Adaptive Transient Synchronization Support Strategy for Grid-Forming Energy Storage Facing Inverter Faults

Abstract

Aiming at the transient synchronization instability problem of grid-forming energy storage under a fault in the grid-connected inverter, this paper proposes an adaptive transient synchronization support strategy for grid-forming energy storage facing inverter faults. First, the equal area rule is employed to analyze the transient response mechanism of the grid-forming energy storage grid-connected inverter under faults, revealing the negative coupling relationship between active power output and transient stability, as well as the positive coupling relationship between reactive power output and transient stability. Based on this, through the analysis of the dynamic characteristics of the fault overcurrent, the negative correlation between the fault inrush current and impedance and the positive correlations among the fault steady-state current, active power, and voltage at the point of common coupling are identified. Then, a variable proportional–integral controller is designed to adaptively correct the active power reference value command, and the active power during the fault is gradually restored via the frequency feedback mechanism. Meanwhile, the reactive power reference value is dynamically adjusted according to the voltage at the point of common coupling to effectively support the voltage. Finally, the effectiveness of the proposed strategy is verified in MATLAB/Simulink.

1. Introduction

1.1. Research Background and Significance

With the in-depth implementation of the “Double Carbon” strategy, a new power system is being accelerated in its evolution toward a “double high” paradigm [1,2], characterized by the high-level penetration of renewable energy and the large-scale integration of power electronic devices. The “strong power source–weak grid” configuration tends to induce a low short-circuit ratio and high grid impedance, leading to the notable degradation of voltage support capabilities [3,4]. As a critical supporting resource in the construction of modern power grids, energy storage is playing an increasingly pivotal role in enhancing the stability and reliability of grid operation [5,6].

1.2. Existing research methods

As the core equipment for energy storage systems, the accurate modeling of grid-connected inverters forms the model foundation for power system research [7,8,9,10]. Grid-following (GFL) inverters rely on a phase-locked loop (PLL) to track the voltage phase at the point of common coupling (PCC) in real time, ensuring operation with a unity power factor [11]. Grid-forming (GFM) inverters do not require detection of the PCC voltage phase; instead, they regulate the output power by simulating the external characteristics of synchronous machines, thereby achieving grid synchronization control [12]. Although the control architectures of these two types of inverters differ, the effective implementation of their control strategies depends on accurate inverter control parameters. The accuracy of inverter control system parameters plays a crucial role in system stability analysis and fault protection design [13]. Currently, the mainstream grid-connected mode of energy storage systems employs grid-following control, imposing inherent limitations on their active voltage and frequency support capabilities [14,15,16,17]. By contrast, grid-forming inverters [18] achieve synchronization with the AC grid through active control of the output power or voltage, emerging as an effective solution to address the poor active support capabilities of energy storage stations. Although the active control principle of grid-forming inverters is borrowed from the operational mechanisms of synchronous generators, notable discrepancies arise in practical applications. First, grid-forming inverters feature complex control architectures [19], and their control parameters exhibit high flexibility without strict physical constraints [20]; second, under large disturbances, grid-forming inverters undergo control mode transitions, leading to power angle characteristic curves that are more complex and variable compared to those of synchronous generators [21]. Such fundamental differences mean that the transient synchronization stability analysis of grid-forming inverters cannot directly adopt the stability analysis frameworks developed for synchronous generators.

In recent years, both domestic and international scholars have conducted extensive research on the impact of grid-forming inverter synchronization control strategies, current–voltage loop design schemes, and fault current limiting strategies on transient synchronization stability, as well as strategies for improving transient stability. In terms of analytical methods, the study in Reference [22] employed the phase plane method to investigate the transient synchronization stability process of grid-forming inverters under multiple control modes, quantitatively revealing how the control parameters of grid-forming inverters affect transient stability. Building upon the traditional equal area criterion (EAC), Reference [23] proposed an improved EAC analysis method incorporating a damping term, which effectively enhanced the estimation accuracy of the transient stability region. Regarding control mode transition research, Reference [24] analyzed the synchronization stability during the switch from grid-forming to grid-following control mode, highlighting its vulnerability to phase-locked loop synchronization issues under weak grid conditions.

For fault current limiting technologies, unlike traditional synchronous generators, energy storage grid-connected systems incorporating numerous power electronic devices are constrained by the overcurrent capabilities of semiconductor devices. Excessive fault currents may trigger large-scale inverter disconnections, thereby threatening system security and stable operation. During faults, the approach in Reference [25] achieves current limiting by directly adjusting the reference value of the inner current loop while maintaining the grid-forming control architecture. However, this method suffers from current saturation during faults, leading to a reduction in the system’s maximum fault clearing angle and potential transient synchronization instability [26]. Reference [27] limits the output current by increasing the output impedance via virtual impedance; however, the calculation of virtual impedance relies on the real-time measurement of the grid-connected impedance, and the virtual impedance introduces shifts in the power angle characteristic curve, affecting the transient synchronization stability.

1.3. The Work in This Article

To address the aforementioned challenges, this paper presents an adaptive transient synchronization support strategy for grid-forming energy storage systems facing inverter faults. First, the EAC is employed to analyze the transient response mechanism of grid-connected inverters in grid-forming energy storage systems under fault conditions, revealing the negative coupling relationship between active power output and transient stability, as well as the positive coupling relationship between reactive power output and transient stability. Based on this analysis, the dynamic characteristics of the fault overcurrent are examined, demonstrating the negative correlation between fault impulse currents and impedance and the positive correlations among fault steady-state currents, active power, and voltage at the PCC.

Subsequently, a variable proportional–integral (PI) controller is designed to adaptively adjust the active power reference command, with active power restoration during faults achieved through a frequency feedback mechanism. Meanwhile, the reactive power reference is dynamically corrected based on the PCC voltage to provide effective voltage support. Finally, multi-scenario simulation results confirm the strategy’s adaptability in various grid fault scenarios.

2. Classical Fault Control Strategies for Grid-Forming Energy Storage Systems During Grid Faults

Figure 1 illustrates the typical control topology of grid-forming energy storage systems during grid integration. In terms of control strategies for grid-forming energy storage grid integration, the primary control approaches include droop control [28], virtual synchronous generator (VSG) control, and others [29]. This paper focuses on VSG control as a case study: the active power–frequency control loop emulates the rotor motion equation of a synchronous generator to ensure system frequency stability under various operating scenarios, while the reactive power–voltage control loop mimics the stator voltage equation of a synchronous generator to effectively regulate the reactive power and support voltage magnitude.

As illustrated in Figure 1, the grid-forming energy storage system maintains DC-side voltage stability via the parallel capacitor C_dc and connects to the grid through a DC/AC inverter. Given the focus on addressing the transient synchronization stability of the AC side in this paper, the DC-side voltage of the energy storage system is assumed to remain stable at U_dc. The inverter output is filtered by an LC network, where L_f denotes the filter inductance, C_f the filter capacitance, and R_f the grid-connected resistance. Additionally, line inductance L_g and resistance R_g exist between the inverter and the grid, with the grid voltage U_g characterized by magnitude U_g and phase angle θ_g. The grid-connected current of the inverter is denoted as i_abc. Owing to the small value of C_f, the capacitor current is negligible, and the capacitor voltage U_pcc has a magnitude and phase angle specified by the power control loop. P_ref and Q_ref represent the active and reactive power references in the outer power loop, respectively, while P_e and Q_e denote the inverter’s output active and reactive powers. J and D signify the virtual inertia and damping coefficients of the active control loop, and K_ie is the integral gain of the reactive voltage control loop. The active control loop outputs a virtual angular frequency ω, with the system reference angular frequency set as ω₀ = 100π. The active power loop generates a reference phase angle θ_ref, while E_dref and E_qref denote the d-axis and q-axis voltage references, respectively, with E₀ being the excitation voltage reference. Here, E_dref is generated by the reactive voltage magnitude control loop, and E_qref is set to zero. VSG control is employed in this study to emulate the dynamic characteristics of a conventional synchronous generator. By measuring the output power in real time, the voltage magnitude and phase angle references are adjusted to enable synchronization between the system and the grid.

2.1. Traditional Fault Control Strategies for Grid-Forming Energy Storage Systems

The classic grid-structured energy storage fault control strategy is introduced in Section 1.2. The active power–frequency and reactive voltage control loops are designed to, respectively, emulate the rotor motion equation of the synchronous generator and the excitation voltage regulation, while the outer power control loop can be derived as [30]

$$J{\omega }_n{\displaystyle \frac{d\omega }{dt}}=P_{ref}-P_e-D{\omega }_n(\omega -{\omega }_n)$$

(1)

$$P_m=P_{ref}+D(\omega -{\omega }_n)$$

(2)

$$E_{dref}=E_{ref}=E_0+{\displaystyle \frac{K_{ie}}{s}}(Q_{ref}-Q_e)$$

(3)

Based on the instantaneous power theory, the active power P_e and reactive power Q_e delivered by the grid-forming energy storage system are expressed as [31]

$$\left\{\begin{array}{c}P={\displaystyle \frac{3}{2}}(u_d{i}_d+u_q{i}_q)\\ Q={\displaystyle \frac{3}{2}}(u_q{i}_d-u_d{i}_q)\end{array}\right.$$

(4)

where u_d and u_q denote the dq-axis components of the inverter output voltage, and i_d and i_q denote the dq-axis components of the inverter output current.

Let the power angle δ be defined as the phase difference between the PCC voltage U_pcc∠θ and the grid voltage U_g∠θ_g; thus,

$${\displaystyle \frac{d\delta }{dt}}={\displaystyle \frac{d\theta }{dt}}-{\displaystyle \frac{d{\theta }_g}{dt}}=\omega -{\omega }_g$$

(5)

where ω_g denotes the angular frequency of the grid voltage. Combining (1), (3), and (5), the third-order model of the inverter is derived as

$$\left\{\begin{array}{l}\stackrel{·}{\delta }=\omega -{\omega }_g\\ J{\omega }_0\stackrel{·}{\omega }=P_{ref}-P_e-D{\omega }_0(\omega -{\omega }_0)\\ {\stackrel{·}{E}}_{dref}=K_{ie}(Q_{ref}-Q_e)\end{array}\right.$$

(6)

This paper presents a sensitivity analysis method for the transient synchronization stability of grid-forming photovoltaic (PV) inverters. First, a mathematical model of the grid-forming PV inverter is established, by considering the impacts of control parameters (e.g., virtual inertia J, virtual damping coefficient D, and integral coefficient) on transient synchronization stability. Subsequently, based on the improved equal area criterion (EAC), a sensitivity index for each control parameter with respect to the transient stability margin is derived, quantitatively characterizing the degree to which parameter variation influences system stability. Finally, a parameter identification method leveraging particle swarm optimization (PSO) is proposed to optimize the control parameters and enhance the system’s transient synchronization stability. Simulation results under various fault ride-through scenarios verify the effectiveness of the proposed approach.

2.2. Transient Response Mechanism of Grid-Forming Energy Storage Systems Under Fault Conditions

The VSG-controlled grid-forming energy storage inverter achieves independent control of the output voltage magnitude and phase via a closed-loop regulation mechanism, thus exhibiting controlled voltage source behavior at its port. The output voltage of the grid-forming energy storage and the grid equivalent EMF can be approximated as an ideal voltage source interconnected system. Based on the simplified analysis of (4), assuming that the grid-connected impedance satisfies X >> R and ignoring the effect of line resistance on power transfer, the simplified expressions for the active power P_e and reactive power Q_e delivered by the grid-forming energy storage inverter are derived as

$$\left\{\begin{array}{l}{P}_e={\displaystyle \frac{3U_{pcc}{U}_g\sin \delta }{X_g}}\\ Q_e{\displaystyle \frac{3U_{pcc}^2-3U_{pcc}{U}_g\cos \delta }{X_g}}\end{array}\right.$$

(7)

In the grid-forming control framework, a three-phase short-circuit fault in the grid causes an abrupt drop in the grid voltage U_g, creating a significant potential difference between the inverter output voltage U_pcc and U_g. Equations (6) and (7) reveal that this voltage deviation drives the inverter’s reactive power Q_e to rise rapidly, thereby inducing a decrease in U_pcc. Under the power coupling effect, the inverter’s actual active power P_e deviates from the reference P_ref, leading to an active power deviation ΔP = P_ref − P_e. Equation (6) shows that this power deviation accelerates the inverter’s output angular velocity ω, causing the power angle δ to increase continuously. Without effective damping, this positive feedback mechanism triggers typical power angle instability, characterized by the non-convergent divergence of δ over time.

The power angle characteristic curves plotted from (7) are shown in Figure 2, where P_e1, P_e2, and P_e3 represent the curves under normal operation, a shallow voltage sag, and a deep voltage sag, respectively, with P_ref1 denoting the active power reference of traditional control. For the shallow sag scenario, P_e2 intersects P_ref1 at a stable equilibrium point δ₁, where the acceleration area S_ABC and deceleration area S_CD satisfy the equal area criterion S_ABC < S_CD [32], ensuring system convergence to δ₁. In contrast, during a deep voltage sag, P_e3 does not intersect P_ref1, and P_ref1 > P_e3 at all power angles, causing the inverter’s angular velocity ω to increase (dω/dt > 0). As δ exceeds the critical stability threshold δ_max, it diverges monotonically, leading to transient instability if the fault is not cleared promptly.

In conclusion, the root cause of system transient instability lies in the electromechanical energy conversion imbalance induced by power mismatch. When the system’s net accelerating power (P_acc = P_ref − P_e) remains positive, the kinetic energy increment ΔW_k stored in the virtual rotor drives the power angle δ to exceed the critical stability threshold δ_max. Based on the EAC, the necessary and sufficient condition for maintaining system transient stability is stated as

$${\displaystyle {\int }_{{\delta }_0}^{{\delta }_1}{P}_{ref}}-P_{e}d\delta \le {\displaystyle {\int }_{{\delta }_1}^{{\delta }_{\max }}{P}_e}-P_{ref}d\delta$$

(8)

From Equation (8), it can be seen that, when the acceleration area is smaller than the deceleration area, the system tends to be stable; otherwise, transient instability occurs. Therefore, the core aspect of improving the power angle stability of the system lies in reducing the acceleration area and increasing the deceleration area. This can be achieved through two control strategies.

(1)

Dynamic active power reference adjustment: As depicted in Figure 2a, P_ref is switched from P_ref1 to P_ref2 during faults. This strategy directly reduces the acceleration area and increases the deceleration area via (8), thereby enhancing the transient synchronization stability.

(2)

Reactive voltage coordinated support: Equations (3) and (6) show that the real-time adjustment of Q_ref to boost U_pcc can also improve system transient stability. As illustrated in Figure 2b, this control strategy shifts the power angle curve from P_e3 to P_e2 during grid faults, reestablishing a stable equilibrium point at δ₁ with P_ref1.

2.3. Dynamic Characteristic Analysis of Grid-Forming Energy Storage Systems During Fault Conditions

VSG-controlled grid-forming energy storage inverters exhibit distinct dynamic characteristics under faults compared to conventional synchronous generators. Whereas conventional synchronous generators can withstand transient currents of 5–8 times their rated value, inverters typically have a limited overcurrent capability of only 1.5–3 times, necessitating further analysis of the transient current in grid-forming energy storage inverters.

Considering Kirchhoff’s voltage law (KVL) and the voltage source characteristics of the VSG controller, the electrical current differential equation during fault inception is

$$L_g{\displaystyle \frac{di}{dt}}+i{R}_g=U_{pcc}\sin (\omega t+\delta )-U_{gf}\sin (\omega t)$$

(9)

where U_gf denotes the grid voltage at the inception of a three-phase short-circuit fault in the grid. Owing to the inertia of the reactive voltage control loop, U_pcc is assumed to remain unchanged. From (9), the transient current during fault is

$$i=I_f\sin (\omega t+\alpha -{\delta }_1)+\left[I_{f0}\sin (\alpha -{\delta }_0)-I_f\sin (\alpha -{\delta }_1)\right]e^{-{\displaystyle \frac{t}{\tau }}}$$

(10)

where I_f denotes the steady-state current magnitude during the fault, I_f0 is the transient current magnitude prior to the fault, $\tau =L_g/R_g$, α is the initial phase, δ₁ is the steady-state power angle during the fault, and δ₀ is the steady-state power angle before the fault.

Shortly after the fault, with t approaching zero, the magnitude of the inrush current at fault inception is primarily determined by the grid impedance. The current magnitude during the fault steady-state period is governed by I_f, for which the expression is given as

$$I_f={\displaystyle \frac{\sqrt{U_{pccf}^2-U_{gf}^2-2U_{pccf}{U}_{gf}\cos {\delta }_1}}{Z_g}}$$

(11)

where U_pccf denotes the PCC voltage during the fault, and the grid impedance is $Z_g=\sqrt{X_g^2+R_g^2}$.

Using the fault steady-state current analytical model developed from (11), the distribution of fault steady-state current I_f for a given operating condition is depicted in Figure 3. Owing to the voltage support provided by VSG control, the magnitude of U_pccf drops more slowly than U_gf, allowing U_gf to be treated as constant for simplified analysis. Figure 3 illustrates that I_f exhibits a positive correlation with power angle δ, such that the dynamic correction of the active power reference can limit I_f. Additionally, I_f shows a negative correlation with the PCC voltage, meaning that optimizing the reactive power control loop in (2) to limit the voltage support capacity can also constrain I_f.

The fault overcurrent characteristics reveal three control optimization paths: (1) dynamic active power reference correction, which reduces I_f by modifying P_ref to keep power angle δ within the safe threshold; (2) voltage support enhancement control, which lowers the If magnitude by adjusting Q_ref to maintain the PCC voltage within safe limits; (3) the activation of virtual impedance control, which restricts the inrush current in Equation (10) by activating virtual impedance during fault inception.

3. Adaptive Support Strategy for Transient Synchronous Stability Based on Fault-Induced Voltage Feedback

3.1. Fault Control Strategy for Grid-Forming Energy Storage

Based on the transient instability mechanism and fault overcurrent characteristics of grid-forming energy storage inverters disclosed in Section 2.2, and taking into account the needs for transient stability and fault overcurrent limitation, this paper presents an adaptive transient synchronous stability support strategy using the fault-induced voltage, comprising adaptive power control and dynamic virtual impedance coordinated control, as illustrated in Figure 4. The adaptive power control includes active and reactive control loops, where U_pcc0 denotes the steady-state PCC voltage magnitude, U_ref is the voltage threshold set to U_ref = 1, K_pw and K_iw are the proportional–integral (PI) coefficients of the adaptive active control loop, and K_q is the proportional coefficient of the adaptive reactive control loop. The active control loop dynamically adjusts the active power reference based on the PCC voltage during faults and restores it adaptively via frequency feedback, enabling the inverter to maintain stable operation while recovering the active power as much as possible. The reactive control loop adjusts the reactive power reference in real time according to the PCC fault voltage to provide grid voltage support. Furthermore, the dynamic activation of virtual impedance serves to limit the inrush current at fault inception and the steady-state overcurrent from gradual active power recovery and voltage support.

In the power control loop, per GB/T 19964-2024 [33], adaptive power command control is activated when the PCC voltage sags below 0.9 p.u. to prevent energy storage stations from disconnecting during grid short-circuit faults. The adaptive reactive power control loop adjusts the reactive power reference in real time based on the PCC voltage sag during faults to stabilize the PCC voltage and enhance the transient synchronous stability; the adaptive active power control loop modifies the active power reference according to the PCC voltage sag and restores the active power dynamically via frequency deviation feedback, ensuring transient process synchronism and active power recovery. In the transient current limitation control loop, virtual impedance is activated when the grid-forming energy storage inverter’s output current i exceeds the threshold (i₀ = 1.5 p.u.). Dynamic virtual impedance switching serves to limit the inrush current during faults and the steady-state overcurrent from power control loops, with the virtual impedance deactivated at other times.

3.2. Adaptive Active Power Control Using Fault Voltage

Figure 2 illustrates that a three-phase grid fault causes grid voltage sag, inducing a deviation between the inverter’s active power output and its reference. Thus, the active control strategy fundamentally adjusts the active power reference in real time according to the U_pcc sag, eliminating the fault-induced power deviation to maintain a constant power angle, reducing the transient response duration, and enhancing the transient power angle stability. The dynamic active power reference is expressed as

$$P_{ref}^{\ast }=P_{ref}-(U_{ref}-U_{pcc})(K_{pw}+{\displaystyle \frac{K_{iw}}{s}})$$

(12)

where $P_{ref}^{\ast }$ denotes the dynamically adjusted active power reference.

The proportional–integral (PI)-based adaptive active power regulator is shown in the red-shaded region of Figure 4. Its control principle adheres to low-voltage ride-through (LVRT) specifications, with the coordinated control mechanism described as follows.

First, the dynamic active power correction module is activated upon detecting U_pcc < 0.9 p.u., a threshold designed to prevent unnecessary power adjustments during shallow sags (U_pcc ≥ 0.9 p.u.). Subsequently, during faults, power modification coefficients K_pw and K_iw are derived from Equation (12), which can be expressed as

$$\left\{\begin{array}{l}{K}_{pw\_\max }={\displaystyle \frac{P_{ref}}{U_{pcc\_\min }^2}}\\ K_{iw\_\max }={\displaystyle \frac{P_{ref}}{U_{pcc\_\min }^2}}\end{array}\right.$$

(13)

where K_{pw_max} and K_{iw_max} denote the maximum correction coefficients for PCC voltage sag.

Since using K_{pw_max} and K_{iw_max} for control leads to excessive active power correction, thereby impeding active power recovery, K_pw and K_iw are set to adaptively adjust the PI controller coefficients in response to frequency deviations. By adjusting the PI coefficients based on frequency deviations, real-time adjustment of the active power reference is achieved, with K_pw and K_iw expressed as

$$\left\{\begin{array}{l}{K}_{pw}=K_{pw\_\max }\Delta \omega \\ K_{iw}=K_{iw\_\max }\Delta \omega \end{array}\right.$$

(14)

where $\Delta \omega$ represents the instantaneous angular frequency deviation of the system. Real-time correction is achieved $P_{ref}^{\ast }$ via the dynamic adjustment of K_pw and K_iw based on (12).

To further investigate the power angle behavior of the fault-voltage-based adaptive active control, phase plane diagrams for different K_{pw_max} and K_{iw_max} values are shown in Figure 5, taking a grid voltage sag to 0.4 p.u. (with the reactive control loop employing the traditional strategy in Figure 1) as an example.

In Figure 5, point A is the initial equilibrium with power angle δ_A. Post-fault, the angular frequency deviates: for smaller parameters (K_{pw_max} = 100, K_{iw_max} = 100), the peak Δω is 2 rad/s, and the maximum power angle at point D is δ_D. Increasing K_pw and K_iw (red dashed line: K_{pw_max} = 300, K_{iw_max} = 300; yellow dashed line: K_{pw_max} and K_{iw_max} =450, K_{iw_max} = 450) reduces Δω toward zero, with fault-time maximum power angles δ_C and δ_B—both significantly smaller than δ_D. Thus, larger adaptive active control PI coefficients K_{pw_max} and K_{iw_max} effectively mitigate the angular frequency deviation and maximum power angle, enhancing the grid-connected inverter stability.

Notably, the core mechanism of the proposed control strategy lies in dynamically adjusting the active power reference during faults, where the active power restoration process forms a closed-loop feedback mechanism with the angular frequency deviation. When the system detects a large angular frequency deviation, it automatically increases the PI coefficients K_pw and K_iw based on the frequency deviation, prompting a reduction in the active power reference to limit accelerating energy accumulation—at this point, the angular frequency change rate is high. As the active power reference is dynamically corrected, the decelerating area gradually increases, causing the angular frequency deviation to decay and triggering an adaptive decrease in K_pw and K_iw, thus enabling the active power reference to recover asymptotically.

In this process, the decelerating area decreases gradually with reference recovery, and the angular frequency change rate decreases synchronously, eventually forming a dynamic balance where the angular frequency deviation converges asymptotically. The strategy does not force the elimination of the angular frequency deviation but ensures that the power angle variation remains within the stable threshold by maintaining the deviation approaching zero.

3.3. Adaptive Reactive Power Control Using Fault Voltage

While the adaptive active control enhances the transient stability, severe grid faults may still cause the power angle to exceed the critical threshold. Section 2.2 reveals that the dynamic adjustment of reactive power reference Q_ref to boost PCC voltage Upcc can enhance inverter synchronism and provide grid voltage support.

Per LVRT specifications, dynamic reactive power adjustment is activated when the PCC voltage sags below 0.9 p.u., maintaining voltage stability by adaptively adjusting Q_ref based on the voltage sag magnitude. The strategy rapidly increases the reactive power output during early fault stages to suppress voltage decline, while dynamically optimizing the reactive support level in mid-stages considering the power angle status, as shown in Figure 4. The reactive power modification expression is

$$Q_{ref}^{\ast }=Q_{ref}+(U_{ref}-U_{pcc})K_q$$

(15)

The reactive power control loop generates the PCC reference voltage. With a control bandwidth significantly larger than the outer voltage control loop, the reactive control loop’s impact on the power angle is assumed to be independent of the outer voltage loop [34], i.e., E_ref = U_pcc. Combining Equations (3), (7), and (15), the PCC voltage is given by

$${\stackrel{·}{U}}_{pcc}={\displaystyle \frac{K_{ie}}{X_g}}\{(Q_{ref}{X}_g-U_{ref}{K}_q{X}_g+U_{pcc}(K_q{X}_g-3U_g\cos \delta )-3U_{pcc}^2\}$$

(16)

With the proposed fault voltage-based adaptive reactive power control strategy, phase plane diagrams for varying K_q under a 0.6 p.u. grid voltage sag are shown in Figure 6. As K_q increases, the maximum power angle decreases from δ_E→δ_D→δ_C→δ_B, with corresponding angular frequency deviation also reduced. Evidently, increasing reactive power enhances the system’s synchronous stability capability.

Figure 7 depicts the PCC voltage for different K_q under the same 0.6 p.u. sag. As K_q increases, the transient PCC voltage magnitude rises in the form U_E→U_D→U_C→U_B, showing a positive correlation with K_q. Concurrently, the corresponding maximum power angle decreases, as increased reactive power first supports the PCC voltage, thereby improving the maximum power angle.

To conclude, the effects of the adaptive reactive control loop parameters on the voltage transient and transient synchronous stability post-grid fault are as follows: (1) the PCC voltage magnitude significantly increases with K_q during voltage sags; (2) increasing K_q elevates the PCC output voltage, thereby boosting the maximum transmitted power and elevating the power angle curve.

3.4. Coordinated Virtual Impedance Switching Control Strategy Based on Fault Current

As analyzed in Section 2.3 regarding the fault transient overcurrent characteristics, a transient inrush current and transient steady-state overcurrent exist during faults. The dynamic active/reactive power reference correction discussed in the previous section affects the current periodic component in transient processes. During active power recovery, the current periodic component rises with active power restoration; excessive reactive power support also increases the current periodic component. Moreover, power control cannot suppress the inrush current at fault inception. Thus, this section sets a current limiting threshold by discriminating the fault current magnitude, automatically activating virtual impedance to limit the fault inception inrush current and current periodic components from power control.

Equation (9) indicates that the fault inception inrush current stems from decaying aperiodic components, and adjusting the grid impedance effectively suppresses the inrush current. Based on this, this section proposes an approach to automatically activate virtual impedance based on the fault current for transient overcurrent limitation, with the detailed principle illustrated in Figure 8.

Figure 8 shows that virtual impedance is automatically activated when fault current i exceeds threshold i₀, and it is deactivated otherwise. Here, i₀ is set to 1.5 p.u. based on the inverter’s power electronics’ maximum current withstanding capabilities, ensuring virtual impedance deactivation when the current periodic component stays below the threshold after the aperiodic component decays to zero under normal operation and fault conditions.

Moreover, the power control loop considers transient power reference dynamic adjustment: the reference varies dynamically with the fault voltage, the reactive power output increases, and the active power first decreases then increases with frequency deviation. As Equation (17) shows, increasing reactive power and gradual active power recovery raise the fault-time output current periodic component, while dynamic virtual impedance switching further mitigates the overcurrent from power fluctuations.

$$I={\displaystyle \frac{\sqrt{P_e^2+Q_e^2}}{\sqrt{{\left(R+R_v\right)}^2+{\left(X+X_v\right)}^2}}}$$

(17)

4. Simulation Verification

For the verification of the proposed adaptive transient synchronous stability support strategy, a grid-forming energy storage system simulation model is established in MATLAB/Simulink R2024, as depicted in Figure 9. The control system and strategy are shown in Figure 4, with the controller parameters listed in

Table 1. Simulation parameters of main circuit and controller for energy storage grid-connected system.

Parameter	Value	Parameter	Value
Rated Capacity/SB	1000 kVA	Line Inductance/Lg	1.2 mH
Active Power/Pref	100 kW	Line Resistance/Rg	0.05 Ω
Reactive Power/Qref	0 kVar	Virtual Inductance/Lv	2 mH
DC Bus Voltage/Udc	750 V	Virtual Resistance/Rv	0.05 Ω
Grid Voltage/Ug	380 V	Moment of Inertia/J	2 kg/m2
Rated Frequency/f	50 Hz	Damping Coefficient/D	30.545 N·m·s/rad
Filter Capacitance/Cf	100 μF	PI Controller/(kpU + kiU/s)	41.56 + 49,900/s
Filter Inductance/Lf	2 mH	PI Controller/(KpI + kiI/s)	0.97 + 93/s
Grid-Connected Resistance/Rf	0.05 Ω	Current Limiter/I0	1.5 p.u.

.

Verification of Adaptive Synchronous Stability Support Strategy

At t = 2 s, shallow and deep voltage sags are simulated by varying the voltage sag degree to evaluate the strategy under different fault severities. The fault duration is fixed at 1 s for both cases. The proposed strategy is validated via simulations, comparing it with the approach in Ref. [35].

(1)

Case 1: Shallow grid voltage sag.

To verify the proposed fault ride-through control strategy under a shallow grid voltage sag, the VSG operates stably before the fault. At t = 2 s, a three-phase short circuit occurs on the grid side, dropping the grid voltage magnitude to 0.7 p.u. with a 1 s fault duration. Figure 10, Figure 11, Figure 12 and Figure 13 present the response waveforms of the grid voltage, PCC voltage, system power angle, frequency, output current, output power, and virtual impedance voltage drop for this scenario.

Figure 10 shows the voltage transient response waveforms under different control strategies. The grid voltage drops to 154 V (0.7 p.u.) at 2 s. As Figure 10b illustrates, the PCC voltage oscillates between 2 s and 2.37 s, with the proposed strategy exhibiting a shorter oscillation duration and better voltage stability. Between 2.37 s and 3 s, the proposed strategy stabilizes the voltage at 164.52 V via adaptive reactive loop control, whereas the comparative strategy—without adaptive reactive control—sees the PCC voltage drop to 151.21 V. Evidently, the proposed strategy effectively supports the PCC voltage.

The frequency and power angle response waveforms for different control strategies are shown in Figure 11. At t = 2 s, a three-phase grid fault induces angular frequency deviation and a power angle shift. Figure 11a shows that the proposed strategy has a maximum angular frequency deviation of 1.10 rad/s, compared to 3.52 rad/s for the comparative strategy, demonstrating smaller frequency fluctuations and superior angular frequency control during faults. Figure 11b indicates the steady-state δ₀ = −0.2368. Within 2.35 s after the fault, the comparative strategy reaches a maximum power angle of δ_max1 = −0.0540, while the proposed strategy shows δ_max2 = −0.1780. Initially, the power angle tracks the angular frequency; at t = 3 s, the proposed strategy stabilizes at δ₂ = −0.4515, versus δ₂ = −0.3553 for the comparative strategy. The larger deviation in the proposed strategy arises from the positive angular frequency deviation driving a continuous power angle increase.

The power waveforms under different strategies are shown in Figure 12. Figure 12a shows that, during early fault stages, the grid voltage drops sharply, with the proposed strategy exhibiting a reactive power fluctuation of 100 kVar before stabilizing at 22 kVar. The comparative strategy—lacking adaptive reactive control—suffers from reactive power fluctuations from fault-induced overcurrent, stabilizing at 0 kVar. This confirms that the proposed strategy effectively regulates the reactive power to support the PCC voltage. Figure 12b shows that, at t = 2 s, the proposed strategy’s active output drops to P_min1 = 65 kW (vs. P_min2 = 25 kW for the comparative strategy). By t = 3 s, the proposed strategy recovers to P₁ = 96 kW, outperforming the comparative strategy’s 69 kW recovery. Overall, the proposed strategy demonstrates superior active power restoration.

Figure 13 depicts the current and virtual impedance voltage drop waveforms for different control strategies. The comparative strategy employs constant virtual impedance switching without adaptive reactive compensation, achieving effective transient current limitation with a peak transient current of I_max1 = 161.38 A. The proposed strategy has a maximum inrush current of I_max2 = 242 A (1.61 p.u.). While its inrush current limiting is less effective than the comparative strategy, the proposed strategy restricts the inrush current to 1.61 p.u.—safeguarding the power electronics—while balancing voltage support and active power recovery. During faults, the steady-state current component, governed by the adaptive power outer loop, trends upward but stays within the 1.5 p.u. limit. Figure 13b shows that the proposed strategy activates virtual impedance at fault inception to limit the inrush current, deactivating it after the inrush current decays to zero. By contrast, the comparative strategy’s continuous virtual impedance activation—as seen in Figure 12 and Figure 13—hinders active power recovery and PCC voltage support.

(2)

Case 2: Deep grid voltage sag.

To verify the proposed control strategy under a deep grid voltage sag, a three-phase short circuit occurs on the grid side at t = 2 s, dropping the grid voltage magnitude to 0.3 p.u. with a 1 s fault duration. Figure 14, Figure 15 and Figure 16 present the grid voltage, PCC voltage, system power angle, frequency, output power, and output current waveforms for this scenario.

Figure 14 shows the voltage transient response waveforms under different control strategies, with the grid voltage dropping to 66 V at 2 s. As Figure 14b illustrates, under a deep voltage sag, the PCC voltage exhibits more severe oscillations between 2 s and 2.4 s, with a longer oscillation duration. Notably, between 2.4 s and 3 s, the proposed strategy stabilizes the PCC voltage at 104.23 V, hardly affecting the overall transient voltage stability. In contrast, the comparative strategy—without adaptive reactive control—sees the PCC voltage drop to 52.72 V, confirming the proposed strategy’s effective PCC voltage support under deep sag conditions.

Figure 15 shows the frequency and power angle response waveforms under different control strategies during a 0.3 p.u. grid voltage sag. As Figure 15a depicts, the proposed strategy exhibits a maximum angular frequency deviation of 1.65 rad/s, versus 2.82 rad/s for the comparative strategy. One second after fault inception, the proposed strategy maintains a smaller angular frequency deviation, demonstrating superior angular frequency control under deep sag conditions. Figure 15b indicates a steady-state δ₀ = −0.2368. Within 2.35 s post-fault, the comparative strategy reaches a maximum power angle of δ_max1 = −0.0832, while the proposed strategy shows δ_max2 = −0.1042, with power angle variations initially in accordance with angular frequency changes. At t = 3 s (fault end), the proposed strategy stabilizes at δ₂ = −0.7520, compared to δ₁ = −0.920 for the comparative strategy, showing a minimal discrepancy. Under a deep sag, the proposed strategy suppresses power angle oscillations at the fault end, effectively controlling frequency deviations and power angle variations to prevent system loss of synchronism.

Figure 16 shows the power waveforms under different control strategies during a 0.3 p.u. grid voltage sag. Figure 16a reveals that the proposed strategy’s reactive power stabilizes at 44 kVar by 2.5 s, eventually reaching 46 kVar. In contrast, the comparative strategy—lacking adaptive reactive control—suffers from reactive power fluctuations from the fault-induced overcurrent, stabilizing at 0 kVar. The proposed strategy effectively manages the reactive power to support the PCC voltage under deep sag conditions. Figure 16b shows that the proposed strategy has a minimum active output of P_min1 = 19.5 kW, versus P_min2 = 11.3 kW for the comparative strategy. The proposed strategy recovers gradually to P₁ = 51.82 kW, outperforming the comparative strategy’s P₂ = 19.42 kW recovery. Evidently, the proposed strategy excels in active power restoration under severer fault conditions.

Figure 17 depicts the current and virtual impedance voltage drop waveforms for different control strategies under a deep voltage sag. Figure 17a shows that the comparative strategy has a maximum inrush current of I_max2 = 310.90 A (2.07 per unit, p.u.), while the proposed strategy exhibits I_max1 = 348.26 A (2.32 p.u.). While coordinating voltage support and active power recovery, both strategies show comparable inrush current limitation. The proposed strategy protects power electronics from damage while enabling active recovery and voltage support. After the inrush current decays, the fault current under the proposed strategy trends upward but stays within the 1.5 p.u. limit. Figure 17b indicates that the proposed strategy repeatedly activates/deactivates virtual impedance between 2 s and 2.4 s to limit the inrush current, deactivating it after inrush decay. Frequent virtual impedance switching impairs the grid-connected voltage initially but stabilizes it after deactivation. Overall, the proposed strategy coordinates active recovery and voltage support during deep sags, maintaining power angle stability and exhibiting robust adaptability.

5. Conclusions

This study employs PI control to dynamically adjust the active power reference and a frequency feedback mechanism to facilitate gradual active power restoration during faults, balancing transient synchronous stability and maximum active power recovery for grid-forming inverters. Furthermore, the reactive power reference is adjusted based on the PCC voltage to enhance inverter synchronism and provide effective PCC voltage support. Finally, a coordinated control strategy for dynamic virtual impedance switching is proposed to limit the initial fault inrush current and steady-state overcurrent from voltage support and active restoration.

Under severe fault scenarios, the proposed strategy outperforms other methods by increasing active power restoration by 39.1%, improving voltage support by 8.6%, and reducing the maximum power angle by 68.62%. Additionally, it limits the inrush current to 1.59 p.u. or below and the steady-state fault current to 1.31 p.u. or below under severe conditions.

In the future, we will conduct further study as follows: (1) benchmarking against advanced methods like MPC and AI-based control; (2) conducting HIL or laboratory prototype tests; and (3) extending the analyses to include asymmetric faults, harmonic distortions, and communication latencies.