Grid-Forming Converters for Renewable Generation: A Comprehensive Review

Abstract

Grid-forming converters (GFMCs) play an increasingly vital role in integrating renewable energy sources into modern power systems. This article reviews GFMCs, emphasizing their importance in enabling reliable, stable, and resilient operation as power systems evolve toward low-inertia, inverter-dominated configurations. Various GFMC topologies are examined based on their suitability for grid-forming functions and performance across different voltage levels. Small-signal modeling approaches are presented to provide deeper insights into system dynamics and converter–grid interactions. The article reviews primary control strategies, including droop control, virtual synchronous machines, and virtual oscillator control, and discusses their impact on synchronization, stability, and power sharing. Finally, the article outlines GFMC applications and challenges, highlighting their impact on system stability.

1. Introduction

The transition from conventional energy sources to renewable options such as wind and solar plays a vital role in shaping the future of power systems. This shift is motivated by growing environmental concerns and the decreasing costs associated with renewable technologies [1,2]. However, the variable and unpredictable nature of these energy sources introduces significant challenges to maintaining grid stability and operational reliability [3]. Addressing these challenges requires advanced integration strategies involving improvements in power electronics, control techniques, grid infrastructure, and supporting regulatory frameworks.

Conventional power systems were originally structured around centralized generation, primarily based on fossil fuels and synchronous generators (SGs), which naturally contributed to system stability through inertia and voltage control [4]. In contrast, modern power systems are moving towards decentralized and converter-dominated architectures. Grid-connected power electronic converters are now central to this transformation, enabling efficient integration of distributed renewable sources and providing essential grid services such as frequency regulation, voltage support, and reactive power compensation [5]. With advanced control algorithms and communication capabilities, these converters enhance system flexibility and stability even under fluctuating renewable outputs. This evolution signifies the emergence of more-electronic power systems. Figure 1 illustrates this ongoing shift from conventional grids to converter-based systems.

In terms of their operational behavior within the grid, power converters can be categorized into two main types: grid-following converters (GFLCs) and grid-forming converters (GFMCs). GFLCs operate as controlled current sources and are commonly used for integrating renewable energy sources (RESs) into the grid [6]. They support functionalities such as direct current regulation, overcurrent protection, maximum power point tracking (MPPT), and unity power factor operation [7]. However, GFLCs rely on phase-locked loops (PLLs) to synchronize with the grid voltage, making them unsuitable for standalone (islanded) operation [6,7]. Furthermore, their performance deteriorates under weak grid conditions, leading to stability issues and limiting their effectiveness in managing renewable variability.

To overcome the operational constraints associated with GFLCs, GFMCs have been developed as an alternative approach for interfacing renewable energy sources with the power grid [8]. These converters function as voltage-controlled devices that can generate and regulate grid voltage and frequency without relying on an external reference. This capability allows them to operate in islanded modes and support autonomous microgrid operation. By directly controlling voltage and frequency, GFMCs are able to manage the variability and intermittency of renewable energy inputs more effectively, making them suitable for both isolated and interconnected systems [9]. Additionally, they can emulate inertia and provide frequency damping through control algorithms, which improves system response during transients and contributes to frequency stability.

The structural configurations of GFLCs and GFMCs, depicted in Figure 2, demonstrate their common underlying topology: both employ a power electronic converter connected to the grid via an LCL filter. This filter consists of a converter-side inductor (L_gi), a filter capacitor (C_gf), and a grid-side inductor (L_gg). The grid is represented as a voltage source (v_sabc) in series with an equivalent inductor (L_s). Key operational parameters include converter-side currents (i_giabc), capacitor voltages (v_gfabc), point of common coupling (PCC) voltages (v_gabc), grid-injected currents (i_ggabc), and dc-link voltage (v_gdc). Despite these structural similarities, GFLCs and GFMCs exhibit significant differences in operational behavior, control methodologies, and functional capabilities.

Figure 3 compares the control architectures of GFLCs and GFMCs. GFLCs synchronize with the grid voltage and generate current references based on active and reactive power commands. However, their contribution to voltage and frequency regulation is minimal, as they operate primarily as current sources dependent on grid conditions [6]. In contrast, GFMCs operate without PLLs, directly regulating the capacitor voltage through real-time measurements. They employ grid-supporting control modules that utilize local voltage and current measurements, ensuring robust performance across diverse operating conditions, including weak grids and islanded systems [6].

Table 1. Comparison of key features of GFLCs and GFMCs.

Features	GFLCs	GFMCs
Maturity	Established and widely deployed	Emerging technology with implementation challenges
Operating Modes	Grid-connected only	Grid-connected and islanded operation
Inertia/Damping	No inherent inertia	Provides virtual inertia and damping
Voltage/Frequency Control	Limited capability	Stable voltage/frequency regulation
Synchronization	Requires PLLs; weak-grid issues	PLL-free synchronization
Applications	Best for stable, large grids	Suitable for weak grids and microgrids
Cost	Lower due to simple design	Higher due to advanced features
Maintenance	Low, proven technology	Higher due to complexity

compares GFLCs and GFMCs in terms of development, operation, control, cost, and maintenance.

GFMCs employ various power electronic topologies selected according to voltage level and performance requirements. Two-level converters are suitable for low-voltage applications due to their simplicity and efficiency, while neutral point-clamped (NPC) converters enhance voltage balancing in medium-voltage systems. Flying capacitor converters (FCCs) enable flexible control via active capacitor voltage management. For medium- to high-voltage applications, cascaded H-bridge (CHB) and modular multilevel converters (MMC) offer high scalability and voltage capability. Parallel multilevel configurations further extend current capacity in large-scale systems.

The accurate modeling of GFMCs is essential for realizing their full potential across these diverse topologies. Small-signal modeling approaches, which rely on linearization around a steady-state operating point, enable detailed analysis of dynamic behavior and stability using state-space or impedance-based formulations. Such modeling techniques are fundamental to the development and validation of robust control strategies under nominal system conditions.

GFMC control architectures are typically organized hierarchically to satisfy multiple operational objectives. The innermost control layer handles voltage regulation and current limitation, often implemented through voltage or current control loops. The intermediate layer governs the exchange of active and reactive power, employing strategies such as droop control, virtual synchronous machines (VSMs), and virtual oscillator control (VOC). The outermost layer facilitates system-level coordination, including power-sharing among distributed converters and integration with centralized functions like automatic generation control. This layered control framework enables GFMCs to deliver essential grid support functionalities. Moreover, recent developments in nonlinear control—such as adaptive control—introduce real-time parameter adjustment capabilities, further enhancing system adaptability under varying grid conditions.

The main contributions of this article are as follows:

(a)

A comprehensive review of GFMC topologies is presented.

(b)

Small-signal modeling techniques for GFMCs are examined to support system analysis and control design.

(c)

Existing and emerging control strategies for GFMCs are reviewed.

(d)

Typical applications of GFMCs in sustainable energy systems are identified and discussed.

(e)

Application-related challenges for GFMCs are analyzed for their impact on stability, operation, and protection.

The paper is organized as follows: Section 2 presents an overview of GFMC topologies. Section 3 discusses small-signal modeling approaches for GFMCs. Section 4 reviews the control strategies employed. Section 5 explores applications of GFMCs in more-electronic power systems. Section 6 examines the challenges associated with GFMCs. Finally, Section 7 concludes the paper.

2. Topological Configurations of Grid-Forming Converters

This section presents the key topological configurations of GFMCs, including two-level converters, NPC converters, FCC, CHB converters, and MMC. The structural features of each topology are described, along with their respective impacts on system performance.

2.1. Two-Level Converter

The two-level voltage source converter is a fundamental topology in power electronics and plays a crucial role in grid-forming applications. It can be implemented in single-phase or three-phase configurations, utilizing semiconductor switches such as insulated gate bipolar transistors (IGBTs) or metal-oxide semiconductor field effect transistors (MOSFETs) [12,13]. As illustrated in Figure 4, the converter consists of a straightforward full-bridge circuit that directly connects the dc bus to the ac grid, making it a cost-effective and structurally simple solution commonly employed in low-voltage systems.

The output voltage of the two-level converter exhibits a square-wave characteristic, with abrupt transitions between voltage levels. This switching behavior introduces significant harmonic distortion into the system, which can negatively impact power quality [12]. Compared to multilevel converter topologies known for their ability to synthesize stepped waveforms with reduced harmonic content, the two-level converter requires additional filtering components and advanced control algorithms to meet grid codes and ensure compatibility [12,14].

In a grid-forming operation, converters must tolerate overcurrent conditions, typically up to three times their rated current. To scale up capacity, paralleling multiple converters is a common practice. Additionally, the integration of silicon carbide (SiC) switches in two-level converters enhances switching frequency capabilities and improves current handling, thereby increasing their suitability for grid-forming applications.

2.2. Neutral Point-Clamped Converter

The NPC topology is commonly employed in GFMC applications due to its ability to handle higher voltage levels and provide improved power quality, which is essential for integrating renewable energy sources into modern power grids [15]. As shown in Figure 5, the NPC converter utilizes four switches per phase leg along with clamping diodes connected to the midpoint of the dc link capacitors. This configuration enables the generation of three voltage levels—positive, zero, and negative—leading to a notable reduction in total harmonic distortion and enhancing power quality.

In grid-forming applications, the multilevel output capability of the NPC converter offers clear advantages over simpler two-level topologies by reducing harmonic distortion in the ac output. This reduction improves power quality and reduces stress on grid components [11].

In addition to renewable energy integration, NPC converters are also applied in other high-power applications such as high-voltage direct current (HVDC) transmission systems and electric vehicle charging stations.

2.3. Flying Capacitor Converter

FCCs provide an effective solution for GFMCs, particularly in medium- and high-voltage grid-connected applications. By using flying capacitors to produce multiple voltage levels, FCCs improve efficiency and enhance power quality. Compared to conventional two-level converters, FCCs offer greater flexibility in precisely adjusting output voltage levels to meet grid demands [16,17].

A three-level FCC can generate positive, neutral, and negative dc voltage outputs, as shown in Figure 6, making it well-suited for accurate voltage waveform synthesis in grid-forming operations. However, practical implementation of FCCs in grid-forming roles remains limited, requiring further research and development to fully realize their capabilities.

FCCs face challenges such as voltage ripple and the need to maintain voltage balance across capacitors [18]. Proper pre-charging of flying capacitors during startup is crucial to prevent high inrush currents, usually managed with resistive voltage dividers or additional resistors [19]. Continuous monitoring and dynamic adjustment of switching states are necessary to preserve voltage balance and correct switching imbalances, ensuring stable and reliable operation.

2.4. Cascaded H-Bridge Converter

The CHB converter is a prominent topology for GFMCs due to its modular design and ability to handle high voltage levels without the need for transformers [20]. As illustrated in Figure 7, the CHB converter consists of series-connected H-bridge units that produce multiple voltage levels, making it well-suited for medium- and high-voltage grid-forming applications [21].

In grid-forming scenarios, CHB converters play a vital role in integrating renewable energy sources and energy storage systems. They efficiently convert variable dc outputs into stable ac power, facilitating smooth grid integration and supporting stability in regions with high renewable penetration [22]. Additionally, CHB converters are essential in medium- and high-voltage battery storage systems, functioning as GFMCs that manage power supply fluctuations. They can also operate as grid-forming static synchronous compensators (STATCOMs), providing reactive power support and maintaining grid voltage stability [22].

2.5. Modular Multilevel Converter

The MMC topology exhibits considerable adaptability, rendering it an effective solution for medium- and high-voltage grid-forming converter applications [23]. MMCs consist of multiple submodules, each implemented as an H-bridge or half-bridge with integrated dc storage capacitors, allowing precise regulation of the ac output voltage. Typically configured in three-phase arrangements, MMCs dynamically modulate voltage levels, a capability essential for integrating renewable energy sources and maintaining overall system stability.

A key characteristic of MMCs is their ability to interface directly with both dc and ac networks, which broadens their applicability across various power system scenarios [24]. This dual interfacing facilitates accurate control over voltage magnitude and phase angle, thereby contributing to the stabilization of grid voltage and frequency.

Additionally, MMC architectures can include parallel-connected submodules, as shown in Figure 8, improving operational efficiency by enhancing current sharing and thermal management among submodules [25]. This approach extends component lifespan and increases fault tolerance by enabling continued operation even in the presence of submodule faults.

3. Small-Signal Modeling of Grid-Forming Converters

This section presents the small-signal modeling of GFMCs in more-electronic power systems, emphasizing their role as ac voltage sources with enhanced power quality for renewable integration. Small-signal modeling includes impedance modeling for single-input-single-output systems and state-space modeling for multiple-input-multiple-output systems, focusing on linear analysis to understand state variable dynamics. Figure 9 shows the modeling flow into state-space and impedance analyses for stability and performance evaluation.

3.1. State-Space Modeling

3.1.1. System Plant Model

Figure 10 illustrates the system plant of the GFMC in block diagram form, where the subscripts d and q correspond to the direct and quadrature axis components, respectively. Here, ω₀ represents the system’s fundamental angular frequency, δ captures small-signal variations, and s denotes the Laplace domain’s complex frequency variable. The plant model in Figure 10 is constructed through the application of Kirchhoff’s current and voltage laws, ensuring its validity for all grid-tied converter (GTC) configurations. By analyzing the summing junctions in Figure 10, mathematical relationships between steady-state parameters (represented by uppercase symbols) can be established.

$$\left[\begin{array}{c}{V}_{\mathrm{gfd}}\\ V_{\mathrm{gfq}}\end{array}\right]=\left[\begin{array}{c}{V}_{\mathrm{sd}}-{\omega }_0(L_{\mathrm{gg}}+L_{\mathrm{s}})I_{\mathrm{ggq}}\\ V_{\mathrm{sq}}+{\omega }_0(L_{\mathrm{gg}}+L_{\mathrm{s}})I_{\mathrm{ggd}}\end{array}\right]$$

(1)

$$\left[\begin{array}{c}{V}_{\mathrm{gd}}\\ V_{\mathrm{gq}}\end{array}\right]=\left[\begin{array}{c}{\displaystyle \frac{V_{\mathrm{sd}}{L}_{\mathrm{gg}}+V_{\mathrm{gfd}}{L}_{\mathrm{s}}}{L_{\mathrm{gg}}+L_{\mathrm{s}}}}\\ {\displaystyle \frac{V_{\mathrm{sq}}{L}_{\mathrm{gg}}+V_{\mathrm{gfq}}{L}_{\mathrm{s}}}{L_{\mathrm{gg}}+L_{\mathrm{s}}}}\end{array}\right]$$

(2)

$$\left[\begin{array}{c}{I}_{\mathrm{gid}}\\ I_{\mathrm{giq}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{ggd}}-{\omega }_0{C}_{\mathrm{gf}}{V}_{\mathrm{gfq}}\\ I_{\mathrm{ggq}}+{\omega }_0{C}_{\mathrm{gf}}{V}_{\mathrm{gfd}}\end{array}\right]$$

(3)

$$\left[\begin{array}{c}{V}_{\mathrm{gid}}\\ V_{\mathrm{giq}}\end{array}\right]=\left[\begin{array}{c}{V}_{\mathrm{gfd}}-{\omega }_0{L}_{\mathrm{gi}}{I}_{\mathrm{giq}}\\ V_{\mathrm{gfq}}+{\omega }_0{L}_{\mathrm{gi}}{I}_{\mathrm{gid}}\end{array}\right]$$

(4)

In the model, V_gd and V_gq refer to the direct and quadrature voltages at the point of common coupling. Additionally, the state-space model of the plants is constructed as follows:

$${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\Delta x_{plant}=A_{plant}\Delta x_{plant}+B_{plant}\Delta u_{plant}$$

(5)

$$\Delta y_{plant}=I\Delta x_{plant}$$

(6)

The expressions of Δx_plant, Δu_plant, Δy_plant, A_plant, and B_plant can be found in [10].

3.1.2. Active and Reactive Power Measurement Model

Accurate control of active and reactive power relies on precise measurement processes, as depicted in Figure 11. Within this mathematical framework, T_p and T_q denote the time constants of low-pass filters applied to the measurement of active and reactive power, respectively. Active and reactive power values are typically derived indirectly through control variables (represented by the subscript c), while dc voltage is measured directly and does not utilize this subscript notation [26,27].

We represent the power measurement component as

$${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\Delta x_{pq}=A_{pq}\Delta x_{pq}+B_{pq}\Delta u_{pq}$$

(7)

$$\Delta y_{pq}=I\Delta x_{pq}$$

(8)

The expressions of Δx_pq, Δu_pq, Δy_pq, A_pq, and B_pq can be found in [10].

3.1.3. AC Current Control Model

Converter currents are managed using single-loop feedback control in ac current regulation systems. The control architecture, shown in Figure 12, integrates a supplementary feedback gain K_id within the current controller design to improve dynamic adaptability [28]. The system model also incorporates time delay compensation, where T_s corresponds to the sampling interval, and the delay term G_d(s) is modeled via a first-order Padé approximation of e^{−1.5×Ts×s} [29].

By analyzing the structure in Figure 12, the converter-current controller’s dynamics can be expressed in state-space form as follows:

$${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\Delta x_{converter\_i}=A_{converter\_i}\Delta x_{converter\_i}+B_{converter\_i}\Delta u_{converter\_i}$$

(9)

$$\Delta y_{converter\_i}=C_{converter\_i}\Delta x_{converter\_i}+D_{converter\_i}\Delta u_{converter\_i}$$

(10)

The expressions of Δx_{converter_i}, Δu_{converter_i}, Δy_{converter_i}, A_{converter_i}, B_{converter_i}, C_{converter_i}, and D_{converter_i} are detailed in [10].

3.1.4. AC Voltage Control Model

GFMCs are equipped with ac voltage controllers, as depicted in Figure 13. In this model, K_vp and K_vi denote the proportional and integral gains of the ac voltage controllers. The ac voltage controller is modeled as follows:

$${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\Delta x_{ac\_v}=B_{ac\_v}\Delta u_{ac\_v}$$

(11)

$$\Delta y_{ac\_v}=C_{ac\_v}\Delta x_{ac\_v}+D_{ac\_v}\Delta u_{ac\_v}$$

(12)

The expressions of Δx_{ac_v}, Δu_{ac_v}, Δy_{ac_v}, B_{ac_v}, C_{ac_v}, and D_{ac_v} are detailed in [10].

3.1.5. Overall State-Space Model

Now that the individual units have been modeled, we can proceed to derive the overall system model. To facilitate understanding, Figure 14 presents the complete system model of the GFMC, incorporating the previously derived units and highlighting the key input and output signals.

The final state-space model for the GFMC is derived as follows:

$${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\Delta x_{GFMC}=A_{GFMC}\Delta x_{GFMC}+B_{GFMC}\Delta u_{GFMC}$$

(13)

$$\Delta y_{GFMC}=C_{GFMC}\Delta x_{GFMC}+D_{GFMC}\Delta u_{GFMC}$$

(14)

The expressions of Δx_GFMC, Δu_GFMC, Δy_GFMC, A_GFMC, B_GFMC, C_GFMC, and D_GFMC are detailed in [10].

3.2. Impedance Modeling

3.2.1. Voltage Control Model

Figure 15 illustrates the block diagram of an LCL-filtered GFMC in the dq reference frame, including the plant and the voltage controller. The solid lines depict the GFMC operating in stand-alone mode, while the grid-tied mode refers to the components represented by the black dotted lines. In this frame, voltage control is commonly implemented using a proportional-integral (PI) controller, which is equivalent to the proportional-resonant (PR) controller in the αβ frame, as discussed in [30].

In the dq frame, the voltage controller G_v (s) typically takes the form:

$$G_{\mathrm{v}}(s)=K_{\mathrm{vp}}+{\displaystyle \frac{K_{\mathrm{vi}}}{s}}$$

(15)

where K_vp is the proportional gain, and K_vi is the integral gain, which is responsible for eliminating steady-state error in voltage tracking. Unlike the PR controller in the αβ frame, which targets resonant frequency tracking at ω₀, the PI controller in the dq frame ensures proper regulation of dc quantities, simplifying control design.

The current controller G_c (s) is often selected as:

$$G_{\mathrm{c}}(s)=K_{\mathrm{cp}}$$

(16)

where K_cp represents the current loop proportional gain and G_if(s) denotes the current feedback transfer function.

(a)

Stand-Alone Mode

For the stand-alone mode, the plant model, describing the relationship between the inverter output voltage v_gi and capacitor voltage v_gf, as well as inverter-side current i_gi within the LC system, can be derived as follows:

$$G_{\mathrm{vLC}}(s)={\displaystyle \frac{v_{\mathrm{gf}}(s)}{v_{\mathrm{gi}}(s)}}={\displaystyle \frac{1}{s^2{L}_{\mathrm{gi}}{C}_{\mathrm{gf}}+1}}$$

(17)

$$G_{\mathrm{iLC}}(s)={\displaystyle \frac{i_{\mathrm{gi}}(s)}{v_{\mathrm{gi}}(s)}}={\displaystyle \frac{s{C}_{\mathrm{gf}}}{s^2{L}_{\mathrm{gi}}{C}_{\mathrm{gf}}+1}}$$

(18)

(b)

Grid-Tied Mode

When the GFMC is connected to the grid, the plant model can be expressed as follows:

$$G_{\mathrm{vLCL}}(s)={\displaystyle \frac{v_{\mathrm{gf}}(s)}{v_{\mathrm{gi}}(s)}}={\displaystyle \frac{L_{\mathrm{gg}}}{s^2{L}_{\mathrm{gi}}{C}_{\mathrm{gf}}{L}_{\mathrm{gg}}+L_{\mathrm{gi}}+L_{\mathrm{gg}}}}$$

(19)

$$G_{\mathrm{iLCL}}(s)={\displaystyle \frac{i_{\mathrm{gi}}(s)}{v_{\mathrm{gi}}(s)}}={\displaystyle \frac{s^2{L}_{\mathrm{gg}}{C}_{\mathrm{gf}}+1}{s^3{L}_{\mathrm{gi}}{C}_{\mathrm{gf}}{L}_{\mathrm{gg}}+s(L_{\mathrm{gi}}+L_{\mathrm{gg}})}}$$

(20)

(c)

Double-Loop Voltage Control with Gif(s) = 1

In the case of double-loop voltage control, we set G_if (s) to 1. Then, the open-loop gain of the islanded GFMC is derived in [31] and given as

$$G_{\mathrm{LC}}(s)={\displaystyle \frac{G_{\mathrm{v}}(s)G_{\mathrm{c}}(s)G_{\mathrm{d}}(s)G_{\mathrm{vLC}}(s)}{1+G_{\mathrm{c}}(s)G_{\mathrm{d}}(s)G_{\mathrm{iLC}}(s)}}$$

(21)

In the case of a grid connection, the open-loop gain is given in [31] and as follows:

$$G_{\mathrm{LCL}}(s)={\displaystyle \frac{G_{\mathrm{v}}(s)G_{\mathrm{c}}(s)G_{\mathrm{d}}(s)G_{\mathrm{vLCL}}(s)}{1+G_{\mathrm{c}}(s)G_{\mathrm{d}}(s)G_{\mathrm{iLCL}}(s)}}$$

(22)

(d)

Single-Loop Voltage Control with G_if(s) = 0

When G_if (s) is set to 0 and G_c (s) is set to 1, this refers to single-loop voltage control schemes without current regulation.

For an islanded system, the open-loop gain is given by

$$G_{\mathrm{LC}}(s)=G_{\mathrm{v}}(s)G_{\mathrm{d}}(s)G_{\mathrm{vLC}}(s)$$

(23)

For a grid-tied system, the open-loop gain is represented in [32] and given as

$$G_{\mathrm{LCL}}(s)=G_{\mathrm{v}}(s)G_{\mathrm{d}}(s)G_{\mathrm{vLCL}}(s)$$

(24)

3.2.2. Power Control Model

The active and reactive power transferred from the GFMC to the grid in a steady state can be expressed as follows [31]:

$$\left\{\begin{array}{l}P={\displaystyle \frac{3V_{\mathrm{o}}[(V_{\mathrm{o}}-V_{\mathrm{g}}\cos {\delta }_0)R_{\mathrm{g}}+V_{\mathrm{g}}{X}_{\mathrm{g}}\sin {\delta }_0]}{2({R_{\mathrm{g}}}^2+{X_{\mathrm{g}}}^2)}}\\ Q={\displaystyle \frac{3V_{\mathrm{o}}[(V_{\mathrm{o}}-V_{\mathrm{g}}\cos {\delta }_0)X_{\mathrm{g}}-V_{\mathrm{g}}{R}_{\mathrm{g}}\sin {\delta }_0]}{2({R_{\mathrm{g}}}^2+{X_{\mathrm{g}}}^2)}}\end{array}\right.$$

(25)

Here, V_o is the converter voltage, while V_g is the grid voltage. δ₀ denotes the steady-state power angle between the GFMC voltage and the grid voltage. R_g is the line resistance. X_g is the line reactance, which is given as X_g = ω₀L_g, where L_g is the line inductance.

By taking the partial derivative of (25), we obtain the small-signal model of the power control as follows:

$$\left\{\begin{array}{l}\widehat{P}=K_{\mathrm{p}\mathsf{\delta }}\widehat{\delta }+K_{\mathrm{pv}}{\widehat{V}}_{\mathrm{o}}\\ \widehat{Q}=K_{\mathrm{q}\mathsf{\delta }}\widehat{\delta }+K_{\mathrm{qv}}{\widehat{V}}_{\mathrm{o}}\end{array}\right.$$

(26)

where the coefficients K_pδ, K_pv, K_qδ, and K_qv can be expressed as [15]

$$\left\{\begin{array}{l}{K}_{\mathrm{p}\mathsf{\delta }}={\displaystyle \frac{3V_{\mathrm{o}}{V}_{\mathrm{g}}(R_{\mathrm{g}}\sin {\delta }_0+X_{\mathrm{g}}\cos {\delta }_0)}{2(R_{\mathrm{g}}^2+X_{\mathrm{g}}^2)}}\\ K_{\mathrm{pv}}={\displaystyle \frac{3\left[2V_{\mathrm{o}}{R}_{\mathrm{g}}+V_{\mathrm{g}}(-R_{\mathrm{g}}\cos {\delta }_0+X_{\mathrm{g}}\sin {\delta }_0)\right]}{2(R_{\mathrm{g}}^2+X_{\mathrm{g}}^2)}}\\ K_{\mathrm{q}\mathsf{\delta }}={\displaystyle \frac{3V_{\mathrm{o}}{V}_{\mathrm{g}}(-R_{\mathrm{g}}\cos {\delta }_0+X_{\mathrm{g}}\sin {\delta }_0)}{2(R_{\mathrm{g}}^2+X_{\mathrm{g}}^2)}}\\ K_{\mathrm{qv}}={\displaystyle \frac{3\left[2V_{\mathrm{o}}{X}_{\mathrm{g}}+V_{\mathrm{g}}(-R_{\mathrm{g}}\sin {\delta }_0-X_{\mathrm{g}}\cos {\delta }_0)\right]}{2(R_{\mathrm{g}}^2+X_{\mathrm{g}}^2)}}\end{array}\right.$$

(27)

Normally, we use low-pass filters to get rid of harmonics in P and Q, which can be modeled as G_f (s) = ω_f/(s + ω_f), where ω_f represents the cutoff frequency, leading to

$$\left\{\begin{array}{l}{P}_{\mathrm{f}}(s)=G_{\mathrm{f}}(s)P(s)/S_0\\ Q_{\mathrm{f}}(s)=G_{\mathrm{f}}(s)Q(s)/S_0\end{array}\right.$$

(28)

where S₀ denotes the rated power of the GFMC, and P_f and Q_f are the per unit values of the measured P and Q, respectively.

The transfer functions for the active power controller (APC) and reactive power controller (RPC), namely, G_p(s) and G_q(s), can, respectively, be expressed as follows:

$$\left\{\begin{array}{l}{G}_{\mathrm{p}}(s)={\displaystyle \frac{{\omega }_{\mathrm{oref}}(s)}{P_{\mathrm{ref}}(s)-P_{\mathrm{f}}(s)}}={\displaystyle \frac{{\omega }_0}{D_{\mathrm{p}}s}}\\ G_{\mathrm{q}}(s)={\displaystyle \frac{V_{\mathrm{oref}}(s)}{Q_{\mathrm{ref}}(s)-Q_{\mathrm{f}}(s)}}={\displaystyle \frac{V_{\mathrm{n}}}{D_{\mathrm{q}}}}\end{array}\right.$$

(29)

where V_n represents the nominal voltage. D_p and D_q indicate the per-unit active and reactive power droop gains, respectively. V_oref is the voltage reference for GFMC.

By integrating the small-signal models of both the plant and the controllers, we arrive at the power loop control block diagram shown in Figure 16, where ${\widehat{P}}_{\mathrm{f}}$ and ${\widehat{Q}}_{\mathrm{f}}$ denote the per-unit filtered active and reactive power, respectively. In this part, we simplify the voltage control as a transfer function T_v(s).

4. Control Strategies of Grid-Forming Converters

This section reviews the primary control strategies used in GFMCs, which are designed to regulate active power and frequency. These include droop control, VSM, VOC, and other advanced methods. These strategies provide a structured framework to ensure stable and reliable operation in GFMC-based power systems.

4.1. Droop Control

Droop control remains a foundational technique in the decentralized operation of power systems. Originally developed for synchronous generators (SGs), it enables autonomous power sharing by modulating frequency and voltage in response to active and reactive power imbalances, thereby eliminating the need for inter-unit communication. This feature is particularly advantageous in systems with increasing penetration of renewable energy sources (RESs) [33]. To ensure grid compatibility, GFMCs are engineered to emulate the power-sharing behavior of SGs through droop control, facilitating synchronization and stable network integration [34].

As illustrated in Figure 16, the droop control strategy for a GFMC is structured to regulate both active and reactive power using dedicated droop coefficients. Within the active power control (APC) loop, the reference active power ${\widehat{P}}_{ref}$ is compared with the measured output power ${\widehat{P}}_f$, and the resulting power error is scaled by the active power droop coefficient D_p to yield the frequency deviation ω. This mechanism adjusts the converter’s output frequency proportionally to power imbalances, thereby promoting power sharing among parallel units.

While conventional droop control is extensively implemented in modern power systems, it is primarily suited to systems with inductive line characteristics, where the relationships between frequency and active power, and voltage and reactive power, hold reliably [35,36]. However, in low-voltage distribution networks—often characterized by predominantly resistive impedance—the standard droop model fails to ensure accurate power distribution. In such environments, modified droop strategies such as virtual impedance emulation and P–V/Q–f droop control are employed to enhance power-sharing accuracy and preserve system stability [37,38].

4.2. Virtual Synchronous Machines

VSMs represent a sophisticated advancement in power system engineering, facilitating the effective integration of RESs into traditional power grids. Unlike conventional power converters that passively follow grid-defined voltage or frequency, VSMs empower GFMCs to actively participate in grid stabilization and management by mimicking the dynamic behavior of SGs. This includes delivering essential services such as inertia, damping, and voltage support [39]. At the heart of VSM technology lies a robust control strategy that transforms conventional GFLCs into grid-forming units [40], which is crucial for maintaining grid stability in the absence of large conventional generators.

VSMs are implemented using P − f and Q − V loops, as illustrated in Figure 17. The P − f loop is responsible for generating the synchronizing angle, while the Q − V loop provides the voltage amplitude reference that the converter tracks [41]. The swing equation is employed to emulate the dynamic response of the system, expressed as:

$$J{\displaystyle \frac{d\omega }{dt}}={\displaystyle \frac{1}{{\omega }_{\mathrm{ref}}}}(P_{\mathrm{ref}}-P)+D_{\mathrm{p}}({\omega }_{\mathrm{ref}}-\omega )$$

(30)

Here, J represents the virtual inertia and D_p denotes the virtual damping. The symbols ω_ref and ω correspond to the reference and measured angular frequencies, respectively, while a similar analogy to P. This equation is critical in evaluating how the VSM responds to disturbances by reflecting the mechanical properties of conventional generators.

Furthermore, the classical Q − V loop equation for VSM control can be shown as:

$$\left|V\right|={\displaystyle \frac{\omega }{s{K}_{\mathrm{v}}}}(D_{\mathrm{q}}\Delta \left|V_{\mathrm{GFMC}}\right|+\Delta Q)$$

(31)

Here, 1/K_v represents the integrator gain, while D_q denotes the voltage damping. The variables Δ|V_GFMC| and ΔQ correspond to the errors in voltage and reactive power, respectively. The interplay between these equations ensures that VSMs not only react to grid conditions but also proactively shape the dynamics of the power system.

To assess the stability of the VSM system, a Lyapunov function V can be employed:

$$V(\delta ,\dot{\delta })={\displaystyle \frac{1}{2}}{k}_1{\delta }^2+{\displaystyle \frac{1}{2}}{k}_1{\dot{\delta }}^2$$

(32)

where k₁ and k₂ are constants representing system stiffness and damping. The time derivative of V must remain negative to ensure system stability.

VSMs are exceptionally effective in diverse applications, notably in maintaining stability in standalone microgrids where they autonomously manage power distribution and demand response, even in the absence of traditional generation sources [42]. This self-regulating capability allows microgrids to operate reliably, ensuring a continuous power supply while accommodating variable loads and generation. In larger integrated power systems, VSMs contribute significantly to enhancing grid resilience by providing a buffer against disturbances, thereby preventing cascading failures.

4.3. Virtual Oscillator Control

The VOC scheme manages GFMCs by using virtual oscillators for frequency synchronization and power-sharing in decentralized grids [42]. There are two primary types of oscillators: Liénard oscillators and consensus-based oscillators, each with unique advantages [43,44,45,46,47,48].

Liénard oscillators, such as the Van der Pol and Dead-zone oscillators, are derived from the Liénard equation and are valued for facilitating frequency synchronization in GFMCs. The Van der Pol oscillator provides self-sustained oscillations for managing variable loads, but its nonlinear behavior may introduce harmonic distortions [49]. The Dead-zone oscillator, with its limited oscillation range, enhances stability against minor fluctuations but may slow recovery from larger disruptions [50].

Consensus-based oscillators promote synchronization across distributed GFMC units without needing precise tuning, making them robust and scalable for microgrids [51]. Advanced types like the dispatchable virtual oscillator dynamically adjust frequency and voltage, supporting real-time power-sharing in volatile grids with high renewable integration, though this adds control complexity [52].

Other VOC types include the Andronov-Hopf oscillator (AHO), which quickly adapts to grid fluctuations, ideal for high renewable penetration, and the unified virtual oscillator, which integrates multiple control goals, such as voltage regulation and frequency synchronization, into one model. While versatile, the unified oscillator requires fine-tuning to balance control objectives. The AHO is notable for its simplicity and defined response, making it effective for tracking power, voltage, and frequency in both grid-connected and islanded modes [48,53].

The control structure of this oscillator is illustrated in Figure 18. The AHO consists of a linear oscillator part with a natural frequency and two negative conductances, −σ and −ϵ²σ, which inject energy into the circuit to sustain oscillations, along with nonlinear state-dependent voltage and current sources, g_v and g_i [54], which can be represented as

$$g_{\mathrm{v}}=\epsilon \alpha (v_{\mathrm{c}}^2+{\epsilon }^2{i}_{\mathrm{L}}^2)\epsilon i_{\mathrm{L}}$$

(33)

$$g_{\mathrm{i}}=\alpha (v_{\mathrm{c}}^2+{\epsilon }^2{i}_{\mathrm{L}}^2)$$

(34)

The dynamic equation of the AHO, accounting for the capacitor voltage v_c and the scaled inductor current i_L, is expressed as follows:

$${\dot{v}}_{\mathrm{c}}={\displaystyle \frac{1}{C}}[-i_{\mathrm{L}}-g_{\mathrm{i}}+\sigma v_{\mathrm{c}}-u_1]$$

(35)

$${\dot{i}}_{\mathrm{L}}={\displaystyle \frac{1}{L}}[v_{\mathrm{c}}-g_{\mathrm{v}}+\sigma \epsilon (\epsilon i_{\mathrm{L}})-\epsilon u_2]$$

(36)

Here [u₁, u₂] = k_iR(φ)(i_αβ − i*_αβ), where i_αβ represents the measured inverter output current in the αβ stationary reference frame. The reference currents i*_αβ are defined as follows:

$$i_{\mathsf{\alpha }}^{\ast }={\displaystyle \frac{2}{3‖v_{\mathsf{\alpha }\mathsf{\beta }}‖}}(v_{\mathsf{\alpha }}{p}^{\ast }+v_{\mathsf{\beta }}{q}^{\ast })$$

(37)

$$i_{\mathsf{\beta }}^{\ast }={\displaystyle \frac{2}{3‖v_{\mathsf{\alpha }\mathsf{\beta }}‖}}(v_{\mathsf{\beta }}{p}^{\ast }-v_{\mathsf{\alpha }}{q}^{\ast })$$

(38)

Here, $‖v_{\mathsf{\alpha }\mathsf{\beta }}‖=\sqrt{v_{\mathsf{\alpha }}^2+v_{\mathsf{\beta }}^2}$ represents the magnitude of the modulation signals [v_α, v_β], which can be obtained from

$${\dot{v}}_{\mathsf{\alpha }}={\displaystyle \frac{\varsigma }{k_{\mathrm{v}}^2}}(2V_{\mathrm{nom}}^2-{‖v_{\mathsf{\alpha }\mathsf{\beta }}‖}^2)v_{\mathsf{\alpha }}-w_{\mathrm{nom}}{v}_{\mathsf{\beta }}-{\displaystyle \frac{k_{\mathrm{v}}{k}_{\mathrm{i}}}{C}}(i_{\mathsf{\beta }}-i_{\beta }^{\ast })$$

(39)

$${\dot{v}}_{\mathsf{\beta }}={\displaystyle \frac{\varsigma }{k_{\mathrm{v}}^2}}(2V_{\mathrm{nom}}^2-{‖v_{\mathsf{\alpha }\mathsf{\beta }}‖}^2)v_{\mathsf{\beta }}+w_{\mathrm{nom}}{v}_{\mathsf{\alpha }}-{\displaystyle \frac{k_{\mathrm{v}}{k}_{\mathrm{i}}}{C}}(i_{\mathsf{\alpha }}-i_{\mathsf{\alpha }}^{\ast })$$

(40)

Here ϛ represents the rate at which the system reaches its steady state.

VOC plays a vital role in GFMCs, especially in renewable-rich systems like wind and solar power plants. It maintains stable voltage and frequency regulation in dynamic grids, accommodating fluctuating energy sources and varying load demands while minimizing disturbances. Key applications include grid stabilization in microgrids, seamless grid-to-island transitions, and use in EV charging stations and battery energy storage systems (BESS) for enhanced reliability and energy distribution.

New control strategies are emerging for GFMCs to address the growing complexity of modern power systems, surpassing traditional droop control, VSM, and VOC. These approaches enable real-time adaptation to grid changes, predictive optimization, and improved system coordination, supporting efficient and stable integration of RESs in dynamic, decentralized grids. The upcoming section will explore these advanced techniques.

4.4. Advanced Control Methods of GFMCs

Adaptive control, developed in the 1960s for regulating systems with uncertain or time-varying dynamics, enables real-time adjustment of control parameters in response to changing grid conditions. For GFMCs, adaptive schemes allow dynamic tuning of performance during disturbances and load fluctuations, contributing to enhanced stability and power quality [55,56]. However, despite their flexibility, such schemes often introduce implementation complexity and may experience instability during rapid parameter transitions.

Model predictive control (MPC), introduced in the 1970s, applies a forecasting framework by utilizing a mathematical model of the GFMC to predict future system states over a finite time horizon. Control inputs are then optimized to meet specific objectives while adhering to operational constraints such as current and voltage limits [57]. This predictive capability allows MPC to handle fast-changing grid dynamics more effectively, improving transient stability and power-sharing [58]. In standalone inverter systems, the control structure predicts current and voltage trajectories to enable anticipatory adjustments. Nevertheless, its precision depends critically on the accuracy of system modeling and requires significant computational resources.

Hierarchical control introduces a multi-level control structure organized across primary, secondary, and tertiary layers, each responsible for specific timescales and functional objectives [59]. The primary level addresses fast, local voltage and frequency control; the secondary level corrects steady-state deviations; and the tertiary level manages global coordination tasks such as power flow optimization and economic dispatch. Figure 19 presents a hierarchical control scheme for microgrids, demonstrating coordinated operation across control layers to ensure both local responsiveness and system-wide stability.

Table 2. Comparative analysis of GFMC control strategies.

Control Strategy	Inertia Support	Power Sharing	Complexity	Operating Scenarios
Droop Control	No	Decentralized sharing with possible steady-state errors	Moderate	Suitable for both islanded and grid-tied systems requiring load sharing
VSM	Yes	Decentralized sharing analogous to synchronous generators	Moderate	Applicable to both conventional and modern power systems
VOC	No	Decentralized sharing with improved synchronization	High	Best for power-electronics-dominated networks

compares control strategies by inertia support, power sharing, and operating conditions, highlighting each method’s strengths and limitations.

5. Application of Grid-Forming Converters

In recent years, GFMCs have become increasingly important in modern power systems. These converters are essential when microgrids are disconnected from the main grid, whether due to faults or other reasons. The following section provides an in-depth review of the various applications of GFMCs.

5.1. Renewable Energy Integration

One of the primary applications of GFMCs is integrating RESs, such as wind and solar, into the grid. Unlike traditional GFLCs that require a stable power source connection, GFMCs provide renewable energy systems with stable voltage and frequency references. This capability allows renewable energy systems to operate independently in islanded or standalone modes when the main grid is unavailable or unreliable [8,9]. This ensures a consistent and reliable power supply from renewable sources, enhancing overall grid resilience and reducing reliance on fossil fuels. Figure 20 shows an integrated renewable energy system, managing renewables, storage, and generators to ensure a reliable energy supply and enhance grid stability.

5.2. AC/DC Microgrid

In hybrid AC/DC microgrids, the roles of AC and DC GFMCs are distinctly defined to address the specific control and stability requirements of their respective subsystems. AC GFMCs are responsible for regulating voltage and frequency within the AC network. They govern the active power–frequency and reactive power–voltage relationships, enabling effective response to load variations while maintaining synchronization and power quality under both grid-connected and islanded modes of operation [60,61]. These converters ensure that the AC subsystem remains dynamically stable under varying operating conditions.

DC GFMCs, on the other hand, regulate the voltage profile of the dc network by managing the relationship between active power and terminal voltage [62,63]. This functionality supports voltage stability and enables coordinated power sharing among parallel-connected dc-dc converters. In addition to primary voltage regulation, DC GFMCs often incorporate secondary control mechanisms to correct steady-state voltage deviations and may implement virtual inertia strategies to mitigate rapid voltage transients [64]. Such control features are critical for enhancing the dynamic performance and power-sharing accuracy in DC microgrids.

5.3. Power Quality Enhancement

GFMCs contribute significantly to power quality enhancement in modern power systems through the integration of advanced control and compensation technologies. One notable application involves their implementation in static synchronous compensators (STATCOMs) or static var generators (SVGs), which deliver dynamic reactive power support and improve voltage regulation under varying load conditions [65,66]. Another important application is in active power filters (APFs), where GFMCs are employed to mitigate harmonic distortions, thereby improving waveform quality and reducing total harmonic distortion.

In grid-forming STATCOMs, the synchronization of the dc-link voltage—commonly achieved through dc-link voltage synchronization (DCVS)—is essential for concurrent voltage regulation and grid synchronization. However, DCVS can introduce low-frequency oscillations, particularly under weak grid conditions. To counteract this, a lead-lag compensator is often incorporated to mitigate phase lag, enhance system stability, and provide synthetic inertia, thereby reducing the rate of change of frequency (RoCoF) during synchronization events [67,68].

Soft open points (SOPs) also play a vital role in supporting power quality and operational flexibility. By enabling controlled active power flow and reactive power compensation across multiple network terminals, SOPs maintain voltage stability during islanding events. Unified control strategies for SOP-integrated GFMCs ensure coordinated converter operation, thereby preserving grid-forming functionality under faulted conditions [69]. Moreover, the integration of current-limiting algorithms allows these systems to manage fault currents—particularly during grounding faults—thus improving operational reliability. Collectively, these advanced functionalities extend the role of GFMCs in maintaining power quality and system stability in evolving power networks.

5.4. High Voltage Direct Current

In HVDC systems, grid-forming MMCs are a prominent choice due to their modular architecture, high efficiency, and capability to handle large power levels [23]. Grid-forming MMCs facilitate the integration of large-scale offshore wind farms by regulating voltage and frequency under weak grid conditions. Unlike traditional approaches that rely on PLLs, these converters employ advanced synchronization techniques, enabling stable operation during power flow transients and effective dc-link voltage control.

In addition to MMCs, grid-forming VSCs equipped with series-connected IGBTs or IGCTs are also employed in HVDC networks [70]. These converters provide critical voltage and frequency regulation, supporting reliable and efficient power transfer across multi-terminal HVDC links. Both multilevel and two-level GFMC architectures are capable of emulating inertia and implementing droop control, which are essential for maintaining system stability under dynamic operating conditions and for improving the performance of HVDC systems integrating renewable energy sources.

6. Application-Related Challenges for Grid-Forming Converters

This section examines key challenges of GFMCs, focusing on synchronization, operational transitions, energy storage integration, and ac fault protection, along with strategies to ensure stable and reliable performance.

6.1. Synchronization Dynamics and Stability in GFMCs

GFMCs synchronize with the grid based on their output active power, similar to synchronous generators, which enhances stability in low-SCR grids compared to PLL-based GFLCs [71,72,73]. This power-based synchronization reduces the adverse negative damping effect associated with PLLs in weak networks. However, in high-SCR systems, even small phase deviations between converter and grid voltages can result in significant active power fluctuations, leading to potential loss of synchronism [74]. Transient stability performance is strongly influenced by the synchronization control strategy: droop-based power synchronization control offers robust, overdamped dynamics and superior fault recovery capability [74], while virtual inertia–based approaches display second-order dynamics comparable to those of synchronous generators, making them more sensitive to severe disturbances [75]. Furthermore, overcurrent limiting, PLL engagement during extreme grid faults, and dynamic coupling between inner and outer control loops can significantly impact stability margins [74,76]. Consequently, the design of robust damping mechanisms, careful tuning of control parameters, and coordinated multi-loop strategies are essential to ensure reliable operation under varying SCR conditions and disturbance scenarios.

6.2. Operational Transition Between Islanded and Grid-Connected Modes

GFMCs must operate reliably in both islanded and grid-connected modes while ensuring a seamless transition between them [77]. Mode transitions can introduce significant voltage, frequency, and power mismatches, such as deviations in amplitude and phase during reconnection or non-zero through-power during disconnection, which may lead to oscillations and instability if not properly managed. In islanded mode, GFMCs are required to autonomously establish and regulate system voltage and frequency, whereas in grid-connected mode, they must follow grid commands for active and reactive power injection [8,78]. Smooth transitions typically employ droop control as the primary layer, with secondary control providing compensation terms to eliminate voltage and phase mismatches before reconnection or to minimize through-power before disconnection [59]. This coordinated approach enables voltage phasor synchronization for reconnection and controlled power reduction for islanding. Such capabilities are increasingly important in distribution systems and dynamic microgrids with high penetration of power electronics-based resources, where multiple GFMCs must frequently switch modes while maintaining system stability and compliance with operational requirements.

6.3. Integration and Control of Energy Storage in GFMCs

Practical implementation of GFMCs requires integration with energy storage systems (ESSs) to enable self-synchronization and provide grid support under both steady-state and transient conditions [79]. Among various ESS technologies such as flywheel, superconducting magnetic storage, batteries, and ultra-capacitors, the hybrid energy storage system (HESS) has emerged as a promising solution, combining ultra-capacitors for rapid high-power response with batteries for high-energy capacity [80]. This multi-time-scale capability enables effective response to different rates of change of frequency (RoCoF), with ultra-capacitors addressing high RoCoF events and batteries handling low RoCoF scenarios. However, HESS integration introduces significant challenges in control coordination, state-of-charge management, and charging/discharging optimization, especially when operating in parallel with GFMC control loops [80]. The absence of standardized design guidelines such as thresholds for triggering different storage units complicates parameter selection, often requiring trial-and-error tuning. Addressing these issues demands coordinated control strategies that ensure stable operation, optimal energy utilization, and compliance with performance, cost, and complexity constraints in diverse grid conditions.

6.4. AC Fault Detection and Protection Strategies for GFMC-Interfaced Grids

The fault characteristics of GFMCs differ fundamentally from synchronous generators due to their limited fault current magnitude and duration, fast current-limiting behavior, and dual-sequence control methods. These differences can compromise the effectiveness of conventional protection schemes, such as overcurrent, negative-sequence, and distance protection, whose operation relies on traditional synchronous machine fault signatures [81]. For instance, fault ride-through controls can distort impedance measurements used by distance relays, and negative-sequence suppression can affect the performance of protection elements designed to detect unbalanced faults [82]. Recent research has proposed integrating control modifications with advanced relay schemes, such as injecting inter-harmonic or synthetic harmonic currents during faults to improve fault identification and location accuracy [83]. Such coordinated approaches enable protection systems to operate reliably despite the altered fault dynamics introduced by GFMC operation. Ensuring robust AC fault protection in converter-dominated grids will require continued development of schemes that simultaneously address hardware safety, system stability, and compliance with evolving grid codes.

7. Conclusions

GFMCs are key components in modern power systems, enabling the effective integration of RESs, stabilizing microgrids, and supporting grid operations through voltage and frequency regulation. Various converter topologies, such as neutral point-clamped, flying capacitor, cascaded H-bridge, and modular multilevel converters, offer advantages in high-voltage operation, power quality improvement, and system scalability. Small-signal modeling provides insights into system dynamics under nominal conditions and facilitates the design of stable and responsive control systems. Additionally, the article compares various grid-forming control strategies, including droop control, virtual synchronous machines, and virtual oscillator control, which are essential for maintaining system stability and reliability in dynamic environments. Potential applications demonstrate the role of GFMCs in advancing sustainable energy systems and enhancing modern energy infrastructure. Furthermore, application-related challenges such as maintaining stability under varying short-circuit ratios, ensuring seamless operational transitions, integrating energy storage, and implementing effective fault protection remain critical areas for future research to ensure the reliable deployment of these technologies in increasingly converter-dominated grids.