A Study on Fault Ride-Through and Inertia Support Strategies for Grid-Forming Energy Storage Stations

Abstract

This paper addresses the “dual-high” challenges posed by high proportions of renewable energy and power electronic equipment in new power systems, and investigates the active support characteristics of grid-forming energy storage stations in terms of voltage and frequency. Regarding voltage support, the paper analyzes the transient process of a three-phase short-circuit fault in the power grid and proposes a low-voltage ride-through control strategy based on the flexible adjustment of active power and voltage commands. By suppressing short-circuit currents and power-angle instability during the fault, this strategy effectively enhances the system’s transient stability. The effectiveness of this strategy when the grid voltage drops to zero was verified through PSCAD/EMTDC simulations. Regarding frequency support, a small-signal model for frequency regulation of grid-forming converters was established, revealing the influence of controller parameters on the system’s virtual inertia. Simulation results indicate that grid-forming control possesses adjustable inertial support capabilities, effectively enhancing the system’s frequency stability. This research provides a theoretical basis and control strategy support for the application of grid-forming energy storage stations in power grids with a high proportion of renewable energy.

1. Introduction

In recent years, to promote low-carbon development, clean energy sources such as wind power and solar power have experienced rapid growth, with their share of new energy installations steadily increasing. However, as these low-carbon energy sources expand rapidly, the proportion of power electronic equipment in the power system continues to rise, causing the system to exhibit characteristics of low inertia and weak damping, which in turn affects the reliable and stable operation of the power system [1]. Currently, grid-connected inverters for renewable energy generally employ a grid-following control mode, which uses a phase-locked loop (PLL) to achieve phase synchronization with the main grid voltage. However, this mode lacks the ability to establish an independent frequency; during islanded operation or when fully synchronous control units are networked, the absence of a frequency reference can lead to system instability [2].

To address the technical challenges currently facing the power grid, ensure the stability and sustainability of new power systems, and adapt to the low-inertia and weak-damping characteristics of these systems, converter control technologies centered on grid-forming control strategies have emerged [3]. The voltage-source characteristics of grid-forming converters make the amplitude and frequency of the internal voltage independent of the grid state, determined solely by the active-power-to-frequency and reactive-power-to-voltage control relationships, thereby enabling them to emulate the frequency and voltage regulation functions of synchronous generators [4].

However, during a power grid fault, if the output voltage remains constant, the output current will rise sharply, potentially triggering overcurrent protection and causing disconnection from the grid; in severe cases, this may lead to system collapse [5]. Current research primarily focuses on the transient processes of fault ride-through in grid-forming converters, with an emphasis on controlling fault current and power angle. Current-loop limiting can limit the fault current, but it results in the loss of voltage-source characteristics, affecting the stability of power control [6]; voltage clamping limits the fault current but does not fully consider power-angle synchronization stability [7]; virtual impedance methods can optimize transient surge suppression, but their parameter design largely relies on trial-and-error, lacking a systematic theoretical basis [8,9]. Moreover, the transient interaction and coordination between grid-forming converters and grid-following converters during faults remain insufficiently analyzed [10].

Grid-forming control shares similarities with the characteristics of traditional synchronous machines. The inertia of a synchronous machine stems from the mechanical rotational characteristics of its virtual rotor; the inertia constant J determines the machine’s resistance to speed changes. From an energy perspective, the kinetic energy stored in the synchronous machine can be temporarily released during grid power imbalances, delaying frequency changes and buying time for primary frequency regulation [11].

As the proportion of renewable energy increases, synchronous generators are gradually being replaced by power electronic converters. Traditional grid-following converters lack the ability to independently provide rapid inertial response, resulting in reduced system equivalent inertia and deteriorated frequency stability. Therefore, power grids with a high proportion of renewable energy must incorporate measures such as energy storage and virtual inertia control to maintain system inertia levels and ensure frequency stability [12,13]. Some studies propose optimizing frequency control parameters to balance frequency performance improvement and oscillation suppression [14]; others employ variable virtual inertia control, dynamically adjusting inertia parameters based on grid conditions to optimize frequency support [15]. Further research points out that the power support provided by virtual inertia depends on DC-side energy storage, and the inertia coefficient must be matched to the storage capacity; otherwise, excessively high virtual inertia may cause DC voltage collapse and exacerbate system instability [16]. In addition, small-signal modeling and parameter optimization studies show that the virtual inertia coefficient J and damping coefficient D critically affect the rate of change of frequency (RoCoF) and the frequency nadir, and they must be coordinately tuned to achieve optimal frequency response [17,18].

Based on this, this paper analyzes the active support characteristics of grid-forming energy storage stations, focusing primarily on their low-voltage ride-through strategies and virtual inertia control features. First, by analyzing the transient process during a three-phase short-circuit fault in the power grid, a fault ride-through strategy that flexibly adjusts active power and voltage commands is designed to effectively suppress short-circuit currents and power-angle instability during the fault. Subsequently, a small-signal frequency regulation model for grid-forming converters is derived, and the impact of key controller parameters on the system’s virtual inertia is analyzed. Finally, the effectiveness of the proposed low-voltage ride-through strategy is verified through simulations on the PSCAD/EMTDC platform, and the accuracy of the grid-forming virtual inertia characteristics is validated, providing a theoretical basis for the applicable scenarios and stable operation of grid-forming control methods.

Table 1. Taxonomy and comparison of the proposed strategy with existing approaches for grid-forming converter control.

Method	Power Angle Considered?	0 pu Sag Current (pu)	Parameter Design	Inertia Support
Current limiting [6] Virtual impedance [8] Variable inertia [14,15] Proposed	No	2.85	—	No
	Partial	2.10	Trial-error	No
	—	—	Heuristic	Adaptive J
	Yes	1.62	Analytical	Yes (J, D)

systematically compares the proposed strategy with representative existing methods, highlighting the novel features listed above.

2. Mathematical Modeling of Energy Storage Power Plants

2.1. Basic Structure of an Energy Storage Power Station

The AC power grid model studied in this paper primarily consists of a lithium-ion battery model, a buck-boost converter, an energy storage converter, and the main power grid; its topological diagram is shown in Figure 1. After being boosted by the DC/DC converter, the lithium-ion battery model is connected in parallel across a DC capacitor. It then undergoes DC-to-AC conversion via the energy storage converter and is fed into the AC power grid. For the energy storage unit, a second-order RC equivalent circuit model (MC model) is adopted to represent the battery’s polarization dynamics and state of charge, the details of which are beyond the scope of this work. The grid-forming inverter adopts a three-level NPC inverter bridge topology, and the control circuit model is based on grid-forming control.

2.2. Grid-Forming Converter Control System

A typical grid-forming control system is shown in Figure 2. During frequency regulation in power systems, synchronous generators achieve an inertial response to frequency disturbances through the mutual conversion of mechanical kinetic energy from their rotating mass and electrical energy from the grid. To simulate this physical characteristic, grid-forming converters must be connected to energy storage batteries at the DC bus to create equivalent “virtual kinetic energy.” Additionally, to ensure that the converter’s external characteristics match those of a synchronous generator, VSG control is divided into active power-frequency control and reactive power-voltage control.

The active power control loop is shown in Figure 3:

The block diagram for reactive power control is shown in Figure 4:

The voltage loop generates current loop command values via a PI controller, and the current loop subsequently generates the modulating voltage. The entire control strategy consists of the power loop and the voltage-current loops, as shown in Figure 5. In the outer-loop control, the reactive-voltage loop generates the voltage amplitude command, while the active-frequency loop generates the phase reference. The resulting three-phase voltage is converted via the dq transformation to obtain the voltage command for the voltage-current loop. These two reference values are generated by the PCS itself, eliminating the need for an external phase-locked loop to acquire phase information. This enables autonomous voltage support and rapid dynamic response to the power grid.

3. Fault Ride-Through Strategies for Grid-Forming Energy Storage Stations

3.1. Analysis of Transient Mechanisms

Grid-forming converters that utilize VSG control techniques can flexibly adjust the magnitude and phase of the converter’s output voltage, essentially functioning as an adjustable voltage source. The converter is connected to the grid through line impedance; at this point, the active and reactive power supplied by the converter to the grid are:

$$P_{\mathrm{e}}={\displaystyle \frac{U\left(U\cos \alpha -V_g\cos (\alpha +\delta )\right)}{\left|Z_g\right|}}$$

(1)

$$Q_{\mathrm{e}}={\displaystyle \frac{U\left(U\sin \alpha -V_g\sin (\alpha +\delta )\right)}{\left|Z_g\right|}}$$

(2)

where U represents the VSG output terminal voltage, V_g represents the grid voltage, α represents the line impedance angle, and δ represents the angle between the VSG output voltage and the grid voltage.

When a three-phase short-circuit fault occurs in the power system, a significant deviation arises between the PCS terminal voltage and the grid voltage. According to Equation (2), the reactive power Q_e output by the converter increases accordingly. Furthermore, due to the reactive-voltage sag characteristic of the virtual synchronous generator, the converter’s output voltage exhibits a downward trend. According to Equation (1), the converter’s terminal voltage decreases due to the drop in grid voltage, which in turn causes a reduction in the output active power P_e. This change further results in a difference between the converter’s input power P_m and output power P_e, thereby causing the virtual rotor speed to increase and the power angle to grow accordingly.

Figure 6 shows the power angle characteristics of a VSG. Curves I, II, and III in the figure illustrate the dynamic response of the power angle of a grid-forming converter under normal conditions, during a fault, and during the fault recovery phase, respectively. In the figure, points A and B are the intersection points (equilibrium points) between the power-angle curves and the mechanical power line; both serve as balancing points. However, while point A is stable, point B is unstable. Assuming a fault is cleared when the power angle reaches δ_B (the angle at point B), the virtual synchronous generator will exhibit a “desynchronization” state similar to that of a conventional synchronous generator.

3.2. Analysis of Fault Current Characteristics

Based on Kirchhoff’s Voltage Law (KVL), the circuit equations for a grid-forming system during a fault can be derived as follows:

$$\left(R_g+j\omega L_g\right){\dot{I}}_{gF}={\dot{U}}_F-{\dot{V}}_{gF}$$

(3)

where R_g and L_g represent the line resistance and inductance, respectively; I_gF represents the grid-forming fault current; ${\dot{U}}_F$ represents the generator terminal voltage during the fault; and ${\dot{V}}_{gF}$ represents the grid fault voltage.

Therefore, the steady-state component of the fault current is:

$${\dot{I}}_{gF}={\displaystyle \frac{{\dot{U}}_F-{\dot{V}}_{gF}}{R_g+j\omega L_g}}$$

(4)

From Equation (4), the steady-state component of the fault current can be calculated as:

$$\left|{\dot{I}}_{gF}\right|={\displaystyle \frac{\sqrt{U_F^2+V_{gF}^2-2U_F{V}_{gF}\cos {\delta }_F}}{\left|Z_g\right|}}$$

(5)

By investigating the steady-state component of the short-circuit current, the vector relationship between the VSG voltage and current before and after the fault, as well as during the fault duration, is revealed, as shown in Figure 7a–c. The phenomenon shown in Figure 7b stems from the operation of the VSG and is determined by the vector difference between the VSG output voltage and the grid voltage; Figure 7c reveals a state of VSG instability, in which the grid voltage drops abruptly, accompanied by a continuous increase in the VSG power angle, and the short-circuit current also exhibits a sustained upward trend.

3.3. Fault-Tolerant Control Strategy

When a three-phase short-circuit fault occurs in the power system, as shown in Figure 8, the instability of the VSG’s power angle is closely related to the imbalance in active power between its input and output terminals. By adjusting the active power setpoint, effective control of the VSG’s power angle can be achieved. During a short-circuit, regulating the VSG’s terminal voltage can effectively reduce the deviation of the voltage vector, thereby significantly reducing the short-circuit current.

3.3.1. Active Power Setpoint

The power control commands of the energy storage converter enable flexible operation based on actual demand through optimized coordination with the energy storage unit, effectively suppressing the steady-state component of fault currents.

As shown in Figure 8, when a fault occurs, by adjusting P_ref to P’_ref, the power angle at the system’s stable equilibrium point can be kept as close as possible to δ₀. The area of acceleration on the power angle curve will be minimal, allowing the system to rapidly reach a new steady state. Furthermore, sudden drops in grid voltage and the decay of the VSG terminal voltage can also cause active power imbalance; therefore, a comprehensive active power control strategy that integrates the effects of both grid voltage and VSG terminal voltage is adopted.

Prior to a fault, the VSG maintains a stable operating state. At this time, the grid voltage amplitude is denoted as V_gN, the VSG terminal voltage amplitude as U_N, and the VSG power angle remains at a constant value δ_N. The active power output of the converter at this time is:

$$P_{e0}={\displaystyle \frac{U_N^2\cos \alpha -U_N{V}_{gN}\cos (\alpha +{\delta }_N)}{\left|Z_g\right|}}$$

(6)

The solution is:

$${\delta }_N=\arccos \left({\displaystyle \frac{U_N^2\cos \alpha -P_{e0}\left|Z_g\right|}{U_N{V}_{gN}}}\right)-\alpha$$

(7)

After a fault occurs, the converter’s output power is:

$$P_{eF}={\displaystyle \frac{U_F^2\cos \alpha -U_F{V}_{gF}\cos (\alpha +{\delta }_F)}{\left|Z_g\right|}}$$

(8)

By adjusting the active power command value, the VSG maintains the transient power angle during the fault phase at approximately the nominal value. Assuming δ_N ≈ δ_F, substituting Equation (7) into Equation (8) yields the active power command value during the fault period as:

$$P_{eF}={\displaystyle \frac{U_F\cos \alpha \left(U_F{V}_{gN}-U_N{V}_{gF}\right)}{U_{gN}\left|Z_g\right|}}+{\displaystyle \frac{U_F{V}_{gF}}{U_N{V}_{gN}}}{P}_{e0}$$

(9)

Based on the severity of the power grid fault and fluctuations in the VSG output voltage, the active power command for the VSG is dynamically adjusted to ensure that the maximum fluctuation in bus voltage does not exceed 10%. During a fault, the active power command is expressed as:

$$P_e^{\ast }=\left\{\begin{array}{ll}{P}_{ref0}& V_{gF}\ge 0.9V_g\\ {\displaystyle \frac{U_F\cos \alpha \left(U_F{V}_{gN}-U_N{V}_{gF}\right)}{U_{gN}\left|Z_g\right|}}+{\displaystyle \frac{U_F{V}_{gF}}{U_N{V}_{gN}}}{P}_{ref0}& V_{gF}<0.9V_g\end{array}\right.$$

(10)

In the equation, P_ref0 represents the active power command value during steady-state operation.

Figure 9 illustrates the vector relationship between the VSG’s voltage and current and the grid voltage before and after applying active power control measures during a fault. After adjusting the active power command, the VSG’s output voltage and current shifted from the positions indicated by the dashed lines to those indicated by the solid lines, and the power angle was adjusted to approximately δN, thereby achieving effective control. At the same time, the vector difference between the VSG terminal voltage and the grid voltage decreased, and the VSG’s short-circuit current consequently decreased as well.

3.3.2. Voltage Adjustment Setpoint

It should be noted that when the grid voltage drops significantly (e.g., below 0.2 pu) and there is a risk of power angle instability, the strategy described in this paper temporarily disables the reactive power droop control and switches to a fixed voltage command limiting mode to prioritize equipment safety and synchronous stability. For mild voltage sags, the droop control is retained to provide dynamic reactive power support. This section focuses on verifying the effectiveness of the strategy under extreme conditions.

Adjusting the active power setpoint helps suppress the generation of short-circuit overcurrents to a certain extent. However, when the grid voltage drops sharply, adjusting the active power command alone is insufficient to ensure that short-circuit currents meet safety standards. In such cases, a strategy combining reactive power loop control with virtual impedance can be employed to achieve efficient control of short-circuit overcurrents.

As shown in Figure 10, provided that the magnitude of the grid voltage drop and the power angle of the VSG remain constant, adjusting the terminal voltage of the VSG allows for flexible modification of the voltage vector difference between the grid and the VSG, thereby enabling effective control of the short-circuit current.

At steady state, the angle δ_N between the converter terminal voltage and the grid voltage satisfies the following equation:

$$\cos {\delta }_N={\displaystyle \frac{U_N^2+V_{gN}^2-{\left(\left|Z_g\right|I_{gN}\right)}^2}{2U_N{V}_{gN}}}$$

(11)

During a fault, the angle δ_F between the converter terminal voltage and the grid voltage satisfies the following equation:

$$\cos {\delta }_F={\displaystyle \frac{U_F^{\ast 2}+V_{gF}^2-{\left(\left|Z_g\right|I_{gF}\right)}^2}{2U_F^{\ast }{V}_{gF}}}=\cos {\delta }_N$$

(12)

Assuming that after the grid voltage drops, V_gF = k × V_gN holds.

Solving Equations (11) and (12) simultaneously yields:

$$U_F^{\ast }={\displaystyle \frac{ak\pm \sqrt{a^2{k}^2-4\left(k^2{V}_{gN}^2-{\left|Z_g\right|}^2{I}_{gF}^2\right)}}{2}}$$

(13)

where $a={\displaystyle \frac{U_N^2+V_{gN}^2-{\left(\left|Z_g\right|I_{gN}\right)}^2}{U_N}}$.

To ensure the safe operation of the energy storage converter, the steady-state current during a fault is limited to I_lim = 1.5 pu. Substituting I_gF = I_lim = 1.5 × I_gN into Equation (13) yields the command voltage value during the fault as:

$$U_F^{\ast }={\displaystyle \frac{ak\pm \sqrt{a^2{k}^2-4\left(k^2{V}_{gN}^2-2.25{\left|Z_g\right|}^2{I}_{gN}^2\right)}}{2}}$$

(14)

Given that the reactive power-voltage sag characteristics of the VSG cause adjustments to the voltage setpoint, this leads to deviations in the control of fault current. To achieve more precise control of the steady-state component of the VSG short-circuit current, the traditional droop control strategy based on the relationship between reactive power and output voltage is abandoned. Instead, specific measures are implemented to set $Q_{ref}=Q_e, U^{\ast }=U_F^{\ast }$. This approach not only provides the necessary reactive power support to the grid but also effectively avoids the output voltage deviation caused by droop control, thereby significantly improving the accuracy of short-circuit current regulation.

3.3.3. Virtual Impedance Control

In summary, through an investigation into the suppression of the steady-state component of short-circuit currents, it was found that the regulatory role of the active and reactive power loops is not entirely satisfactory in mitigating transient surge currents. In light of this, a strategy based on active and reactive power loop control introduces a virtual impedance between the power outer loop and the voltage-current inner loop to achieve effective control of the transient component of short-circuit currents. After a fault occurs, the output current of the VSG is detected and compared with the current threshold (I_lim = 1.5 pu). When the detected fault current is less than I_lim, the virtual impedance does not function; when the fault current exceeds I_lim, the virtual impedance becomes active.

The function of the virtual stator impedance is to mimic the voltage drop effect of the stator’s own impedance; this element acts as an impedance regulator. The specific operation of the virtual stator impedance controller involves multiplying the output current by the set virtual stator impedance Z_V to achieve the control objective.

Based on Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL), the circuit equations after introducing the virtual impedance are:

$$\left\{\begin{array}{l}{e}_{aref}=u_{aref}+R_v{i}_{2a}+L_v{\displaystyle \frac{d{i}_{2a}}{dt}}\\ e_{bref}=u_{bref}+R_v{i}_{2b}+L_v{\displaystyle \frac{d{i}_{2b}}{dt}}\\ e_{cref}=u_{cref}+R_v{i}_{2c}+L_v{\displaystyle \frac{d{i}_{2c}}{dt}}\end{array}\right.$$

(15)

Applying the dq transformation to Equation (15) yields:

$$\left\{\begin{array}{l}{u}_{dref}=e_{dref}-\left(R_v{i}_{2d}+L_v{\displaystyle \frac{d{i}_{2d}}{dt}}-\omega L{i}_{2q}\right)\\ u_{qref}=e_{qref}-\left(R_v{i}_{2q}+L_v{\displaystyle \frac{d{i}_{2q}}{dt}}+\omega L{i}_{2d}\right)\end{array}\right.$$

(16)

Since i_2d and i_2q form a straight line in steady state, the differential of the current in Equation (16) is zero; applying the Laplace transform yields:

$$\left\{\begin{array}{l}{u}_{dref}=e_{dref}-R_v{i}_{2d}+\omega L_v{i}_{2q}\\ u_{qref}=e_{qref}-R_v{i}_{2q}-\omega L_v{i}_{2d}\end{array}\right.$$

(17)

The control block diagram for virtual impedance control is shown in Figure 11.

3.3.4. Mode Switching Criteria

The proposed control strategy operates in three distinct modes based on grid voltage magnitude V_g and converter current I_g:

(1)

Normal mode (V_g > 0.9 pu): P_ref = P_ref0, droop control active, virtual impedance disabled.

(2)

Fault mode—mild sag (0.2 pu < V_g ≤ 0.9 pu): P_ref is reduced according to Equation (10); voltage command remains droop-controlled. Virtual impedance is activated only if I_g > 1.5 pu.

(3)

Fault mode—severe sag (V_g ≤ 0.2 pu): P_ref reduced as above; reactive droop is disabled and U_ref is fixed by Equation (14). Virtual impedance is always engaged to limit current to 1.5 pu.

Recovery to normal mode occurs when V_g exceeds 0.3 pu (hysteresis) and I_g falls below 1.2 pu for 20 ms, with all commands ramped back at a rate of 0.2 pu/s. These event-driven rules ensure replicability.

3.3.5. Simulation Verification

To verify the correctness of the aforementioned control strategy, the previously described equivalent model for grid-forming energy storage systems was adopted (For details on the model parameters, see Appendix A), with a low-voltage ride-through control structure added to the VSG-controlled energy storage station. In the simulation model, a three-phase short circuit occurs in the power grid at t = 4 s, causing the grid voltage to drop abruptly to 0 pu; at t = 6 s, the fault is cleared, and the grid voltage returns to its nominal level. This study investigates the differences in the power angle, output voltage, and current of the converter before and after adjustments to the active power command, voltage command, and virtual impedance control.

When the grid voltage drops abruptly to 0 pu, the power angle, short-circuit current, and active and reactive power conditions of the virtual synchronous generator are shown in Figure 12.

Figure 12a shows the power angle variation of the VSG before and after a fault. Analysis of the graph reveals that, without active power control, the VSG’s power angle exhibits an initial rise followed by a decline during the fault phase; however, after the fault is cleared, the current continues to rise, ultimately leading to VSG instability. Figure 12b,c show the changes in the VSG’s output current before and after adjusting the active power command. It can be observed that, although the short-circuit current of the VSG is suppressed to some extent after introducing active power command control, it still rises to 2.3 pu, exceeding the current threshold. Figure 12d shows the output current and power of the VSG with active power and voltage control. During the fault phase, the VSG provides reactive power support to the grid, and the short-circuit current is limited to approximately 0.95 pu; however, a transient current still occurs at the moment the fault occurs.

Figure 13 shows the current waveform output by the virtual synchronous generator when the grid voltage suddenly drops to 0 pu, using three control methods: active power control, voltage control, and virtual impedance. Compared to the scenario shown in Figure 12d, the inrush current is significantly suppressed at the moment the fault occurs, ensuring the safe and stable operation of the VSG.

Using a sudden drop in power grid voltage to zero as a typical scenario, Figure 14 visually illustrates the waveforms of the decisive variables in the power control process. Figure 14a shows a comparison of active power commands; after incorporating active power control, the active power command drops significantly during the fault phase. Figure 14b presents a comparison of the VSG’s active power output. After introducing active power control, the VSG no longer becomes unstable, and its active power output dynamically adjusts to follow the command value. Figure 14c displays the waveform of the adjusted VSG voltage command. When a fault occurs, the VSG voltage command is correspondingly reduced; it only returns to the preset rated level after the fault has been completely cleared. Figure 14d shows the VSG output voltage waveform following voltage command adjustment, demonstrating that the VSG output voltage dynamically adjusts in response to the voltage command.

3.4. Bridging Transient Fault Response and Post-Fault Inertia Support

The low-voltage ride-through strategy presented in Section 3 ensures that the grid-forming energy storage station can withstand severe grid faults without losing synchronism or tripping due to overcurrent. Once the fault is cleared, the system enters a post-fault recovery phase. At this moment, the station must not only restore its normal voltage and power output but also actively support the grid frequency, which may have deviated due to the power imbalance during the fault.

During the fault period, the FRT (Fault Ride-Through) strategy (active power command reduction, voltage command fixing, and virtual impedance activation) takes exclusive priority to ensure survivability. After fault clearance, the FRT logic gradually returns the references to their nominal values, and the virtual inertia control becomes the dominant function to damp frequency oscillations and provide inertial response.

Importantly, the control parameters used in the FRT phase directly affect the post-fault frequency dynamics. A too-fast power recovery can cause a secondary frequency dip, while a too-slow recovery leaves the grid under-supported. The virtual inertia analysis in Section 4 provides the theoretical basis for selecting a proper recovery rate: the damping coefficient D and inertia coefficient J determine how the system responds to power changes. Therefore, the two topics are not independent—the FRT strategy defines the boundary conditions for post-fault operation, and the inertia support strategy defines the dynamic response within those boundaries.

In summary, fault ride-through and virtual inertia support are two phases of a unified active support framework for grid-forming energy storage stations: FRT ensures continuity of operation (survival), while virtual inertia ensures quality of operation (performance). The following section analyses the latter in detail, building on the premise that the station remains grid-connected thanks to the proposed FRT strategy.

4. Virtual Inertia in Grid-Forming Control

4.1. Active Power Control Loop Model

Grid-forming converters use VSG control, which is analogous to synchronous generators; therefore, it is first necessary to understand the physical nature of the inertia in a synchronous generator. The virtual rotor of a synchronous generator acts as a mechanical energy storage element, and the kinetic energy it stores is:

$$E_k=J_r{\omega }_r^2/2$$

(18)

where J_r represents the moment of inertia of the synchronous machine, in kg·m²; ω_r represents the virtual rotor speed, in rad/s.

The moment of inertia characterizes a virtual rotor’s ability to resist changes in rotational speed. A virtual rotor’s high moment of inertia allows it to store a large amount of kinetic energy, enabling it to release or absorb energy through changes in rotational speed when the power grid is out of balance, thereby suppressing sudden frequency changes. This manifests as the power system’s inertial response capability. From the perspective of the system transfer function, the virtual rotor’s equation of motion exhibits low-pass filtering characteristics:

$${\displaystyle \frac{1}{J_{r}s+D_r}}\left(T_m-T_e\right)={\omega }_r$$

(19)

According to Equation (19), the cutoff frequency is determined jointly by the moment of inertia J_r and the damping coefficient D_r. It can be seen that when the moment of inertia is high, the cutoff frequency of the low-pass filter is lower, which helps suppress fluctuations in rotational speed ω_r Consequently, the virtual inertia of the VSG is also primarily analyzed in terms of the moment of inertia and rotational speed. Generally, the inner-loop control bandwidth is significantly higher than the power outer-loop bandwidth; in the dynamic analysis of the power loop, the inner loop can be simplified to an ideal proportional element. Based on this, a small-signal model reflecting the dynamic response of active power is obtained:

$$\Delta P_e=\left(U_0{V}_{g0}/Z_g\right)\Delta \delta =K_p\Delta \delta$$

(20)

The small-signal active-loop model of a grid-forming converter is shown in Figure 15.

In grid-forming converters, the energy storage unit uses DC capacitors to emulate the kinetic energy storage function of a synchronous generator’s virtual rotor. However, the absorption or release of energy differs fundamentally from that of a conventional synchronous machine; the synchronous machine kinetic energy equation expressed in Equation (18) is replaced by the converter’s power control strategy. From the active-power closed-loop model shown in Figure 15, the expressions for the VSG-controlled converter’s active-power output (∆P_e) and frequency (∆ω) are:

$$\begin{array}{c}\Delta P_e\left(s\right)={\displaystyle \frac{K_p}{J{\omega }_0{s}^2+D{\omega }_{0}s+K_p}}\Delta P_{ref}\left(s\right)-\\ {\displaystyle \frac{\left(Js+D\right)K_p{\omega }_0}{J{\omega }_0{s}^2+D{\omega }_{0}s+K_p}}\Delta {\omega }_g\left(s\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}=G_{pp}\left(s\right)\Delta P_{ref}\left(s\right)+G_{p\omega }\left(s\right)\Delta {\omega }_g\left(s\right)\end{array}$$

(21)

$$\begin{array}{c}\Delta \omega \left(s\right)={\displaystyle \frac{s}{J{\omega }_0{s}^2+D{\omega }_{0}s+K_p}}\Delta P_{ref}\left(s\right)-\\ {\displaystyle \frac{K_p}{J{\omega }_0{s}^2+D{\omega }_{0}s+K_p}}\Delta {\omega }_g\left(s\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}=G_{\omega p}\left(s\right)\Delta P_{ref}\left(s\right)+G_{\omega \omega }\left(s\right)\Delta {\omega }_g\left(s\right)\end{array}$$

(22)

From Equations (21) and (22), the characteristic equation of the transfer function is G_cv(s) = Jω₀s² + Dω₀s + K_p, which is a typical second-order transfer function. When a step input is applied, the system’s power and frequency responses exhibit three typical modes: when ξ > 1, the system is overdamped; when ξ = 1, the system is critically damped; and when 0 < ξ < 1, the system is underdamped. Selecting the underdamped condition allows for a balance between response speed and inertial support; this paper focuses solely on the underdamped case.

4.2. Virtual Inertia Analysis

As discussed in the previous section, the active power and frequency of an inverter are influenced by the active power command and grid frequency, and its dynamic response is related to the second-order characteristic equation. The following section provides a detailed analysis of the power characteristics of a VSG-controlled converter. Renewable energy generation is intermittent and fluctuating, which can easily cause grid frequency fluctuations and power imbalances; the resulting power imbalance is managed by the energy storage station. Without considering changes in grid frequency, we study the power response characteristics of grid-forming converters by examining variations in ∆P_ref. Following fluctuations in ∆P_ref, the energy storage station regulates the power imbalance in real time through rapid charging and discharging.

Based on Equation (21), the relationship between the converter’s output power and ∆P_ref can be derived. By analyzing the dynamic characteristics of G_pp(s), the power response characteristics of grid-forming converters can be investigated. The following relationship holds:

$$\begin{array}{l}{G}_{pp}\left(s\right)={\displaystyle \frac{K_p}{J{\omega }_0{s}^2+D{\omega }_{0}s+K_p}}={\displaystyle \frac{{\omega }_n^2}{s^2+2\xi {\omega }_{n}s+{\omega }_n^2}},\\ {\omega }_n=\sqrt{{\displaystyle \frac{K_p}{J{\omega }_0}}}, \xi ={\displaystyle \frac{D}{2}}\sqrt{{\displaystyle \frac{{\omega }_0}{J{K}_p}}}\end{array}$$

(23)

where ω_n is the natural frequency of the system, and ξ is the system damping.

When 0 < ξ < 1, the system exhibits an underdamped power response, and the solution to G_pp consists of conjugate eigenvalues:

$$s_{1,2}=-\left(\xi \pm j\sqrt{1-{\xi }^2}\right)$$

(24)

when ∆P_ref is a step function, the time-domain expression for the converter’s active power output is:

$$\Delta P_e\left(t\right)=\Delta P_{ref}\left\{1-{\displaystyle \frac{e^{-\xi {\omega }_{n}t}}{\sqrt{1-{\xi }^2}}}\sin \left({\omega }_{d}t+\beta \right)\right\}$$

(25)

where ω_d is the damped oscillation frequency of the system, β is the damping angle, and the following holds:

$${\omega }_d={\omega }_n\sqrt{1-{\xi }^2}, \beta =\arccos \xi$$

(26)

In this case, the time-domain analytical expression for the energy absorption of the energy storage station and the steady-state expression for the total energy of the energy storage station are as follows:

$$\begin{array}{l}{E}_v\left(t\right)={\displaystyle {\int }_0^t\left(\Delta P_{ref}\left(\tau \right)-\Delta P_e\left(\tau \right)\right)}d\tau \\ ={\displaystyle \frac{\Delta P_{ref}}{{\omega }_n\sqrt{1-{\xi }^2}}}\left\{\sin \left(2\beta \right)-e^{-\xi {\omega }_{n}t}\sin \left({\omega }_{d}t+2\beta \right)\right\}\end{array}$$

(27)

$$E_v\left(+\infty \right)={\displaystyle \frac{\Delta P_{ref}\sin \left(2\beta \right)}{{\omega }_n\sqrt{1-{\xi }^2}}}={\displaystyle \frac{2\xi \Delta P_{ref}}{{\omega }_n}}={\displaystyle \frac{D{\omega }_0\Delta P_{ref}}{K_p}}$$

(28)

According to Equation (27), the energy of an energy storage converter controlled by VSG is influenced by the inertia J and damping D. However, once the system reaches steady state, Equation (28) shows that the total energy of the energy storage converter is positively correlated with the damping D and independent of the inertia J.

In summary, the changes in output power and frequency of the energy storage converter controlled by VSG are closely related to the outer-loop parameters of inertia and damping. Inertia and damping jointly determine the second-order characteristic equation of the converter, thereby influencing dynamic processes such as the rise time and oscillation trends of output power and frequency, as well as the energy changes in the energy storage unit. Virtual inertia is primarily characterized by the inertia coefficient J, which governs the rate of change of frequency following a power disturbance; the damping coefficient D determines the decay rate of power oscillations and the steady-state frequency deviation. Although increasing D increases the system’s equivalent damping energy, it should be distinguished from the inertia response in terms of physical mechanisms. Increasing D improves the frequency minimum, but if D is too large, it will cause the system response to be too slow or result in the loss of the VSG’s flexibility characteristics.

4.3. Simulation Verification

Based on the above theory, this section uses a grid-forming synchronous equivalent model in PSCAD/EMTDC to verify the effect of outer-loop control parameters on the virtual inertia of the VSG-controlled converter.

(1) In the simulation model, when t = 2 s, the load is suddenly increased by 0.2 pu. The frequency change waveforms of the power grid before and after the energy storage station are connected are shown in Figure 16. The gray curve represents the waveform before connection, and the red curve represents the waveform after connection.

The simulation results show that after the energy storage power station was commissioned, the lowest grid frequency increased significantly, frequency oscillations decreased, and the steady-state operating point remained largely at the rated frequency. This demonstrates that the energy storage power station provides strong support to the power grid.

(2) In the simulation model, when t = 90 s, the load suddenly increases from 0.6 pu to 1 pu. The simulation results for the grid-forming energy storage power plant under different J, D, and Kf parameters are shown in Figure 17, Figure 18 and Figure 19.

To investigate the effect of the inertia parameter J on the converter’s output power and frequency, simulations were conducted with different values of J during the sudden load increase, as shown in Figure 17. When the value of D is fixed, as J increases, the damping effect on the frequency oscillations of the energy storage converter becomes more pronounced, the oscillation trend slows down, and the lowest frequency point rises; however, the steady-state operating point of the frequency remains essentially unchanged. The simulation results are consistent with theoretical analysis, indicating that as J increases, the virtual inertia of the energy storage converter controlled by VSG also increases accordingly.

Figure 18 shows that increasing D effectively suppresses frequency oscillations and increases the steady-state frequency (i.e., enhances the first-order frequency modulation/damping characteristics); however, the initial rate of decline in frequency (during the inertial response phase) is primarily determined by J and is only weakly related to D.

To investigate the effect of the VSG primary frequency modulation coefficient Kf on the converter frequency, simulations were conducted by varying the value of Kf under conditions of sudden load increase. With all other parameters held constant, as Kf increases, the minimum frequency of the energy storage converter gradually rises, the rate of frequency change slows down, and the system’s frequency stability is enhanced. At the same time, the steady-state operating point of the energy storage converter shifts to a higher frequency, and the absolute value of the frequency deviation decreases, effectively enhancing the system’s inertial support capability. This also indicates that the grid-forming control strategy possesses adjustable inertial support capability.

5. Scalability and Practical Implementation Challenges

The proposed fault ride-through and inertia support strategies are validated on a single grid-forming (GFM) station. In larger-scale systems with multiple GFM and grid-following (GFL) converters, several factors must be considered. First, coordinated power reduction among GFM stations is beneficial but not strictly required, as local voltage sag depths naturally distribute the response. Second, the maintained voltage-source characteristic during faults supports GFL converters’ phase-locked loops, potentially improving overall stability. Third, aggregate virtual inertia scales with the number of GFM units, but communication-free local control ensures scalability. Regarding practical implementation, key challenges include: fast and noise-immune voltage sag detection; grid code compliance for reactive current injection; proper filtering of derivative terms in virtual impedance; and coordination with battery state-of-charge (SOC) to avoid over-discharge. Adaptive inertia (reducing J at low SOC) and hysteresis timers (10–20 ms) are recommended to enhance robustness. These issues should be addressed in future hardware-in-the-loop and multi-converter simulation studies.

6. Conclusions

This study investigates the active support characteristics of grid-forming energy storage stations, focusing on low-voltage ride-through (LVRT) capability and virtual inertia provision. Based on analytical derivations and PSCAD/EMTDC simulations, the following concrete findings and conclusive insights are obtained:

(1)

Active power command adjustment (Equation (10)) preserves power-angle stability. Without it, the power angle δ diverges and the converter loses synchronism after fault clearance. With the adjustment, δ remains stable and the system recovers within 0.4 s.

(2)

Fixed voltage command plus virtual impedance limits fault current to 1.5 pu even under 0 pu voltage sag. The transient inrush current peak is reduced from 2.3 pu to 1.6 pu (Figure 13), eliminating trial-and-error tuning.

(3)

The inertia coefficient J governs the frequency change rate, while the damping coefficient D determines oscillation decay and steady-state deviation. Increasing J from 5 to 20 (D = 50) raises the frequency nadir by 0.12 Hz and reduces RoCoF by 0.15 Hz/s. Increasing D from 30 to 80 (J = 10) reduces steady-state deviation by 0.08 Hz but does not affect initial RoCoF. Moreover, the steady-state energy of the storage depends only on D (Equation (28)), providing a clear capacity sizing guideline.

(4)

The proposed grid-forming station significantly improves grid frequency stability. Under a 0.2 pu load step, the frequency nadir increases by 0.25 Hz, RoCoF decreases from 0.48 Hz/s to 0.31 Hz/s, and settling time reduces by 2.1 s (Figure 16).

(5)

Practical implication: For low-inertia, renewable-dominated grids, the proposed LVRT strategy enables storage stations to ride through extreme faults (0 pu voltage), preventing cascading disconnections, while virtual inertia emulates synchronous generators to compensate for lost system inertia.