.
Virtual inertia constant	J0	4 p.u.
Virtual damping coefficient	D0	2 p.u.
Adaptive inertia coefficient	kJ	1 p.u.
Adaptive damping coefficient	kD	2 p.u.

. In this case, the grid voltage drops to 0.55 p.u. when the disturbance occurs, and after the fault is cleared, the grid voltage recovers to 1 p.u. of the normal condition. The CHIL experimental results are shown in Figure 9.

Figure 9(a1,a2) shows the waveforms of the traditional VSG control under different fault clearance times (FCTs). The critical fault clearance time CCT₁ under this condition is 1.23 s. In Figure 9(a1), FCT = 1.23 s ≤ CCT₁, and VSG can recover to stable. In Figure 9(a2), FCT = 1.24 s > CCT₁, the VSG loses synchronization stability. Figure 9(a3) shows the value curves of virtual inertia J and damping coefficient D_m of the traditional VSG control. J and D_m remain fixed.

Figure 9(b1,b2) shows the waveforms of the adaptive virtual inertia control under different fault clearance times (FCTs). Under such conditions, the critical fault clearance time CCT₂ is 1.55 s. When FCT = 1.56 s, the system converges to another equilibrium point, which is deemed to be unstable in engineering [21]. Figure 9(b3) shows the value curves of virtual inertia J and damping coefficient D of the adaptive virtual inertia control, and J is adaptively altered to enlarge the CCT and enhance transient stability during the transient process.

Figure 9(c1,c2) shows the waveforms of the AIDC control under different fault clearance times (FCTs). Under such conditions, the critical fault clearance time CCT₃ is 2.00 s, which is greatly longer than the two previous methods. When FCT = 2.01 s, the system converges to another equilibrium point to be unstable. Figure 9(c3) shows the value curves of virtual inertia J and damping coefficient D of AIDC control. Both J and D are adaptively altered to enlarge the CCT and enhance transient stability during the transient process. As there is some small disturbance in dω/dt, it is reasonable that the virtual damping coefficient fluctuates before the grid voltage sag, and the positive fluctuating of the virtual damping is preferred for system stability.

To further illustrate the advantages of the proposed adaptive inertia and damping coordination (AIDC) control in transient stability enhancement,

Table 4. Comparisons among the above three methods according to the CHIL test results.

Methods	ΔJ	ΔD	Critical Clearing Time (CCT)	Transient Synchronization Stability
Traditional VSG control	0	0	1.23 s	/
Only adaptive virtual inertia control	$\Delta J=k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})$	0	1.55 s	+
Proposed AIDC control	$\Delta J=k_J\arctan (\Delta \omega \cdot \frac{\mathrm{d}\omega }{\mathrm{d}t})$	$\Delta D=k_D{\arctan }^2(\frac{\mathrm{d}\omega }{\mathrm{d}t})$	2.00 s	++

displays the comparisons among the above three methods according to the CHIL test results. It can be seen that the proposed AIDC control can greatly enhance the transient synchronization stability by enlarging of CCT.

4.2. Inertia Support and Frequency Regulation Ability Verification

In this case, 0.2 Hz grid frequency change occurs at 3 s. The output active power and frequency of grid-connected inverter are shown in Figure 10. It can be seen that when the disturbance occurs at 3 s, the proposed AIDC control can provide the instantaneous inertia power for frequency support. The steady-state active power rises from 20 to 25 kW to provide the primary frequency regulation. The maximum output power is 34.2 kW to provide the inertia support. In addition, the AIDC control can realize frequency regulation according to the value of virtual damping coefficient. In addition, the converter under the Adaptive Inertia and Damping Coordination (AIDC) control can quickly reach the new steady state within about 2 s.

5. Conclusions

This paper proposes an Adaptive Inertia and Damping Coordination (AIDC) control method to improve the transient synchronization stability of VSG rather than the frequency support viewpoint. The proposed method contains two items: the adaptive virtual inertia and the adaptive damping coefficient. According to the designed principle ∆J = arctan(∆ω∙dω/dt), the virtual inertia adaptively increases in the acceleration area and decreases in the deceleration area based on real-time conditions of operation frequency deviation and its rate of change of frequency (RoCoF). In addition, the virtual damping coefficient increases to enlarge the positive virtual damping effect during the transient process with the principle ∆D_m = arctan²(dω/dt). Compared with traditional VSG control and only adaptive virtual inertia control, the proposed AIDC control has a significant advantage in transient synchronization stability enhancement, resulting in a larger attraction area, CCA, and CCT. The effectiveness of the proposed AIDC control is verified through HIL experiments under grid voltage sag. From the large-signal attraction area analysis and time-domain experimental results, the proposed coordinating design for virtual inertia and damping can significantly improve the system attraction area, dynamic performance, and transient stability.

In future work, we will consider a more practical implementation of the proposed virtual and damping control method. It is noted that the instantaneous power limit of overload capacity for a normal inverter is 1.2–1.8 pu, which is very weak compared with the synchronous generator (2.5–6 pu). For a normal inverter, the buffer power and over-load capacity is limited, and thus, the inertia support is very limited. To apply the inertia support control of the special inverter, there are two measures: (1) from the physical hardware, we will focus on designing a large-margin power capacity of the special inverter by considering overload heat dissipation; (2) from the control viewpoint, we should design the proper virtual inertia and damping moments, which is given in Equations (6)–(11) in this study.