Transient Damping-Type VSG Control Strategy Based on Flexibly Adjustable Cutoff Frequency

Abstract

To address the insufficient adaptability of virtual synchronous generators (VSGs) under traditional fixed-value damping control in multiple application scenarios and the lack of regulatory flexibility in transient damping control with a fixed cutoff frequency, a transient damping-type VSG control strategy with flexibly adjustable cutoff frequency is proposed. The aim is to break through the regulatory limitations of the fixed cutoff frequency, quantify the inverse coordination relationship between the cutoff frequency and the equivalent damping coefficient, establish a dynamic adjustment mechanism of the cutoff frequency based on the system natural oscillation frequency, damping ratio, and power grid parameters, and clarify the value range from 0 to ω_cmax as well as the real-time adaptation algorithm. First, the influence of damping on active power and frequency is analyzed through the VSG model. Second, combined with the characteristic analysis of different damping types, the advantages of transient damping in transient response capability under various operating conditions are derived. Furthermore, the role of the cutoff frequency in transient damping on output characteristics is specifically analyzed, a transient damping design method with flexibly adjustable cutoff frequency is proposed, and the value range of the cutoff frequency is calibrated. Finally, a hardware-in-the-loop experimental platform is established for experimental testing. The strategy effectively eliminates the output power deviation when the system frequency deviates, enhances the transient response capability of the VSG under different operating conditions, and exhibits superior output characteristics.

1. Introduction

The penetration rate of new energy sources such as wind power and photovoltaic (PV) power in power systems continues to increase, and the power grid is gradually transforming into a new-type power system dominated by new energy. However, the power electronic devices relied on by new energy generation lack the inherent inertia and damping characteristics of traditional synchronous generators, leading the system to face severe challenges such as low inertia and weak support [1,2]. Under disturbances like sudden load changes and fluctuations in new energy output, the power grid frequency is prone to significant deviations, and may even trigger cascading failures, seriously threatening the safe and stable operation of the power system. Against this background, grid-forming converters based on virtual synchronous generator (VSG) technology, by virtue of their ability to simulate the rotor motion and excitation characteristics of synchronous generators, exhibit external voltage source characteristics. They can provide inertia support, frequency regulation services, and voltage support for the system, becoming one of the key technologies to address the stability issues of new energy power grids [3].

Damping control, as the core link of VSG grid-forming control, directly affects the system’s dynamic response speed, stability, power oscillation suppression effect, and power distribution accuracy [4]. Its rational design is crucial to the operating performance of grid-connected devices and power grid security. Currently, the mainstream damping control forms of VSG mainly include three types: fixed-frequency damping control, grid frequency damping control, and transient damping control [5]. Ref. [6] classifies operating phases based on angular frequency deviation, active power deviation, and the rate of change of these deviations, and enhances the dynamic performance of the photovoltaic-storage microgrid through adaptive optimization of these parameters. Ref. [7] proposes an enhanced power recovery control strategy that coordinates virtual impedance and virtual damping to improve frequency and power stability. Ref. [8] reveals the differences in the action mechanisms of different damping controls by comparing the output characteristics of typical strategies such as fixed-frequency damping and grid frequency damping, providing a basic reference for the selection of damping control forms. However, its research focuses on the characteristic comparison of existing fixed-parameter damping controls, does not involve the dynamic regulation design of key parameters in transient damping, and fails to solve the problem of insufficient adaptability of transient damping with a fixed cutoff frequency under multiple operating conditions. Refs. [8,9,10] present improved adaptive control strategies to enhance the frequency response characteristics of VSG during grid connection and under disturbances, thereby strengthening the system’s frequency response. Ref. [11] proposes an additional damping torque method that provides an extra damping ratio for the system while ensuring the original droop characteristics and inertia remain unaffected.

The aforementioned studies mainly focus on fixed-frequency damping control and grid frequency damping control, concentrating on steady-state stability without considering the role of damping in transient stability. To address this issue, ref. [12] adopts a phase plane diagram to study the influence mechanism of VSG damping parameters on system transient stability, improving the transient power angle stability of the system. Ref. [13] analyzes the influence law of damping coefficients on the dynamic oscillation and steady-state deviation of output active power, and proposes an improved transient damping strategy based on active power differential feedback. Ref. [14] presents an optimal parameter design scheme for a transient damping method, enhancing the system transient stability. Ref. [15] proposes a decentralized mutual damping suppression method, which increases the damping of VSG during dynamic processes and accelerates frequency convergence, thereby suppressing power and frequency oscillations and improving system dynamic performance. Refs. [16,17,18] analyze the dynamic behavior of VSG, realize inertia adjustment under transient operating conditions, and determine transient damping parameters under different inertia requirements.

Traditional damping control does not consider the influence of damping on transient stability, and transient damping with a fixed cutoff frequency has limitations in frequency support.

To address the aforementioned issues, based on existing research, this paper takes three typical strategies—fixed-frequency damping control, grid frequency damping control, and transient damping control—as the research objects, and proposes a transient damping-type VSG control strategy with a flexibly adjustable cutoff frequency. First, the strategy establishes a VSG system model covering rotor motion characteristics and excitation characteristics, clarifies the requirements of application scenarios, and combines the characteristic analysis of different damping types to derive the advantages of transient damping in transient response capability under various operating conditions. Furthermore, it specifically analyzes the role of the cutoff frequency in transient damping on output characteristics, proposes a transient damping design method with flexibly adjustable cutoff frequency, and calibrates the value range of the cutoff frequency. This strategy reveals the damping action mechanism and the influence law of key parameters, clarifies the applicable scenarios of various control methods, provides technical support for the selection of damping control forms, parameter calibration, and multi-scenario adaptation of grid-forming control strategies, and further improves the frequency stability and operational reliability of the new-type power system.

2. Control Principle and Applicable Scenarios of Grid-Forming Converters

2.1. Based on the Grid-Forming Control Principle of VSG

Grid-forming converters take virtual synchronous generator (VSG) technology as the core control logic. By simulating the rotor motion characteristics and excitation adjustment mechanism of synchronous generators, they achieve autonomous control of active power–frequency and reactive power–voltage, while completing energy conversion and transmission relying on a specific system topology. The essence of the rotor motion equation of synchronous generators is that “the imbalance between mechanical power and electromagnetic power drives the change of angular frequency”, and the traditional equation is:

$$J{\displaystyle \frac{d\omega }{dt}}=T_m-T_e-D(\omega -{\omega }_0)$$

(1)

In the formula, J denotes the rotor moment of inertia, T_m is the mechanical torque, T_e represents the electromagnetic torque, D stands for the damping coefficient, ω is the rotor angular frequency, and ω₀ denotes the rated angular frequency.

Since power and torque satisfy P = Tω, and ω ≈ ω₀ in actual operation (the fluctuation range of angular frequency is small), the torque relationship can be converted into a power relationship. The inertia time constant H is introduced to characterize the system’s inertia characteristics, and the equation is rewritten as:

$$2H{\displaystyle \frac{d\omega }{dt}}=P_{set1}-P_e+K_d({\omega }_0-\omega )$$

(2)

In the formula, P_set1 denotes the input mechanical power reference value, P_e is the output electromagnetic power, K_d = Dω₀ stands for the damping power coefficient, ω represents the inverter output angular frequency, and ω₀ is the microgrid rated angular frequency.

To simulate the primary frequency regulation characteristic of synchronous generators, a droop link is introduced. Since primary frequency regulation has a static frequency deviation, it is also necessary to introduce an integral link to realize secondary frequency regulation and eliminate the static deviation. The formula for the modified active power reference value P_set1 is:

$$P_{set}=P_{ref}+\left({\displaystyle \frac{1}{m_p}}+{\displaystyle \frac{k_{ip}}{s}}\right)({\omega }_{ref}-\omega )$$

(3)

In the formula, P_ref denotes the initial active power reference value, m_p is the frequency regulation coefficient, ω_ref represents the reference angular frequency, and k_ip stands for the secondary frequency regulation integral coefficient.

Reactive power–voltage control adopts PI feedback control, as shown in the following formula:

$$E=\left(k_p+{\displaystyle \frac{k_i}{s}}\right)\left[D_{\mathrm{q}}(Q_0-Q_{\mathrm{e}})+(U_0-U)\right]+U_0$$

(4)

In the formula, E denotes the amplitude of the VSG output voltage; k_p and k_i are the proportional coefficient and integral coefficient of the control link, respectively; D_q stands for the droop coefficient; Q₀ and U₀ represent the reactive power set value and voltage set value, respectively; Q_e and U are the reactive power output and the amplitude of the AC side phase voltage, respectively.

2.2. Scenarios with VSG Control

VSGs are usually composed of energy storage units, inverter devices, and corresponding control algorithms. In this study, it is assumed that the system is equipped with sufficient energy storage units, and its state of charge can meet the system’s output requirements, with the research focus placed on the VSG control strategy. A simple applicable scenario with VSG units is shown in Figure 1, where T1∼T4 are AC transformers and KM denotes static switches.

In this scenario, the adaptability of system damping is insufficient. Any sudden load change will lead to the supply–demand imbalance of the microgrid system, thereby changing the rotational speed of synchronous generator sets and further affecting the stability of the system frequency. However, using VSG devices with fast response characteristics can reduce the frequency deviation caused by sudden load changes, thereby improving the frequency stability of the microgrid.

3. Analysis of Damping Characteristics

Damping is the core of VSG grid-forming control, and its importance is reflected in three aspects: firstly, it quickly compensates for power deficits and suppresses oscillations through damping term feedback regulation to maintain system frequency stability; secondly, it balances steady-state accuracy and dynamic response to adapt to multiple operating conditions by means of parameter regulation such as damping coefficient and cutoff frequency; thirdly, it reduces grid-connected inrush current, avoids faults caused by damping–inertia coupling imbalance, and ensures the grid-connection and operational safety of converters. Below is a theoretical analysis of the action mechanisms of different damping types [12,19,20].

3.1. Mechanism of the Effect of Different Damping Types on Active Power Control Loop

Fixed-frequency damping control (M1), grid frequency damping control (M2), and transient damping control (M3) are expressed as follows.

$$M(\omega ,{\omega }^{*})=\left\{\begin{array}{l}{M}_1(\omega ,{\omega }_0)=D_{\mathrm{p}}(\omega -{\omega }_0)\hfill \\ M_2(\omega ,{\omega }_{\mathrm{g}})=D_{\mathrm{p}}(\omega -{\omega }_{\mathrm{g}})\hfill \\ M_3(\omega ,{\omega }_0)=D_{\mathrm{p}}(\omega -{\omega }_0)s/(s+{\omega }_{\mathrm{c}})\hfill \end{array}\right.$$

(5)

In the formula, D_p denotes the damping coefficient; ω_c is the cutoff frequency, which is the blue-highlighted part in the control block diagram of Figure 2 according to Equation (5).

When adopting the M1 control mode, ω* is selected as ω₀, which cancels out with the ω₀ added in the feedforward term of the overall control. At this time, the active power control link can be simplified to the following formula:

Under the M1 damping control, when the grid frequency ω_g deviates from the rated angular frequency ω₀, the frequency difference (ω − ω₀) of M1 persists, leading to a fixed error in the steady-state power output. Under transient operating conditions such as sudden load changes or frequency disturbances, M1 is dominated by damping action to achieve transient power increase, which can quickly compensate for the system power deficit. Moreover, the larger the damping coefficient D_p, the stronger the transient power support, and the more significant the suppression effect on power oscillations.

When adopting the M2 control mode, the bus frequency needs to be obtained from the point of connection. At this time, an input variable ω_g is added to the system, and the active power loop derived by substituting it into the equation is as follows:

$${\delta }_{\mathrm{GFM}\text{-}{\omega }_{\mathrm{g}}}={\displaystyle \frac{1}{s}}\left({\displaystyle \frac{P_0-P_{\mathrm{e}}+D_{\mathrm{p}}({\omega }_{\mathrm{g}}-{\omega }_0)}{2Hs+D_{\mathrm{p}}}}+{\omega }_0\right)$$

(6)

Here, ω_g is obtained by the Phase-Locked Loop (PLL) tracking the grid frequency. For practical PLLs, different control parameters will affect their tracking performance. This paper assumes that the PLL parameters are reasonably designed and the input variable meets the actual control requirements.

Under the M2 damping control, in the steady state, the VSG output frequency ω synchronizes with the grid frequency ω_g, and the frequency difference (ω − ω_g) approaches 0, resulting in a zero output of the damping term. At this time, error-free regulation of the steady-state power is achieved. During the transient process of sudden load changes, M2 is dominated by inertia action to achieve transient power increase, while the damping term exhibits a reverse suppression effect. Consequently, the transient power increase is reduced, leading to insignificant transient power support.

When adopting the M3 control mode, as can be seen from Equation (2), a first-order High-Pass Filter (HPF) is added to the fixed-frequency damping control channel, such that the effect of the damping term is limited by the HPF. Its transfer function is similar to that of Equation (6), as shown below:

$$\begin{array}{l}{\delta }_{\mathrm{GFM}\text{-}{\omega }_{\mathrm{c}}}={\displaystyle \frac{1}{s}}\left({\displaystyle \frac{P_0-P_{\mathrm{e}}}{2Hs+D_{\mathrm{p}}s/(s+{\omega }_{\mathrm{c}})}}+{\omega }_0\right)\\ ={\displaystyle \frac{1}{s}}\left({\displaystyle \frac{(P_0-P_{\mathrm{e}})(s+{\omega }_{\mathrm{c}})}{2H{s}^2+2H{\omega }_{\mathrm{c}}s+D_{\mathrm{p}}s}}+{\omega }_0\right)\end{array}$$

(7)

Different from the M1 and M2 control modes, the M3 control mode achieves the synergy between steady-state accuracy and dynamic response through the filtering characteristics of the HPF.

Under steady-state operating conditions, the HPF weakens the damping effect in the low-frequency band, reduces the sensitivity of the damping term to static deviations of the grid frequency, and avoids the steady-state power error similar to that of M1 caused by the grid frequency deviating from the rated value, ultimately achieving “error-free regulation” comparable to that of M2. In transient operating conditions such as sudden load increases and fluctuations in renewable energy output, the HPF retains the damping effect in the high-frequency band, enabling the damping term to quickly respond to system power deficits. At this time, the peak value of transient power support is close to that of M1, while avoiding the insufficient transient support of M2 caused by inertia dominance, thus effectively balancing the core contradiction between “steady-state error” and “weak transient support” in traditional damping control.

3.2. Analysis of System Transient Power–Frequency Characteristics and Stability

In traditional grid-forming fixed-parameter control, when the damping coefficient D_p is a constant value: as the inertia coefficient H increases, the system frequency variation will decrease, but the fluctuation of the electromagnetic power P_e will intensify within the transient time, and the system transient settling time will become longer; when H decreases, the fluctuation of P_e will reduce, but the frequency variation will increase. When H is a constant value: an excessively small D_p will lead to system oscillatory instability, while an excessively large D_p will result in a longer transient settling time of the system.

As shown in Figure 3 above, when the load power P_L in the microgrid remains constant, the system operates in a steady state with the frequency equal to the reference frequency f_ref. When a sudden increase in load power occurs, the main response characteristic of the system frequency is a change from a decrease to recovery. In the time interval t₁~t₂, affected by the system power deficit, the primary frequency regulation of the generator sets first comes into play, and the system frequency decreases at this time. In the time interval t₂~t₃, to maintain system frequency stability, the frequency regulation generator sets start to implement secondary frequency regulation, and the frequency gradually rises and recovers. In the time interval t₃~t₄, affected by system inertia, the frequency continues to rise slightly, and then recovers in the time interval t₄~t₅. The same logic applies to the other time intervals.

From Figure 3 again, in the time interval t₁~t₂, the angular frequency variation Δω < 0 and the rate of angular frequency change dω/dt < 0. As can be seen from Equation (2), increasing the inertia coefficient H and damping coefficient D_P at this time can enable the inverter-based power supply to undertake more system power deficits, thereby further reducing the system frequency variation and providing better support for the system. In the time interval t₂~t₃, the frequency recovers with Δω < 0 and dω/dt > 0. Reducing H and gradually restoring D_p to its initial value at this stage can alleviate the problem of power oscillation overshoot caused by the earlier increase in inertia and enable the system to return to the steady state relatively faster.

4. Transient Damping Control Strategy with Flexible Adjustable Cut-Off Frequency

4.1. Analysis of VSG Transfer Function Under Transient Damping Mode

The transmission of active power in the transmission line can be expressed as the following formula.

$$\left\{\begin{array}{l}{P}_{\mathrm{e}}={\displaystyle \frac{E^2}{Z_{\mathrm{n}}}}\cos ({\theta }_{\mathrm{zn}})-{\displaystyle \frac{EU}{Z_{\mathrm{n}}}}\cos (\theta +{\theta }_{\mathrm{zn}})\hfill \\ Z_{\mathrm{n}}\angle {\theta }_{\mathrm{zn}}=R_{\mathrm{n}}+j{\omega }_{0}X\hfill \end{array}\right.$$

(8)

In the formula, Z_n denotes the total transmission line impedance; R_n is the total transmission line resistance; X represents the total transmission line reactance; θ_zn is the line impedance angle; U denotes the point of common coupling (PCC) voltage.

In practical transmission lines, the line reactance is much larger than its resistance; thus, this study assumes the line to be a purely inductive circuit, and the formula can be simplified as follows.

$$P_{\mathrm{e}}={\displaystyle \frac{EU}{X_{\mathrm{n}}}}\sin (\theta )\approx {\displaystyle \frac{EU}{X_{\mathrm{n}}}}\theta ={\displaystyle \frac{EU}{X_{\mathrm{n}}}}s(\omega -{\omega }_{\mathrm{g}})$$

(9)

For the M3 control mode, the relationship between the VSG output frequency and the grid frequency variation derived from Equation (7) is as follows:

$$\begin{gathered} \begin{array}{cc}{P}_{\mathrm{e}\text{-}{\omega }_{\mathrm{c}}}={\displaystyle \frac{EU}{X_{\mathrm{n}}s}}(\omega -{\omega }_{\mathrm{g}})& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\end{array} \\ =\left[\begin{array}{ccc}{G}_{D_{\mathrm{p}}-P_{0}3}(s)& 0& 0\\ 0& -G_{D_{\mathrm{p}}-{\omega }_{\mathrm{c}}}(s)& 0\\ 0& 0& G_{D_{\mathrm{p}}-{\omega }_{\mathrm{c}}}(s)\end{array}\right]\left[\begin{array}{c}{P}_0\\ {\omega }_{\mathrm{g}}\\ {\omega }_0\end{array}\right] \end{gathered}$$

(10)

In the formula, G_Dp-P03(s) denotes the power channel transfer function of the M3 control mode; G_Dp-ωc(s) represents the frequency disturbance transfer function of the M3 control mode.

For the M3 control mode, the transient power increase follows Equation (10), i.e.,

$$\begin{array}{l}\Delta P_{\mathrm{e}1}=-G_{\mathrm{Dp}\text{-}{\omega }_c}(s)·\Delta {\omega }_{\mathrm{g}}\\ ={\displaystyle \frac{-EU\left[2H{s}^2+(2H{\omega }_{\mathrm{c}}+D_{\mathrm{p}})s\right]·\Delta {\omega }_{\mathrm{g}}}{2H{X}_{\mathrm{n}}{s}^3+(2H{X}_{\mathrm{n}}{\omega }_{\mathrm{c}}+D_{\mathrm{p}}{X}_{\mathrm{n}})s^2+EUs+EU{\omega }_{\mathrm{c}}}}\end{array}$$

(11)

In the low-frequency band, the system tends to a steady state, and the HPF characteristics result in a significant weakening of the value of the damping channel. In this frequency band, the formula is as follows:

$$\begin{array}{l}\Delta P_{\mathrm{e}1}=-G_{\mathrm{Dp}\text{-}{\omega }_c}(s)·\Delta {\omega }_{\mathrm{g}}\\ \approx -{\displaystyle \frac{s}{s+{\omega }_{\mathrm{c}}}}(2H{\omega }_{\mathrm{c}}+D_{\mathrm{p}})\Delta {\omega }_{\mathrm{g}}\end{array}$$

(12)

As can be seen from Equation (12), the cutoff frequency has a certain strengthening effect on the inertia action, while exerting a negative suppression effect on the damping action. As the cutoff frequency decreases, the phase margin decreases and the gain increases relatively. This is because the weakening effect of the HPF on the damping term is reduced, and the strengthening of the weakening effect on the inertia action occurs; the feedback value of the damping channel increases relatively, which is numerically equivalent to the fixed-frequency damping control in terms of the damping channel, and the output transient power also increases accordingly. As the cutoff frequency increases, the degree of weakening of the low-frequency components of both inertia and damping actions intensifies, but the high-frequency components of the inertia action are enhanced. Thus, the inertia action becomes stronger, and the damping action becomes weaker. As the input signal frequency gradually increases, the effect of the HPF gradually weakens, and the control characteristics approach those of the fixed-frequency damping control, with its variation law consistent with the latter.

4.2. Transient Damping Strategy with Flexibly Adjustable Cutoff Frequency

For transient damping control, due to the constant cutoff frequency, its transient response may lack adaptability in different application scenarios. Thus, this paper analyzes the influence of different cutoff frequency values on the VSG transient power output and their coordination with the frequency response.

The selection of the cutoff frequency must satisfy the requirements of the system inertia and damping ratio while being compatible with the core characteristics of transient damping control. The derivation process is as follows:

By combining the VSG rotor motion equation (Equation (2)) with the simplified active power transmission formula (Equation (9)), considering the low-frequency band ω = ω₀, and neglecting the term of the HPF ${\displaystyle \frac{s}{{\omega }_c+s}}$ as s approaches 0, the system’s dynamic characteristics satisfy the constraints of a second-order linear system:

$$2H{\displaystyle \frac{d\Delta \omega }{dt}}+D_p\Delta \omega =\Delta P_{set1}-\Delta P_e$$

(13)

where denotes the electromagnetic power deviation. Meanwhile, according to the differential relationship between angular frequency and power angle $\Delta \omega ={\displaystyle \frac{d\Delta \delta }{dt}}$, substituting into Equation (13) yields:

$$2H{\displaystyle \frac{d^2\Delta \delta }{d{t}^2}}+D_p{\displaystyle \frac{d\Delta \delta }{dt}}+{\displaystyle \frac{EU}{X_n}}\Delta \delta =\Delta P_{set1}$$

(14)

Dividing both sides of Equation (14) by 2H and rearranging into the standard form of a second-order linear system:

$$\stackrel{..}{\Delta \delta }+2\zeta {\omega }_n\stackrel{.}{\Delta \delta }+{\omega }_n^2\Delta \delta ={\displaystyle \frac{\Delta P_{set1}}{2H}}$$

(15)

In the formula: ω_n is the system natural oscillation frequency, reflecting the inherent oscillation characteristics of the system; ζ is the damping ratio, reflecting the system’s oscillation attenuation capability. Both are jointly determined by VSG control parameters (D_p, H) and power grid parameters (E, U, X_n).

By comparing the coefficients of Equations (14) and (15), establishing an equality relationship and solving it, Equation (16) can be obtained.

The natural oscillation frequency (ω_n) and damping ratio (ζ) of the VSG system are key parameters that constrain the cutoff frequency. The derivation is based on the synchronous generator characteristics and transmission line impedance model, as follows:

$$\left\{\begin{array}{l}{\omega }_n=\sqrt{{\displaystyle \frac{EU}{2H{X}_n}}}\hfill \\ \zeta ={\displaystyle \frac{D_p}{\sqrt{8HEU/X_n}}}\hfill \end{array}\right.$$

(16)

where E denotes the amplitude of the VSG output voltage; U is the point of common coupling voltage; H represents the inertia time constant; X_n is the equivalent total reactance of the system outgoing transmission line; D_p denotes the damping coefficient.

In transient damping control, the High-Pass Filter (HPF) makes the equivalent damping coefficient (D_p−ωn) depend on the cutoff frequency, and matches the damping effect at the system natural oscillation frequency; the derivation yields:

$$D_{p-{\omega }_c}=D·{\displaystyle \frac{{\omega }_n^2}{{\omega }_n^2+{\omega }_c^2}}$$

(17)

Substituting the expression of ω_n yields:

$$D_{p-{\omega }_c}={\displaystyle \frac{D_p}{1+\frac{2H{X}_n{\omega }_c^2}{EU}}}$$

(18)

This formula quantifies the “adjustability” of the cutoff frequency ω_c on the damping effect. On one hand, ω_c has an inverse relationship with the equivalent damping coefficient D_p−ωc: the smaller the ω_c, the stronger the damping effect, i.e., it degenerates into fixed-value damping control (M1), which is suitable for weak grid scenarios; the larger the ω_c, the weaker the damping effect, i.e., it adapts to strong grid scenarios and achieves error-free regulation. On the other hand, the inherent parameters of the power grid directly constrain the adjustable range of ω_c: for example, if the system inertia H is small, the sensitivity of D_p−ωc to ω_c decreases; if the line reactance X_n is large, the regulatory effect of ω_c is more significant. In addition, this formula can pre-calculate the relationship curve between ω_c and D_p−ωc to determine the value range; during the operation phase, ω_c can be dynamically adjusted to ensure that the damping effect is always adapted to the current operating conditions.

4.3. Range of Cutoff Frequency

Considering the minimum system inertia requirement (H_min) and the minimum damping ratio requirement (ζ_min), substitute the equivalent damping coefficient into the damping ratio formula to back-calculate the upper limit of the cutoff frequency (ω_nmax):

$${\zeta }_{\min }={\displaystyle \frac{D_{p-{\omega }_c}}{\sqrt{8H_{\min }EU/X_n}}}$$

(19)

Substituting and rearranging the expression of D_p−ωc, the upper limit of the cutoff frequency is obtained as follows:

$${\omega }_{\mathrm{cmax}}=\sqrt{{\displaystyle \frac{EU}{2H_{\min }{X}_n}}\left({\displaystyle \frac{D_p}{{\zeta }_{\min }\sqrt{8H_{\min }EU/X_n}}}-1\right)}$$

(20)

Equation (17) defines the adjustable range of the cutoff frequency to ensure the stability and adaptability of the VSG system in multiple scenarios. It constrains the upper limit of the cutoff frequency ${\omega }_{c\max }$ through the minimum inertia time constant H_min and the minimum damping ratio ζ_min, ensuring that the system remains stable even under worst-case operating conditions and avoiding oscillations caused by excessive weakening of the damping effect. On the other hand, Equation (17) quantifies the influence of power grid parameters on the adjustment range; for example, if the line reactance X_n is large, the cutoff frequency can be adjusted over a wider range to meet the damping requirements.

In engineering practice, the adjustment interval can be calculated based on this first, and then the cutoff frequency can be dynamically adjusted according to the scenario to achieve a balance between “stability and adaptability”. In particular, it provides a key quantitative basis for the VSG damping control design in power grids with high penetration of renewable energy.

Since the transient damping control (M3) converts to the actual fixed-value damping control (M1) when the cutoff frequency ω_c = 0, the minimum cutoff frequency should be 0. Considering the characteristics of transient damping control (M3), the value range of the cutoff frequency is as follows:

$$0\le {\omega }_c\le {\omega }_{\mathrm{cmax}}$$

(21)

In practical application scenarios, to enable the transient damping strategy with flexibly adjustable cutoff frequency to quickly adapt to scenarios in engineering, it is necessary to first determine the initial value of the cutoff frequency. On the premise of satisfying the constraints of the value range, this initial value must realize “scenario-adaptive initialization” by combining the rated power grid parameters and transient power support requirements. Specifically, the initial value of the cutoff frequency is equivalently calculated and substituted into the VSG equation, ensuring it is fully adapted to the scenario needs as well as the rated power grid parameters and transient power support requirements.

Based on the power transmission equation and transient power support requirements, the correlation between various parameters and the initial cutoff frequency ω_c is established.

$${\omega }_{c0}=k_1·{\displaystyle \frac{U_N·\Delta P_{\max }}{S_{N·2\pi f}{L}_n}}+k_2·\sqrt{{\displaystyle \frac{EU}{2H{X}_n}}}$$

(22)

In the formula: k₁ and k₂ denote the scenario-adaptive weight coefficients, which are determined through practical tests. In weak grid scenarios, k₁ takes a larger value; in strong grid scenarios, k₂ takes a larger value, X_n = 2πfL_n. In weak grids, k₁ = 0.7 and k₂ = 0.3; in strong grids, k₁ = 0.3 and k₂ = 0.7.

An increase in k₁ can enhance damping to suppress oscillations, but an excessive value will prolong the transient settling time; an increase in k₂ (adapted to strong grids) can reduce steady-state errors, but an insufficient value will lead to insufficient transient support.

Based on Equation (19), the real-time update needs to respond to the dynamic changes of the system frequency. Adaptive adjustment is realized based on the frequency variation and frequency change rate; combined with the weight coefficients, a linear correlation model between the real-time cutoff frequency and the dynamic factor is established as follows:

$${\omega }_{ct}={\omega }_{c0}+k_3·e^{\Delta \omega }+k_4·e^{\left|{\displaystyle \frac{d\omega }{dt}}\right|}$$

(23)

where ω_ct denotes the real-time cutoff frequency; ω_c0 represents the initial cutoff frequency; k₃ is the weight coefficient for frequency variation, which suppresses steady-state deviations; k₄ is the weight coefficient for frequency change rate, which enhances transient response.

An increase in k₃ can enhance the suppression of steady-state deviations, and an increase in k₄ can improve the transient response speed; coordination is required to avoid damping–inertia coupling imbalance.

In strong grids, k₃ = 0.05 and k₄ = 0.12.

Finally, the specific expression of the real-time cutoff frequency is as follows:

$${\omega }_c=\left\{\begin{array}{l}0,{\omega }_c<0\\ {\omega }_{c0},\left|\mathsf{\Delta }\omega \right|\le T_1\cap \left|{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}\right|\le T_2\\ {\omega }_{c0}-k_3{e}^{\Delta \omega }-k_4{e}^{\left|{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}\right|},\left|\mathsf{\Delta }\omega \right|>T_1\cap T_2<\left|{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}\right|\\ \cap \mathsf{\Delta }\omega ·{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}>0\\ {\omega }_{c0}+k_3{e}^{\Delta \omega }+k_4{e}^{\left|{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}\right|},\left|\mathsf{\Delta }\omega \right|>T_1\cap T_2<\left|{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}\right|\\ \cap \mathsf{\Delta }\omega ·{\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}<0\\ {\omega }_{c\max },{\omega }_c>{\omega }_{c\max }\end{array}\right.$$

(24)

The overall control block diagram is shown in Figure 4.

5. Experimental Test Results

5.1. Hardware-in-the-Loop (HIL) Test Platform

A hardware-in-the-loop (HIL) test platform based on the OP5600 real-time simulator and a DSP-based actual controller is established, as shown in Figure 5 RT-LAB is used to simulate the main circuit of the system, while the proposed control strategy is implemented in the DSP controller. Typical operating conditions are set to verify the control strategy, and an oscilloscope is employed to complete the recording and monitoring functions of variables such as frequency and power under various operating conditions.

OP5600 realizes the digital modeling of VSG grid-connected main circuit (including DC power supply, filter link, power grid and load) through RT-LAB (OP5600) software. The simulation step is set to 100 μs, and the PCC voltage, grid-connected current and other electrical quantities are output in real time. Secondly, the DSP controller collects and preprocesses the above electrical quantities through the AD sampling module, and obtains the accurate grid frequency and frequency change rate through the first-order low-pass filtering. Then, according to the pre-stored scene weight coefficient (weak grid k₁ = 0.7, k₂ = 0.3, strong grid k₁ = 0.3, k₂ = 0.7), the initial value setting of the cut-off frequency is completed, and the real-time dynamic correction of the cut-off frequency is realized by combining the frequency deviation and the change rate (weight k₃ = 0.05, k₄ = 0.12), and the amplitude is limited to 0~25 rad/s. Then, the real-time equivalent damping coefficient is integrated into the discrete VSG core equation. The voltage amplitude and phase angle are solved and the PWM drive signal is generated and sent to the main circuit model. Finally, the data monitoring and verification are completed by oscilloscope and RT-LAB acquisition module.

To verify the effectiveness of the aforementioned transient damping strategy with flexibly adjustable cutoff frequency in theoretical derivation and formula design, and to clarify its actual control performance and scenario adaptability advantages under different operating conditions, this section will conduct experimental verification from dimensions such as steady-state accuracy, transient response, and multi-scenario switching by establishing an experimental platform. It will compare the output characteristic differences between the proposed strategy, traditional damping control (M1), and transient damping control (M3), and quantitatively analyze the improvement effect of the flexible adjustment of the cutoff frequency on system stability and adaptability.

Taking single machine simulation as an example, the specific parameters are shown in

Table 1. VSG Simulation Parameters.

Model Parameters	Values	Control Parameters	Values
DC Voltage/V	600	Inertia Time Constant J	3
Switching Frequency/kHz	10	Damping Coefficient Dp	80
Filter Inductor/mH	9.1	Reactive Power Droop Coefficient Dq	10
Filter Capacitor /μF	30	PI Coefficients of the Voltage Loop	1, 1
Filter Internal Resistance/mΩ	0.2	PI Coefficients of the Current Loop	1, 2.5
Grid Voltage/V	690	Standard Angular Frequency ω0/(rad/s)	314.16
Control Step Size/μs	50	Simulation Step Size/μs	100

.

5.2. Experimental Test Results—Verification of the Active Power Command

In order to verify the effectiveness of the proposed strategy, three VSG power oscillation suppression strategies are simulated, including fixed damping strategy, constant transient damping strategy and transient damping improved VSG control strategy with flexible adjustment of cut-off frequency, as shown in Figure 6. When the fixed damping strategy is adopted, the active command changes abruptly at 1 s, and the active power still has obvious oscillation, and the active overshoot is 0.23 p.u., and the steady-state time is about 0.34 s. At 2 s, the grid frequency changes abruptly, and the active overshoot is 0.12 p.u. When the constant transient damping strategy is adopted, the active command changes suddenly at 1 s. Compared with the fixed damping strategy, the active power oscillation is suppressed to a certain extent when the high frequency component of active power is introduced. The active overshoot is reduced to 0.1 p.u., and the steady state time is reduced to 0.15 s. At 2 s, the grid frequency changes suddenly, and the active overshoot is about 0.07 p.u. When the proposed control method is adopted, according to Figure 6, it can be seen that the active power oscillation basically does not exist at this time, and the VSG output active power can be smoothly transitioned. Compared with the other three methods, the steady-state error decreases more obviously. The simulation results show that the proposed control method can better suppress the active power oscillation of VSG.

When the fixed damping strategy is adopted, the output current waveform is shown in Figure 7. Obvious oscillations occur in the VSG output current when there are sudden changes in the active power command and grid frequency. For the constant transient damping strategy, the output current waveform is presented in Figure 8. Compared with Figure 7, the oscillation of the VSG output current is attenuated to a certain extent; however, oscillation phenomena can still be observed in the VSG output current during sudden changes in the active power command and grid frequency. When the control strategy proposed in this paper is adopted, as illustrated in Figure 9, the VSG output current can smoothly transition to a steady state under both sudden changes in the active power command and grid frequency, with basically no oscillation or overshoot issues. Therefore, the simulation results further demonstrate that the proposed control method in this paper can more effectively suppress active power oscillations.

5.3. Experimental Test Results—Strategy Comparison Under Load Sudden Change Scenarios

To verify the control performance of the proposed strategy under transient disturbances, the load step-increase scenario is selected for the experiment.

Figure 10 intuitively presents the dynamic response differences between the proposed transient damping strategy with flexibly adjustable cutoff frequency, traditional fixed-frequency damping control (M1), and transient damping control with fixed cutoff frequency (traditional M3) under the load step-change scenario. In the experiment, the converter initially outputs 1 p.u. active power; after the load step change, a power deficit occurs in the system and causes frequency fluctuations. The damping term of the proposed strategy initiates a response immediately upon the load step change, with a shorter activation delay compared to the traditional M3, and its response activation time is basically equivalent to that of M1. The maximum frequency drop of the proposed strategy is only 0.02 Hz, which is significantly lower than 0.024 Hz of the traditional M3 and 0.028 Hz of M1. This benefit stems from the strategy’s ability to enhance damping support through a low cutoff frequency during the transient phase, quickly compensate for the power deficit, and suppress excessive frequency fluctuations.

5.4. Experimental Test Results—Strategy Comparison Under Different Short-Circuit Ratios

To verify the adaptability of the proposed strategy under different grid strengths, tests are conducted under the scenarios of Short-Circuit Ratio (SCR) = 2 (weak grid) and SCR = 10 (strong grid), with the results shown in the following figures.

Figure 11 compares the active power output characteristics of the proposed strategy and traditional control strategies under weak grid and strong grid scenarios. In the weak grid scenario, the grid’s supporting capacity is weak, making it prone to power oscillations and frequency instability. The proposed strategy automatically adjusts the cutoff frequency to a low range, significantly enhancing the equivalent damping coefficient. Its peak transient power support reaches 0.93 kW, which is higher than 0.6 kW of the fixed-cutoff-frequency transient damping control (M3) and much higher than 0.44 kW of the fixed-frequency damping control (M1), thus effectively supporting active power compensation. Under transient disturbances in the strong grid scenario, the proposed strategy automatically increases the cutoff frequency to a high range, weakening the damping effect in the low-frequency band. Compared with the fixed-cutoff-frequency transient damping control (M3), the active power fluctuation is reduced by 4.3%, and it is significantly smaller than that of the fixed-frequency damping control (M1).

6. Conclusions

To address the problems of insufficient adaptability of traditional VSG damping control under multiple scenarios and the lack of flexibility in transient damping regulation with fixed cutoff frequency, this paper focuses on the core of “flexible adjustment of the cutoff frequency”. Through theoretical modeling and simulation experiments, the control mechanism and adaptive characteristics of the proposed strategy are revealed. The main contributions are as follows:

(1) An innovative transient damping-type VSG control strategy with dynamically adjustable cutoff frequency is designed to break through the adaptability limitations of traditional fixed cutoff frequencies. Through the synergistic effect of the High-Pass Filter (HPF) and dynamic adjustment of the cutoff frequency, dual optimization of “steady-state error-free regulation” and “strong transient support” is achieved, solving the core contradictions of traditional fixed-frequency damping control (M₁) with steady-state errors and grid frequency damping control (M₂) with weak transient support, and providing a new paradigm for VSG damping control under multiple operating conditions. By introducing a dynamically updatable cutoff frequency into the transient damping channel, the strategy breaks the adaptability limitation of fixed cutoff frequencies to changes in operating conditions. At a low cutoff frequency, it can simulate the stability characteristics of fixed-frequency damping control to weaken power oscillations; at a high cutoff frequency, it enhances the response speed of the inertial effect to adapt to scenarios with fluctuating transient power demands, effectively balancing the contradiction between steady-state accuracy and dynamic response.

(2) Through frequency domain analysis and transfer function modeling, the inverse coordination relationship between the cutoff frequency and the equivalent damping coefficient is quantified for the first time, and a quantitative correlation formula (Equation (15)) based on the system natural oscillation frequency, damping ratio, and power grid parameters is derived. The adaptation law is clarified: reducing the cutoff frequency in weak grid scenarios can enhance the damping effect, and increasing the cutoff frequency in strong grid scenarios can achieve error-free regulation, providing theoretical support for precise parameter regulation. It initiates a response quickly after a load step change; the activation delay of the proposed strategy is significantly shorter than that of the traditional M₃ and basically equivalent to that of M₁, enabling it to quickly participate in the transient power regulation process and gain time for power deficit compensation. The maximum frequency drop of the proposed strategy is only 0.02 Hz, which is significantly lower than 0.024 Hz of the traditional M₃ and 0.028 Hz of M₁.

(3) Combined with the requirements of the system’s minimum inertia (H_min) and minimum damping ratio (ζ_min), the value range of the cutoff frequency “0~ω_cmax” is defined; an initial value calculation method with scenario-adaptive weight coefficients (k₁, k₂) and a real-time adjustment algorithm integrating frequency variation and its rate of change are proposed, forming a full-process parameter design scheme of “value range—initial tuning—real-time update” to ensure the engineering practicality and scenario adaptability of the strategy. Through frequency domain analysis and transfer function modeling, it is found that there exists a coordinated regulation relationship between the damping coefficient and the cutoff frequency: in weak grid or load step-change scenarios, appropriately reducing the cutoff frequency can enhance the damping effect on suppressing power oscillations, reducing the transient power overshoot by 4.3% compared with fixed cutoff frequency control; in steady-state operation scenarios of strong grids, increasing the cutoff frequency can weaken the damping effect in the low-frequency band, avoid the accumulation of steady-state power errors, and achieve effective active power compensation.

(4) Significant performance advantages under multiple scenarios are verified: Hardware-in-the-Loop (HIL) experiments show that the maximum frequency drop of the proposed strategy in the load step-change scenario is only 0.02 Hz, which is 28.6% and 14.3% lower than that of the traditional M₁ and M₃ strategies, respectively; the peak transient power support in the weak grid (SCR = 2) scenario reaches 0.93 kW, which is 55% higher than that of M₃, effectively suppressing power oscillations; the active power fluctuation in the strong grid (SCR = 10) scenario is reduced by 4.3% compared with the transient damping control with a fixed cutoff frequency, avoiding the accumulation of steady-state power errors and significantly enhancing the dynamic stability of VSG under different grid strengths and disturbance conditions.