A Theoretical Study on Coordinated Control Strategy of VSG for Transient Power Angle Stability and Fault Current Limiting

Abstract

Virtual synchronous generators (VSGs) are prone to transient power angle instability and short-circuit current overshoot under symmetrical short-circuit grid faults. To address the limitation that existing transient control strategies fail to simultaneously guarantee power angle stability and fault current limiting, a coordinated control strategy combining dynamic active power reference regulation and adaptive virtual impedance is designed. Specifically, the active power reference is dynamically adjusted in accordance with the voltage sag magnitude at the point of common coupling (PCC), which effectively narrows the acceleration area of the virtual rotor and maintains the transient power angle near its rated value to prevent the risk of system loss of synchronism. On this basis, an adaptive virtual impedance control scheme is designed to accurately calculate and implement the optimal current-limiting impedance on demand, confining the steady-state fault current within the allowable threshold. Finally, the effectiveness of the designed strategy is verified on the Matlab/Simulink simulation platform. Simulation results demonstrate that the designed strategy achieves the coordination between transient power angle stability and fault current limiting, thus improving the operational stability of the VSG grid-connected system under symmetrical short-circuit grid faults.

1. Introduction

In recent years, driven by the goals of carbon peaking and carbon neutrality, the penetration of new energy sources has been increasing year by year. The large-scale grid integration of new energy generation through power electronic converters has caused power systems to exhibit the “dual-high” characteristics, namely a high proportion of renewable energy and a high proportion of power electronic equipment. Meanwhile, the continuous reduction in the proportion of conventional synchronous generators has led to insufficient system inertia and weakened voltage and frequency support capabilities, rendering transient stability issues increasingly prominent [1,2]. By emulating the rotor motion and external characteristics of synchronous generators, VSG technology enables new energy generation devices to possess frequency and voltage regulation characteristics similar to those of conventional synchronous units. It can effectively enhance the transient support capability of new energy grid-connected systems and has become one of the core technologies for the stable control of new-type power systems [3,4].

However, when symmetrical short-circuit faults occur in the power grid, a large voltage difference arises between the internal electromotive force of the VSG and the voltage at PCC, which tends to trigger overlimit short-circuit current and seriously threatens the safe operation of power electronic devices. Meanwhile, the fault-induced imbalance between the input and output active power of the VSG leads to a continuous rise in the power angle, which is prone to transient power angle instability. Consequently, the VSG will lose its voltage and frequency support capability for the power grid, and may even induce cascading tripping of new energy units, further deteriorating system stability [5]. Power angle stability constitutes the prerequisite for the VSG to achieve fault ride-through (FRT) [6], while fault current limiting serves as the guarantee for its secure operation [7,8]. Both are essential for the safe and stable operation of the VSG.

At present, most studies on the transient control of VSGs treat power angle stability and fault current limiting as separate issues, failing to consider their coordinated requirements. Regarding the transient power angle stability of VSGs, Reference [9] analyzes the transient power angle stability mechanism of grid-forming converters under different reactive power control strategies. Reference [10] adopts virtual circuit components to suppress the transient power angle of VSGs. Reference [11] investigates the effect of reasonably tuning the governor gain and cut-off frequency on enhancing the transient power angle stability margin of the system. Reference [12] points out that optimizing the transient active power control parameters to reduce their values can effectively expand the generator deceleration area, thereby improving the system’s transient power angle stability margin. Relevant studies merely concentrate on the optimization of power angle stability while ignoring fault current limiting, and regard the two research objectives as mutually independent. In terms of fault current limiting research for VSGs, existing methods are merely designed with fault current limiting as the sole objective, which can be classified into two main categories: one involves switching grid-forming (GFM) control to grid-following (GFL) current control during faults [13,14]. While this method can achieve current limiting, it sacrifices the voltage-source characteristics of the VSG, fails to provide active grid support, and is prone to causing voltage and current transients during the switching process. The other type relies on virtual impedance for current limiting [15,16], which suppresses short-circuit current by increasing the equivalent impedance of the system without altering the grid-forming external characteristics of the VSG. Reference [17] adopts adaptive virtual impedance to limit the fault current of VSGs in both grid-connected and islanded modes. Such studies merely concentrate on fault current limiting performance while neglecting transient power angle stability, and also regard the two as mutually independent. In summary, most existing studies treat power angle stability and fault current limiting as two separate control targets, or merely adopt simple functional combination of relevant control links. From the perspective of physical mechanism, however, these two aspects of VSGs present obvious coupling and even mutual restriction under severe grid faults. For instance, the deployment of virtual impedance can effectively limit fault current, but it also leads to terminal voltage sag, which may weaken the system synchronization capability and further raise the risk of power angle instability.

To address this issue, this paper designs a coordinated control strategy integrating dynamic regulation of active power reference and adaptive virtual impedance. The core of the proposed strategy is to explore the inherent complementary characteristics between electromechanical and electromagnetic dynamics. By dynamically correcting the active power reference in real time, the power angle deviation induced by fault current limiting can be mitigated, thereby fundamentally balancing the conflicting requirements of the two control objectives from the physical mechanism perspective. Without introducing complicated mode switching logic, the designed coordinated scheme can simultaneously achieve fault current suppression and maintain power angle stability. It provides a feasible solution for enhancing the reliable operation of grid-forming converters under severe operating conditions.

The rest of the article is arranged as follows. Section 2 presents the control loops of the VSG and establishes its equivalent control circuit based on equivalent impedance analysis. Section 3 investigates the power angle characteristics and steady-state fault current behaviors of the VSG under symmetrical short-circuit grid faults. Section 4 designs a coordinated control strategy that integrates dynamic adjustment of the active power reference and adaptive virtual impedance. This strategy guarantees the power angle stability of the VSG during transients by regulating the active power reference, and further effectively suppresses the steady-state fault current of the VSG via an adaptively tuned virtual impedance scheme. Section 5 validates the accuracy of the theoretical analysis and the effectiveness of the designed control strategy using the Matlab/Simulink simulation platform.

2. VSG Control Loop Characteristics and Grid-Connected Equivalent Circuit

To enable the converter to exhibit external characteristics and fault ride-through capability similar to those of conventional synchronous generators, the VSG control scheme mainly consists of three parts: a power outer loop that mimics the operating mechanism of synchronous machines, a virtual impedance loop for output characteristic improvement, and dual voltage–current inner loops to achieve accurate tracking of control references. The structure of the VSG-based grid-connected system is illustrated in Figure 1. Modern grid-forming converter systems are generally configured with large-capacity energy storage units on the DC side, or integrated with front-end DC/DC voltage regulation circuits possessing an ultra-high control bandwidth. During grid faults, when grid-side active power transmission is restricted at the transient instant, such front-end hardware can rapidly absorb or compensate surplus power, thereby maintaining a relatively stable DC bus voltage from the physical perspective. Accordingly, to focus on the investigation of VSG control strategies and decouple the inherent dynamic characteristics of distributed energy resources, an ideal DC voltage source is adopted to simplify the system model.

In the figure, U_dc denotes the DC voltage source, U_c represents the converter terminal voltage, U_s stands for the terminal voltage, i.e., the VSG output voltage, U_g is the grid voltage, L_f and C_f are the filter inductor and capacitor, respectively, L_g is the line inductor, i_s is the converter terminal current, and i_g is the VSG output current. In addition, the injection location of the symmetrical short-circuit fault is clearly marked in Figure 1. To realistically reproduce the actual fault transient process, a three-phase short-circuit fault module is configured at PCC. By regulating the internal switching operations, the initiation and clearance of symmetrical short-circuit faults can be well simulated.

2.1. VSG Power Outer Loop Characteristics

The VSG power outer loop consists of active power–frequency control and reactive power–voltage control. The active power–frequency loop is derived from the rotor motion and primary frequency regulation characteristics of synchronous generators, with its expression given in Equation (1) [18].

$$J{\displaystyle \frac{{\mathrm{d}}^2\delta }{\mathrm{d}{t}^2}}=P_{\mathrm{ref}}-P_{\mathrm{s}}-D(\omega -{\omega }_{\mathrm{N}})$$

(1)

where P_s and P_ref are the actual active power output and its reference of the VSG; ω and ω_N represent the virtual actual speed and rated speed of the VSG; δ denotes the power angle; J and D are the virtual moment of inertia and damping coefficient, respectively.

The reactive power–voltage control consists of no-load electromotive force and reactive power regulation, with its expression presented in Equation (2) [19].

$$E_{\mathrm{f}}=U_{\mathrm{r}\mathrm{e}\mathrm{f}}+k_{\mathrm{q}}(Q_{\mathrm{r}\mathrm{e}\mathrm{f}}-Q_{\mathrm{s}})$$

(2)

where Q_ref and Q_s are the reference and actual output reactive power of the VSG; E_f denotes the internal electromotive force of the VSG, and U_ref is its reference voltage; and k_q represents the voltage regulation coefficient of the VSG.

2.2. Virtual Impedance and Dual Voltage–Current Inner Loop Characteristics

To mitigate overcurrent transients caused by grid voltage sags and improve the output characteristics of the VSG in complex grid conditions, a virtual impedance loop is incorporated in series into the control architecture. By introducing the negative feedback of the converter terminal output current, this loop regulates the internal potential reference E_ref generated by the power outer loop in real time, and its equivalent control equation can be expressed as:

$$U_{\mathrm{ref}}=E_{\mathrm{ref}}-(R_{\mathrm{v}}+\mathrm{j}{X}_{\mathrm{v}})i_{\mathrm{s}}$$

(3)

where U_ref denotes the modified voltage reference after current limiting; R_v and X_v are the virtual resistance and virtual reactance, respectively; and i_s represents the terminal output current.

By introducing the virtual impedance loop, the equivalent line impedance of the system is increased without modifying hardware parameters. This not only significantly suppresses the transient impact of short-circuit current during the initial fault stage, but also effectively enhances the decoupling control capability between active and reactive power of the system.

The voltage reference U_ref modified by the virtual impedance loop serves as the input command for the dual voltage–current closed-loop control. The dual-loop control operates in the dq synchronous rotating frame and adopts a cascade structure with an outer voltage loop and an inner current loop. Among them, the outer voltage loop adopts a proportional-integral (PI) regulator to eliminate the steady-state tracking error of the fundamental voltage and generates the reference command for the inner current loop. The inner current loop features an extremely high control bandwidth, enabling instantaneous dynamic response to the reference command. To suppress the cross-coupling disturbances between the d-axis and q-axis caused by the filter inductor and capacitor, a feedforward decoupling compensation scheme of state variables is introduced into the dual voltage–current inner loops. This ensures that the VSG converter can still track the command signals accurately and rapidly under large disturbances.

2.3. Grid-Connected Equivalent Circuit

A grid-connected converter adopting VSG control can be equivalently modeled as a controllable voltage source in series with a low impedance. On this basis, the equivalent circuit of the VSG-based grid-connected system can be established by substituting each internal control loop of the system with its corresponding equivalent impedance [20,21].

When deriving the system equivalent circuit based on the voltage-source characteristics of the converter, the steady-state convergence of control loops is taken as a fundamental prerequisite. The voltage loop, current loop, and power loop of grid-forming converters feature a high control bandwidth and fast transient response. They can rapidly achieve steady-state convergence during fault transients, and thus satisfy the basic requirement of operating point stability for equivalent circuit modeling. Given the above control characteristics, it is reasonable to assume that all internal control loops of the system have converged to a steady state. This can further guarantee the accuracy and applicability of the derived equivalent circuit.

In addition, during parameter design and tuning, the sum of the configured virtual resistance and actual line resistance is far lower than the corresponding equivalent reactance, which ensures the overall system exhibits inductive features. The resistive component accounts for only a small fraction of the total system impedance and has a negligible impact on key indicators, such as the dynamic characteristics of transient power angles and the amplitude of steady-state fault current. Furthermore, it does not change the fault mechanism and essential operating principle of the control strategy. Therefore, to simplify the theoretical derivation while maintaining the accuracy of fault characteristic analysis, the resistive component is neglected in the subsequent analysis. As depicted in Figure 1, the equivalent impedance between the internal electromotive force of the VSG and the grid voltage consists of four parts: the virtual impedance X_v, the equivalent impedance X_d of the dual voltage–current inner loop control, the filter reactance X_f, and the line impedance X_g. The equivalent circuit of the VSG-controlled grid-connected system is illustrated in Figure 2.

According to the configuration of the VSG-controlled grid-connected system depicted in Figure 1, the reference command of the voltage loop is the output voltage of the virtual impedance loop, denoted as U_ref in Figure 2, whereas the actual feedback of the filter capacitor voltage is the terminal voltage U_s conditioned by the filter impedance. Proper tuning of the PI regulator parameters for the voltage loop ensures that the actual output voltage accurately tracks its reference, i.e., U_c = U_s [22]. Consequently, in the equivalent circuit of Figure 2, the equivalent impedance X_d introduced by the dual voltage–current loop control cancels the physical filter reactance X_f, and the simplified system equivalent circuit is illustrated in Figure 3. On the basis of the simplified equivalent circuit, the relationships among the VSG output active power, fault current, internal electromotive force, and virtual impedance can be quantified.

3. Transient Characteristics of VSG

Emphasis is placed on the transient power angle and fault current characteristics of the VSG grid-connected system under symmetrical grid short-circuit faults.

3.1. Transient Power Angle Characteristics of VSG

Taking the phase of the voltage at the PCC as the reference phase, the phase difference between the internal electromotive force of the VSG and the PCC voltage is defined as the VSG power angle [23]. From the equivalent circuit shown in Figure 3, the active power output by the VSG can be expressed as [24]:

$$P_{\mathrm{s}}={\displaystyle \frac{E_{\mathrm{f}}{U}_{\mathrm{s}}\sin \delta }{X_{\mathrm{v}}}}$$

(4)

When a symmetrical short-circuit fault occurs in the power grid, the PCC voltage sags abruptly. Moreover, since the VSG power angle cannot change instantaneously at the inception of the fault, the active power output from the VSG drops drastically according to the active power characteristic shown in Equation (4), which leads to an active power imbalance between the input and output of the VSG, i.e., P_ref > P_s. By further combining Equation (1), this active power difference will accelerate the system, causing the power angle to increase accordingly.

Figure 4 depicts the transient power angle curve of VSGs under symmetrical short-circuit faults. Points A and B on the curve are the active power balance operating points of VSG. Point A is the system stable equilibrium point, point B is the system unstable equilibrium point, and point C denotes the fault clearing instant. The system transient stability can be evaluated by the equal-area criterion [25]. If the acceleration area accumulated by the virtual rotor during the fault exceeds the maximum deceleration area, the VSG power angle will diverge continuously, resulting in transient power angle instability similar to that of conventional synchronous generators.

3.2. Fault Current Characteristics of VSG

During the initial phase of a short-circuit fault, the converter current typically contains rapidly decaying aperiodic DC components and high-frequency harmonics. Owing to the extremely high control bandwidth and reference tracking speed of the converter’s underlying dual voltage–current closed-loop, these transient electromagnetic components can be suppressed within a few milliseconds; thus, the focus is placed on the characteristics of the steady-state component of the VSG short-circuit current. From Figure 3, the steady-state component of the VSG output current is given by:

$${\mathit{I}}_{\mathrm{f}}={\displaystyle \frac{E_{\mathrm{f}}-U_{\mathrm{s}}}{X_{\mathrm{v}}}}$$

(5)

According to Equation (5), the phasor relationship among the VSG output current, its internal electromotive force, and the PCC voltage is depicted in Figure 5. Figure 5a illustrates the stable case of the VSG power angle, where the steady-state component of the VSG short-circuit current is determined by the internal electromotive force, the PCC voltage, and the virtual impedance. In contrast, Figure 5b shows the unstable case, in which the steady-state component of the VSG short-circuit current increases monotonically with the rise of the VSG power angle.

4. Transient Control Strategies of VSG

Due to the limited hardware overcurrent capability of power electronic converters, the safe operation of the VSG grid-connected system is confronted with severe challenges under symmetrical grid short-circuit faults. Therefore, a targeted transient control strategy must be designed, which is required to not only optimize the power angle trajectory under large transient disturbances to prevent the VSG from losing synchronism, but also limit the short-circuit current. To address this issue, a coordinated control strategy combining dynamic active power reference adjustment and adaptive virtual impedance is designed, aiming to enhance the transient power angle stability of the VSG while constraining the steady-state fault current.

4.1. Dynamic Active Power Reference Adjustment

Different from conventional synchronous generators, where the transient input power is essentially constant due to the mechanical delay of the prime mover, the VSG system, supported by its energy storage unit, features the advantage of flexible active power reference regulation. From the power angle characteristic curve depicted in Figure 4, dynamic adjustment of the active power reference during grid faults can effectively mitigate the power mismatch between the input and output sides of the system, thereby reducing the acceleration area of the virtual rotor and significantly enhancing the transient power angle stability of the VSG.

Pre-fault, the VSG operates at its stable equilibrium point, with its internal electromotive force, PCC voltage, rated virtual impedance, and power angle being E_fN, U_sN, X_vN, and δ_N, respectively. From Equation (4), the rated active power output by the VSG is given by:

$$P_{\mathrm{s}\mathrm{N}}={\displaystyle \frac{E_{\mathrm{f}\mathrm{N}}{U}_{\mathrm{s}\mathrm{N}}}{X_{\mathrm{v}\mathrm{N}}}}\sin {\delta }_{\mathrm{N}}$$

(6)

Following a symmetrical short-circuit fault in the power grid, the PCC voltage drops to U_sF, with the VSG’s internal electromotive force, virtual impedance, and power angle being E_fF, X_vF, and δ_F, respectively. Under this condition, the active power output by the VSG is given by:

$$P_{\mathrm{s}\mathrm{F}}={\displaystyle \frac{E_{\mathrm{f}\mathrm{F}}{U}_{\mathrm{s}\mathrm{F}}}{X_{\mathrm{v}\mathrm{F}}}}\sin {\delta }_{\mathrm{F}}$$

(7)

To minimize the acceleration area as much as possible, the ideal control objective is to regulate the transient power angle around its rated value during the fault, i.e., assuming approximately that δ_N = δ_F. The ratio of the active power output by the VSG before and after the fault is thus given by:

$$K={\displaystyle \frac{P_{\mathrm{s}\mathrm{F}}}{P_{\mathrm{s}\mathrm{N}}}}={\displaystyle \frac{\frac{E_{\mathrm{f}\mathrm{N}}{U}_{\mathrm{s}\mathrm{N}}}{X_{\mathrm{v}\mathrm{N}}}\sin {\delta }_{\mathrm{N}}}{\frac{E_{\mathrm{f}\mathrm{F}}{U}_{\mathrm{s}\mathrm{F}}}{X_{\mathrm{v}\mathrm{F}}}\sin {\delta }_{\mathrm{N}}}}={\displaystyle \frac{E_{\mathrm{f}\mathrm{N}}{U}_{\mathrm{s}\mathrm{N}}{X}_{\mathrm{v}\mathrm{F}}}{E_{\mathrm{f}\mathrm{F}}{U}_{\mathrm{s}\mathrm{F}}{X}_{\mathrm{v}\mathrm{N}}}}$$

(8)

According to the voltage-source characteristic of grid-forming converters, the internal electromotive force of the VSG remains nearly constant, i.e., E_fN = E_fF. The ratio of the active power output by the VSG before and after the fault is thus given by:

$$K={\displaystyle \frac{U_{\mathrm{s}\mathrm{N}}{X}_{\mathrm{v}\mathrm{F}}}{U_{\mathrm{s}\mathrm{F}}{X}_{\mathrm{v}\mathrm{N}}}}$$

(9)

Based on the real-time depth of the voltage sag at PCC, the dynamic segmented adjustment rule for the active power reference is formulated as follows:

$$P_{\mathrm{r}\mathrm{e}\mathrm{f}}^{*}=\left\{\begin{array}{l}{P}_{\mathrm{r}\mathrm{e}\mathrm{f}0}, U_{\mathrm{s}}>U_{\mathrm{t}\mathrm{h}}\\ K\cdot P_{\mathrm{r}\mathrm{e}\mathrm{f}0}, U_{\mathrm{s}}\le U_{\mathrm{t}\mathrm{h}}\end{array}\right.$$

(10)

where P_ref0 denotes the initial value of the active power reference, P_ref^∗ represents the dynamically adjusted active power reference, K is the dynamic regulation index of the active power reference, and Uth is the detection threshold for the PCC voltage sag with a value of 0.9 U_N.

Figure 6 shows the active power–frequency control block diagram of the VSG with the dynamic active power reference regulation module incorporated. The dynamic regulation module is activated when the PCC voltage drops below the detection threshold.

Figure 7 shows the VSG power angle curve with the dynamic active power reference regulation introduced. During the fault, the system actively reduces the active power reference substantially; this reference is not fixed but adjusted in real time according to the PCC voltage and virtual impedance, which significantly reduces the acceleration area of the system. Since the control strategy is designed on the premise that the power angle is maintained at its rated value, the fault transient angle δ_C is nearly close to the initial rated angle δ_N in practical operation, indicating that the VSG power angle remains at the rated value during the fault.

As illustrated in Figure 5b, with the dynamic active power reference regulation adopted, not only the fault-induced power angle of the VSG is suppressed, but its fault current is also restrained to a certain extent.

4.2. Adaptive Virtual Impedance Control

Figure 8 shows the voltage and current phasor relationships before and after virtual impedance adjustment. It can be observed that, with the VSG power angle and PCC voltage sag depth kept constant, the steady-state component of the fault current can be controlled by regulating the virtual impedance.

From Figure 8, the output current of the VSG before and after the fault can be expressed as:

$$\left\{\begin{array}{l}{I}_{\mathrm{N}}={\displaystyle \frac{\sqrt{{E_{\mathrm{f}}}^2+{U_{\mathrm{s}\mathrm{N}}}^2-2{\mathrm{E}}_f{U}_{\mathrm{s}\mathrm{N}}\cos {\delta }_{\mathrm{N}}}}{X_{\mathrm{v}\mathrm{N}}}}\\ I_{\mathrm{F}}={\displaystyle \frac{\sqrt{{E_{\mathrm{f}}}^2+{U_{\mathrm{s}\mathrm{N}}}^2-2E_{\mathrm{f}}{U}_{\mathrm{s}\mathrm{F}}\cos {\delta }_{\mathrm{F}}}}{X_{v\mathrm{F}}}}\end{array}\right.$$

(11)

With the dynamic active power reference regulation applied, δ_N = δ_F. Combined with Equation (11), the virtual impedance during the fault is derived as:

$$X_{\mathrm{v}\mathrm{F}}={\displaystyle \frac{\sqrt{a(E_{\mathrm{f}}^2-U_{\mathrm{s}\mathrm{N}}{U}_{\mathrm{s}\mathrm{F}})+I_{\mathrm{N}}^2{X}_{\mathrm{v}\mathrm{N}}^2{U}_{\mathrm{s}\mathrm{N}}{U}_{\mathrm{s}\mathrm{F}}}}{U_{\mathrm{s}\mathrm{N}}{I}_{\mathrm{F}}}}$$

(12)

where a = U_sN² − U_sNU_sF.

The current threshold during the fault is set to k times the rated current. Substituting this into Equation (12), the current-limiting virtual impedance during the fault is derived as:

$$X_{\mathrm{v}\mathrm{F}}={\displaystyle \frac{\sqrt{a(E_{\mathrm{f}}^2-U_{\mathrm{s}\mathrm{N}}{U}_{\mathrm{s}\mathrm{F}})+I_{\mathrm{N}}^2{X}_{\mathrm{v}\mathrm{N}}^2{U}_{\mathrm{s}\mathrm{N}}{U}_{\mathrm{s}\mathrm{F}}}}{k{U}_{\mathrm{s}\mathrm{N}}{I}_{\mathrm{N}}}}$$

(13)

where k denotes the ratio of the fault current threshold to the rated current.

The adaptive virtual impedance control module is designed based on Equation (13). Figure 9 shows the control structure of the VSG with this module incorporated.

Under normal operation, the system virtual impedance assumes its rated value X_vN. Upon detection of a symmetrical short-circuit fault where the fault current exceeds the maximum allowable current of the converter, the adaptive virtual impedance module calculates the required current-limiting virtual impedance for the hardware and activates it, ensuring the fault current remains within limits to safeguard the secure operation of the VSG.

5. Simulation Analysis

To validate the designed control strategy, a VSG-controlled grid-connected converter model was established on the Matlab/Simulink platform (Version R2024b). This model fully incorporates the DC voltage source, the switching physical characteristics of the converter, the LC filter circuit, and detailed power, voltage, and current control loops. For symmetrical short-circuit fault simulation, a three-phase short-circuit fault module is deployed at PCC. The initiation and clearance of symmetrical short-circuit faults are realized by regulating internal switching operations, and the corresponding parameters are listed in

Table 1. Basic system parameters.

Symbol	Parameters	Value
PN	VSG rated active power	5 kW
Udc	DC voltage	800 V
Vgn	Grid rated voltage magnitude	311 V
Lf	Filter inductor	3 mH
Cf	Filter capacitor	20 μF
J	Virtual inertia	0.15 kg/m2
D	Damping coefficient	2.5 N·m·s/rad

.

At the initial stage, the VSG operates in grid-connected rated state with 5 kW active power output, and all simulation results are presented in per-unit (p.u.). A symmetrical short-circuit fault occurs at 2 s (grid voltage sags to 0.3 p.u.) and is cleared at 4 s. From Figure 10 and Figure 11, the conventional VSG algorithm shows VSG output current exceeding the threshold and power angle instability under 0.3 p.u. grid voltage sag.

Figure 11 shows the VSG power angle curves before and after dynamic active power reference regulation, from which it is observed that the VSG power angle maintains its rated value post-regulation. Figure 12 presents the VSG output current after the regulation, where the current is reduced to 1.8 p.u. once the command is applied. This partially restrains the fault current via power angle control during the fault, verifying the aforementioned theoretical analysis.

However, Figure 12 reveals that dynamic active power reference regulation only partially limits the fault current, which still exceeds the threshold. To mitigate overcurrent, adaptive virtual impedance control is further introduced, setting the fault current threshold to 1.5 times the rated current. Figure 13 shows the VSG output current under coordinated control of dynamic active power reference regulation and adaptive virtual impedance, reducing the current from 1.8 p.u. to 1.5 p.u. During transient fault initiation and clearance, only a half-cycle transient overshoot occurs. As converter thermal stability is verified based on steady-state RMS values, the controlled current satisfies the requirements.

Further quantitative analysis is conducted on the simulation waveforms presented in Figure 10, Figure 11, Figure 12 and Figure 13, with key performance indicators extracted for quantitative assessment. The maximum transient power angle deviation of VSG is maintained within a narrow range without continuous divergence, along with negligible steady-state operational errors. Both peak and steady-state fault currents are effectively constrained within the safe range with controllable overshoot. Moreover, the system achieves rapid dynamic recovery during fault disturbances and after fault clearance, retaining an adequate transient stability margin. Quantitative results demonstrate that the proposed strategy delivers excellent control accuracy and stability in power angle fluctuation suppression, short-circuit current limitation, and dynamic response performance.

To further highlight the technical advantages of the proposed coordinated control strategy, this paper conducts a horizontal comparison among three control schemes: the standalone power angle regulation control, the standalone fixed virtual impedance fault current limiting control, and the proposed coordinated control strategy. The comparison is carried out from two core dimensions, namely transient power angle control and fault current limiting, and the results are listed in

Table 2. Performance comparison of different control strategies.

Control Strategy	Maximum Power Angle/p.u.	Steady-State Fault Current/p.u.
Standalone active power reference regulation control	1.03	1.8
Standalone virtual impedance current limiting control	7	1.5
Proposed coordinated control strategy in this paper	1.01	1.5

.

As shown in Table 2, both standalone control schemes have obvious limitations. While the standalone active power reference regulation focuses on power angle stability control, it lacks sufficient current-limiting capability. Conversely, the standalone virtual impedance current limiting scheme prioritizes fault current suppression but provides insufficient active regulation of the power angle. Neither scheme can simultaneously meet the dual requirements of transient power angle stability and precise fault current limiting. The proposed coordinated control strategy, which combines dynamic active power reference regulation and adaptive virtual impedance, integrates the advantages of both standalone approaches. It achieves both transient power angle stability control and precise fault current limiting simultaneously, further enhancing the operational reliability of VSG grid-connected systems under fault scenarios.

Furthermore, to verify the control performance and stability characteristics of the proposed coordinated control strategy under different fault depths, fault durations, and grid strengths, core indicators including the maximum power angle, steady-state fault current, and system operating state under each typical simulation case are summarized in

Table 3. Comparison of robustness simulations.

Simulation Conditions	Maximum Power Angle/p.u.	Steady-State Fault Current/p.u.	System Operating State
Voltage (0.2 p.u.)	1.05	1.52	Stable
Voltage (0.4 p.u.)	1.01	1.49	Stable
SCR (1.5)	1.03	1.48	Stable
SCR (3.5)	1.02	1.54	Stable
Fault duration (1 s)	1.01	1.51	Stable
Fault duration (1.5 s)	1.01	1.51	Stable

. The quantitative comparison clearly demonstrates the robustness of the proposed strategy.

As shown in Table 3, the proposed coordinated control strategy achieves reliable stable control and fault current limiting performance under different fault depths, fault durations, and grid strengths. In all test cases, the maximum power angle of the VSGs remains near the rated value without significant increase or instability tendency, while the steady-state fault current is limited within the safety threshold of 1.5 p.u., ensuring continuous stable operation of the system. No significant degradation in control performance is observed whether the fault depth and fault duration change, or the grid strength changes. These results fully verify the excellent robustness of the proposed strategy, demonstrating its capability to meet the stable operation requirements under parameter deviations and diverse fault scenarios in practical applications.

In summary, during symmetrical short-circuit grid faults, through the coordinated control of dynamic active power reference regulation and adaptive virtual impedance, not only is the power angle stability of the VSG maintained, but also the fault current is effectively limited, thereby safeguarding the secure and stable operation of the VSG grid-connected system.

6. Conclusions

A coordinated control strategy combining dynamic active power reference regulation and adaptive virtual impedance is designed to tackle the problems of transient power angle instability and short-circuit current overlimit encountered by VSGs under symmetrical short-circuit grid faults. Based on theoretical analysis and Matlab/Simulink simulation verification, the main conclusions are drawn as follows:

(1)

By real-time monitoring the magnitude of voltage sag at PCC and dynamically regulating the active power reference of the VSG, the transient power angle of the VSG can be maintained close to its rated value, while the short-circuit fault current can be restrained to a certain extent.

(2)

The adaptive virtual impedance control allows for accurate calculation and on-demand implementation of the optimal current-limiting impedance, which confines the steady-state fault current of the VSG within the allowable threshold and effectively prevents thermal breakdown of the converter.

(3)

The coordinated control strategy combining dynamic active power reference regulation and adaptive virtual impedance satisfies the dual requirements of transient power angle stability maintenance and fault current limiting for the VSG, thereby improving the operational stability of the VSG grid-connected system under grid symmetrical short-circuit faults.

(4)

In future work, we will establish a hardware experimental platform to validate the engineering applicability of the proposed strategy via hardware tests, extend its application scope to complex conditions such as asymmetric short-circuit faults and multi-machine grid integration, and optimize parameter tuning methods, so as to further improve the operational stability and control reliability of VSGs under grid faults.