Abstract
Virtual synchronous generator (VSG) is prone to transient power angle instability under grid fault, which weakens its voltage and frequency support ability to the grid. During the grid fault, the evolution characteristics of VSG transient power angle and terminal voltage are closely coupled with the grid fault voltage. Using the VSG terminal voltage to sense the grid fault information, the active control of VSG transient power angle under different fault depths can be realized without detecting the grid voltage. Therefore, this paper first analyzes the transient power angle characteristics of VSG and the transient characteristics of terminal voltage, analyzes the mapping relationship between them and the grid fault voltage, and establishes the terminal voltage information perception mechanism. Based on this, an adaptive control framework for VSG transient power angle is constructed. The active power command value is dynamically adjusted by using the terminal voltage sensing information to reduce the imbalance of VSG active power input and output during the fault period. Furthermore, a control parameter tuning method based on terminal voltage sensing information is proposed to ensure the transient stable operation of VSG under different fault depths. Finally, the correctness of the theoretical analysis and the effectiveness of the proposed method are verified by simulation and experiment.
1 Introduction
In response to the challenges of climate change and energy security, the global power system is undergoing a profound low-carbon transformation. In this process, intermittent renewable energy represented by wind power and photovoltaic gradually replaces traditional synchronous generators and becomes an important part of power supply (Frasetyo et al., 2021; Zhou et al., 2020; Cheema et al., 2022; Sun et al., 2026). This structural change makes the grid-connected inverter evolve from a simple power regulation unit to a core interface between the new energy generation and the power grid. However, under the traditional vector control strategy, the inverter presents an external characteristic of voltage source with approximate zero inertia and weak damping, and it is difficult to provide the inertia support and power oscillation damping required for frequency stability (Lv et al., 2024; Okafor and Folly, 2023; Rafi et al., 2021). With the continuous improvement of the penetration rate of power electronic interfaces, the equivalent inertia of the system continues to decline, and the deterioration of frequency dynamics has become a key bottleneck restricting the consumption level of renewable energy. In order to overcome this limitation, the virtual synchronous generator (VSG) technology is proposed. The core idea is to introduce the rotor motion equation and excitation regulation mechanism of the synchronous generator into the inverter control, so that the power electronic interface presents inertia and damping characteristics (Li et al., 2016; Yuan et al., 2024; Mallemaci et al., 2021; Qu et al., 2021; Xiong et al., 2022). At present, VSG has become an important research direction in the field of network structure control.
Under small disturbance conditions, the stability analysis and parameter design of VSG have been fully studied (Hu et al., 2017; Pournazarian et al., 2021; Pourmohammad and Toulabi, 2021). However, during the grid fault, the amplitude of the grid voltage drops sharply, and the active power transmission capacity of the VSG decreases accordingly. There is a significant mismatch between the active power command value on the input side and the actual active power on the output side, which accelerates the evolution of the power angle. At the same time, the VSG terminal voltage also changes transiently with the depth of the grid fault voltage. If the fault duration is long or the voltage drop is deep, the coupling evolution of the power angle and the terminal voltage will lead to the transient power angle instability of the VSG similar to that of the traditional synchronous generator (Sun et al., 2022; Tang et al., 2021; Ge et al., 2022), which will weaken its voltage and frequency support ability to the power grid.
Aiming at the transient stability problem of VSG under large disturbance, some scholars have carried out improvement research from two aspects: parameter setting and control structure. In terms of parameter setting, (Ge et al., 2026) uses the real-time deviation between the grid voltage and the VSG output voltage to correct the active power command value, and limits the fault current while ensuring the stability of the power angle. However, this method relies on the real-time detection of the grid voltage, increases the detection branch and introduces the control delay. In (Wu et al., 2024), the critical clearing angle (CCA) and critical clearing time (CCT) were quantitatively analyzed based on the equal area rule, and the design criteria of control parameters for CCA and CCT were proposed. In (Ge et al., 2023), this paper quantifies the CCA and CCT stability boundaries of VSGs under different parameters and faults, proposes an equal proportional area criterion for virtual inertia tuning, and designs a transient control scheme to improve both indices, which is verified via simulations and experiments. In terms of control structure, (Shuai et al., 2019) used Lyapunov direct method to analyze the transient power angle stability of VSG, and fed back the voltage to the active control loop, but did not give a systematic tuning method of feedback parameters. In (Chen et al., 2022), the active loop deviation is introduced into the reactive power control loop, and the reactive power regulation is used to raise the output voltage during the fault to improve the transient stability of the grid. However, the parameter design does not fully consider the stable operation requirements under different fault depths. In summary, the existing methods still have the problem of relying on grid voltage detection or adjustment parameters and lack of fault depth adaptability.
In order to improve the transient power angle stability of VSG under grid fault, this paper proposes an adaptive control method of VSG transient power angle based on terminal voltage information perception. Firstly, the evolution characteristics of VSG transient power angle and terminal voltage during the fault period are analyzed, and the mapping relationship between them and the grid fault voltage is established. It is clear that the terminal voltage deviation can be used as the local perception of the grid fault depth and power angle acceleration trend. Based on this, the existing terminal voltage deviation signal in the reactive-voltage control loop is introduced into the active-frequency control loop to construct a transient power angle adaptive control framework. The terminal voltage deviation is used as the sensing input, and the active power command value is adaptively adjusted to dynamically reduce the VSG active power input and output imbalance during the fault, without additional detection of the grid voltage. Furthermore, according to the terminal voltage sensing information, the setting method of control parameters is given to ensure the transient stable operation of VSG under different fault depths. Simulation and experimental results verify the correctness of the theoretical analysis and the effectiveness of the proposed method.
2 Analysis of VSG transient characteristics
2.1 VSG power angle transient characteristics
The main circuit and control structure of the VSG are shown in Figure 1. In the figure, uo and io are the output voltage and current of VSG, respectively. Le and Lf are line inductance and filter inductance; Cf is the filter capacitor; ω0 and ω represent the rated angular frequency and the actual angular frequency of VSG, respectively. J and D represent virtual inertia and damping coefficient respectively. Pref and Qref are the command values of active and reactive power, and Pe and Qe are the actual values of active and reactive power. δ is the power angle, E is the VSG voltage command value, Uref represents the rated voltage, and kq is the reactive power-voltage droop coefficient.
FIGURE 1
According to Figure 1, the VSG power control loop includes active-frequency control and reactive-voltage control. Among them, the VSG active-frequency loop control equation is:
The active power transmitted by VSG to the power grid is:
In the formula, Uo and Ug are the output voltage amplitude and grid voltage amplitude of VSG, and XΣ is the sum of line reactance and grid reactance.
According to the (Equation 2), the output active power of VSG under fault conditions is obtained as follows:
In the formula, PeF is the active power output by VSG after fault, δF is the fault power angle, UoF is the fault voltage output by VSG, and UgF is the fault grid voltage.
According to (Equation 1), the VSG active power-frequency control loop equation can be changed as:
Let Pn be the reference value of the actual output active power of VSG, then Pn = Pref −DΔω.
According to (Equation 1), the rotor motion equation of VSG can be obtained:
According to (Equations 3,5), the power angle curve and power angle time-varying curve of VSG under different fault depths can be obtained, as shown in Figure 2. In the figure, the red area represents the acceleration area, the blue area represents the deceleration area, the curve I represents the power angle curve under normal operating conditions of the power grid, and the curves II and III represent the power angle curves under different fault depths. When the fault is light, the grid voltage and the VSG terminal voltage drop is small, the active power input and output imbalance is limited, the acceleration area is less than the deceleration area, and the VSG is finally stabilized at the c point, as shown in Figures 2a,b. When the fault deepens, the grid voltage drop further weakens the VSG active power transmission capacity and increases the input and output imbalance. If the fault continues, the power angle will continue to increase and transient instability will occur, as shown in Figures 2c,d. It can be seen that the fault voltage depth of the power grid directly affects the power angle transient evolution of the VSG.
FIGURE 2
2.2 VSG terminal voltage transient characteristics
The control equation of VSG reactive power-voltage loop is:
The output reactive power of the VSG is expressed by Equation 7:
During the fault, let UoF = E, combined with (Equations 3,6), the VSG terminal voltage can be obtained as:
In the formula, , .
According to (Equation 8), Figure 3 shows the variation surface of VSG terminal voltage UoF with fault grid voltage UgF and reactive power-droop coefficient kq. From Figure 3, it can be seen that UoF decreases with the decrease of UgF. The more serious the grid fault is, the more obvious the voltage drop of VSG port is. Under the same UgF condition, the change of kq will also affect the terminal voltage level, but under the deep fault, its regulation effect is limited by the decrease of grid voltage. It can also be seen from (Equation 8) that there is a clear mapping relationship between UoF and UgF after the control parameters are determined. Therefore, the terminal voltage deviation ΔU = Uref -UoF can be used as the local perception of the grid fault depth, and the fault information contained in the terminal voltage can be further used for VSG transient power angle regulation.
FIGURE 3
Substituting the VSG terminal voltage expression into (Equation 4), the VSG output active power expression during the fault is:
According to (Equation 4), when the grid fault deepens, UgF and UoF decrease synchronously, the active power transmission capacity of VSG decreases, and the imbalance between active power input and output increases, which in turn accelerates the change of power angle. The time-varying curve of VSG power angle with different reactive power-voltage droop coefficient kq is drawn as shown in Figure 4. It can be seen from Figure 4 that the VSG reactive power-voltage droop coefficient kq will affect the VSG transient power angle. Based on (Equations 8–10), it can be seen that the decrease of grid fault voltage leads to the deviation of VSG terminal voltage, which further leads to the imbalance of VSG active power input and output, and ultimately leads to the instability of VSG transient power angle. This provides a theoretical basis for actively adjusting the active power command value by using the terminal voltage deviation information.
FIGURE 4
3 VSG transient power angle adaptive control strategy
During the grid fault, the VSG terminal voltage UoF deviates from the rated voltage Uref. The deviation can be directly obtained by the reactive power-voltage control loop, and its expression is:
When the fault deepens, the VSG output reactive power and the terminal voltage deviation ΔU change accordingly; at the same time, the active power transmission capacity decreases, and the VSG active power input and output imbalance increases. According to the mapping relationship established in Section 1, ΔU not only reflects the depth of power grid fault, but also characterizes the acceleration trend of power angle. Therefore, ΔU is introduced into the VSG active power-frequency control loop to adaptively adjust the active power command value, which can dynamically reduce the power imbalance during the fault without detecting the grid voltage. The control framework is shown in Figure 5.
FIGURE 5
After introducing the terminal voltage deviation signal, the equivalent active power command value of VSG is adjusted to:
In the formula, M1 is the adjustment parameter of active power command, and its value is determined according to the depth of power grid fault represented by terminal voltage deviation.
It can be seen from (Equation 11) that after the fault occurs, the controller reduces the equivalent active power command value according to the terminal voltage deviation ΔU, making it closer to the actual output active power of the VSG, thereby reducing the active power input and output imbalance. According to the equal area rule, the power angle acceleration area decreases, which is beneficial to suppress the continuous growth of the power angle during the fault. It can be seen from (Equation 11) that after the fault occurs, the controller reduces the equivalent active power command value according to the terminal voltage deviation ΔU, making it closer to the actual output active power of the VSG, thereby reducing the active power input and output imbalance. According to the equal area rule, the power angle acceleration area decreases, which is beneficial to suppress the continuous growth of the power angle during the fault.
After the introduction of terminal voltage information sensing and transient power angle adaptive control, during the fault period, the rotor motion equation of VSG becomes:
In the formula, , , , .
To obtain the feasible range of the adjustment parameter M1, the equal-area criterion in (Tang et al., 2021) is adopted. It should be noted that, during the fault duration, the damping term DΔω is retained in the rotor motion (Equation 12), and the reactive power-voltage loop dynamics are incorporated into the active power analysis through the terminal voltage expression of (Equation 8). Subsequently, the acceleration region and deceleration region of the VSG can be represented by Equations 13, 14:
Under the traditional control, the VSG usually only has a continuous acceleration process during the fault period, dδ/dt > 0, the power angle continues to increase, and finally transient instability occurs. It can be seen from (Equation 11) that after the reasonable setting of M1, the larger the terminal voltage deviation ΔU, the greater the reduction of the active power command value, which can make the system form a deceleration area during the fault, as shown in Figure 6.
FIGURE 6
According to the equal area rule, the adjustment parameter M1 should balance the acceleration area and deceleration area in the fault stage. As the fault deepens, the terminal voltage deviation ΔU increases, and the controller correspondingly enhances the active power command regulation to limit the power angle to continue to accelerate. When transient stability conditions are satisfied, there are as given by Equation 15:
According to the (Equations 8,13), the relationship between fault voltage, terminal voltage deviation and power angle dynamics can be established. The steady-state operating point before the fault is taken as the initial state, and the system satisfies δt = 0 = δA,Δω = 0,dΔω/dt = 0. Further, the differential equation of VSG about time is obtained as follows:
In the formula, y, y′ and y″ represent the power angle, power angle change rate and angular frequency change rate of VSG respectively, and y|(t = 0), y'|(t = 0) and y''|(t = 0) represent the values of its initial time, which are δA, 0 and 0 respectively.
The design flowchart for adjustment parameter M1 is illustrated in Figure 7. Given the reactive-voltage droop coefficient kq, the terminal-voltage fault mapping relationship described by Equation 8 is adopted to establish the correlation between terminal-voltage deviation ΔU and grid fault depth. Combined with the equal-area criterion for VSG transient stability, the rotor motion differential equation under fault conditions is solved to derive the feasible range of M1. A 10% safety margin is reserved within the theoretical feasible region to guarantee practical transient stability margin. In real-time implementation, the controller only needs the locally measured terminal voltage to calculate ΔU and select a proper M1, without additional grid-voltage measurement. The effect of kq on power-angle dynamics is implicitly incorporated into the parameter-design procedure via the terminal-voltage perception quantity ΔU. When kq changes, the feasible range of M1 can be recalculated following the identical workflow.
FIGURE 7
The relationship between the adjustment parameter M1 and the grid fault voltage UgF satisfying the transient stability condition can be obtained by solving the integral of (Equation 16). Further, the UgF−UoF mapping established by (Equation 8) is used to convert the fault depth into the local measurable terminal voltage deviation ΔU, so as to determine the value range of M1 under different terminal voltage deviations, as shown in Figure 8. In engineering applications, the controller only needs to collect the VSG terminal voltage and calculate ΔU, without additional detection of the grid voltage. In order to ensure the stable operation margin, this paper sets aside 10% safety margin within the theoretical value range.
FIGURE 8
4 Simulation and experimental verification
In order to verify the effectiveness of the proposed active power command adaptive adjustment framework and adjustment parameter tuning method, a simulation model is built in MATLAB/Simulink and experimental verification is carried out. Under different fault depths, the controller selects the corresponding adjustment parameter M1 according to the terminal voltage deviation ΔU, and the system parameters are shown in Table 1.
TABLE 1
| Parameters | Actual value/per unit value |
|---|---|
| Active power reference Pref/kW | 40/1.0pu |
| Reactive power command value Qref/kVar | 0/0pu |
| Factor of inertia J/(kg·m2) | 188.4 |
| Damping coefficient D/(N·s·m/rad) | 1,200 |
System parameters.
4.1 Simulation verification
The simulation results of VSG grid-connected system under different grid fault depths are shown in Figures 9, 10. When the grid voltage drops to 0.3pu and the fault lasts for 1.5s, the VSG terminal voltage, power angle and output power under the traditional control oscillate continuously during the fault period, the power angle cannot converge, and the system undergoes transient instability, as shown in Figure 9a. After adopting the proposed method, the controller adaptively reduces the active power instruction value according to the terminal voltage deviation, and reduces the imbalance of active power input and output during the fault period. The terminal voltage, power angle and output power tend to be stable after a short adjustment, and the VSG can maintain transient stable operation during the fault duration, as shown in Figure 9b.
FIGURE 9
FIGURE 10
In order to further verify the adaptability of the proposed method to different fault depths, the grid voltage is set to drop to 0.35pu and the fault lasts for 1.5s. It can be seen from Figure 10a that the electrical quantities such as VSG output power and terminal voltage continue to oscillate under traditional control, and the power angle diverges and transient instability occurs. After adopting the proposed method, the terminal voltage deviation signal triggers the adaptive adjustment of the active power command value, and the VSG can remain stable during the fault. Its active power and terminal voltage tend to be stable after falling, and the reactive power output increases, which can continue to provide certain voltage support for the power grid. The results show that the method can adapt to different fault depths according to the local terminal voltage information without inputting the grid voltage information.
4.2 Experimental verification
Figure 11 shows the experimental waveforms under grid voltage sag of 0.3 pu. Without the proposed controller M1 = 0, the active power reference remains Pref = 1.0 pu during the fault. After voltage sag, the active power output of the VSG drops to 0.22 pu. The accelerating area increases while the maximum available decelerating area decreases, leading to a negative stability margin and continuous divergence of power angle, which indicates transient instability, as illustrated in Figure 11a. With the proposed controller, the active power reference is adaptively adjusted via (2-3) according to the terminal voltage deviation ΔU. Under this condition, ΔU = 0.47 pu and M1 = 91 are adopted. The active power reference is reduced from 1.0 pu to 0.52 pu, which effectively alleviates the active power imbalance and satisfies the transient stability criterion. After fault regulation, the active power stabilizes at 0.58 pu, the terminal voltage maintains 0.52 pu, and the reactive power rises to 0.42 pu to provide continuous voltage support, as shown in Figure 11b.
FIGURE 11
Figure 12 presents the experimental results for a 0.35 pu grid voltage sag. Under conventional control, the VSG active power decreases from 1.0 pu to 0.28 pu after fault occurrence. The accelerating area exceeds the available decelerating area, violating the equal-area criterion for transient stability. The power angle diverges monotonically, resulting in system instability, which matches the waveforms in Figure 12a. When the proposed controller is activated, ΔU = 0.53 pu and M1 = 103 are selected. The active power reference is reduced to 0.48 pu, greatly mitigating the active power mismatch and enlarging the decelerating area to meet the stability requirement. In the post-fault steady state, the active power output settles at 0.52 pu, the terminal voltage remains at 0.47 pu, and the reactive power increases to 0.48 pu to support the grid voltage, as depicted in Figure 12b.
FIGURE 12
Consistent trends can be observed under the two fault severities. The experimental results are well consistent with simulation outcomes. Comparative analysis demonstrates that the proposed control strategy can extract fault depth information embodied in terminal voltage to adaptively regulate the active power reference. It optimizes the distribution of accelerating and decelerating areas and significantly improves the transient stability of VSGs during voltage sags, ensuring stable operation under various fault degrees.
5 Conclusion
Aiming at the problem of transient power angle instability of VSG under grid fault, this paper analyzes the correlation characteristics between transient power angle, terminal voltage and grid fault voltage, proposes an adaptive control method of VSG transient power angle based on terminal voltage information perception, and gives a control parameter setting method based on terminal voltage perception information. The main conclusions are as follows.
The depth of grid fault voltage affects both the VSG terminal voltage and active power transmission capacity. By analyzing the characteristics of transient power angle and terminal voltage, the mapping relationship between grid fault voltage, terminal voltage deviation, active power imbalance and transient power angle is established. It is clear that the terminal voltage deviation can be used as the local perception of fault depth and power angle acceleration trend.
A VSG transient power angle adaptive control framework based on terminal voltage information perception is constructed. This method takes the existing terminal voltage deviation in the reactive power-voltage loop as the sensing input, dynamically adjusts the active power command value, and reduces the VSG active power input and output imbalance during the fault, without additional detection of the grid voltage.
A control parameter tuning method based on terminal voltage sensing information is proposed. Different fault depths are mapped to terminal voltage sensing quantities, and the corresponding parameter value ranges are determined. The simulation and experimental results show that the proposed method can suppress the divergence of power angle under different voltage drop depths and ensure the transient stable operation of VSG.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
SZ: Writing – original draft. PR: Writing – review and editing. MH: Writing – original draft. XY: Writing – review and editing. KF: Writing – original draft. YC: Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This research was funded in part by the Smart Grid National Science and Technology Major Project (grant number 2024ZD0800600).
Conflict of interest
Authors SZ, MH, XY, KF, and YC were employed by Electric Power Research Institute of Guizhou Power Grid Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This study received funding from China Southern Power Grid Co., Ltd. The funder had the following involvement in the study: technical discussions on model construction and mechanism analysis.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
equal area criterion, terminal voltage information perception, transient power angle, transient stability control, virtual synchronous generator
Citation
Zhang S, Ren P, He M, You X, Fan K and Cai Y (2026) Adaptive control method of VSG transient power angle based on terminal voltage information perception. Front. Energy Res. 14:1945371. doi: 10.3389/fenrg.2026.1945371
Received
22 July 2026
Revised
22 August 2026
Accepted
27 August 2026
Published
25 September 2026
Volume
14 - 2026
Edited by
Xingshuo Li, Nanjing Normal University, China
Updates
Copyright
© 2026 Zhang, Ren, He, You, Fan and Cai.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Peng Ren, renppp@hnu.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.