Abstract
The renewable energy sources (RESs) dominated power grid is an envisaged infrastructure of the future power system, where the commonly used grid following (GFL) control for grid-tied converters suffers from lacking grid support capability, low stability, etc. Recently, emerging grid forming (GFM) control methods have been proposed to improve the dynamic performance and stability of grid-tied converters. This paper reviews existing GFM control methods for the grid-tied converters and compares them in terms of control structure, grid support capability, fault current limiting, and stability. Considering the impact of fault current limiting strategies, a comprehensive transient stability analysis is provided. In addition, this paper explores the typical applications of GFM converters, such as AC microgrid and offshore wind farm high-voltage direct current (OWF-HVDC) integration systems. Finally, the challenges to the GFM converters in future applications are discussed.
HIGH penetration of renewable energy sources (RESs), e.g., wind power and photovoltaic solar, has gained increasing attention in recent years to deal with the climate change problem and pave ways to build a carbon-neutral society [
To improve the frequency response, enhanced GFL control methods such as current-controlled droop control [
Considering the issues of GFL control in RESs dominated grid, the grid forming (GFM) control is proposed to provide grid support capability. The GFM control is initially designed as constant voltage/frequency (VF) control, which operates as an ideal voltage source to form the AC voltage autonomously. Due to the constant output voltage and frequency, the GFM converter can only integrate with passive power grids (without SGs or GFM converters) [
Despite the mentioned grid-friendly merits, the GFM converters may suffer from small-signal stability issues when subjected to grid disturbances in strong active grids [
Aiming at investigating the GFM control for future RESs dominated grid, this paper carries out the overview of the state-of-the-art of GFM control with a focus on control structures, AC fault current limiting capability, stability, application prospects, and future challenges. The outline of this paper is organized as shown in

Fig. 1 Overall framework of this paper.
Typical GFL control consists of the PLL for synchronizing with the power grid and the vector current control for regulating output power. Reference [

Fig. 2 Equivalent structure of GFL converter.
The common GFL control is the active and reactive power (PQ) control using the proportional-integral (PI) controller, which is shown in

Fig. 3 Structure of typical GFL PQ control.
To improve the frequency response under grid disturbances, there are two grid-supporting GFL control methods that can provide VF support or inertia support for power grids. One is current-controlled droop control, which is depicted in

Fig. 4 Structure of current-controlled droop control.
Compared with PQ control, a droop loop is added to regulate the output power. Hence, the converter can respond to grid disturbances, and has grid frequency/voltage regulation capability like SGs. However, this control cannot provide inertia support for the power grid.
The other is the current-controlled VSG control, which aims to provide inertia support for power grids [
(1) |

Fig. 5 Structure of current-controlled VSG control.
where is the converter output frequency; and are the mechanical power and electromagnetic power of the SG, respectively; and are the mechanical torque and electromagnetic torque of the SG, respectively; is the moment of inertia of the rotor; and is the damping coefficient of SG. At the initial stable state, , and is the nominal power. Assuming maintains constant, (1) can be expressed as:
(2) |
Although some improvements have been implemented, the inner control of the grid-supporting GFL control methods is still unchanged. Thus, those enhanced methods still operate as the controlled current sources without stand-alone operation capability. In addition, the inherent stability issue caused by PLL in RESs dominated grid is still a potential risk [
Intrinsically different from GFL converter, GFM converter is a controlled voltage source with the ability to generate AC voltage autonomously [
VF control is designed to maintain the output voltage amplitude and frequency constant through the closed-loop control, which is often applied in passive power grids, such as islanded grids or uninterruptable power supply (UPS) systems. However, due to the constant voltage source characteristic, VF-controlled converter has no power-sharing capability, which cannot operate in active power grids.
As shown in

Fig. 6 Structure of VF control.
When integrating with active power grids, the GFM converter is required to have the ability to share power with other voltage sources. Based on the VF control, the PSL is designed to mimic the rotor characteristics of SG, which has the ability of power-sharing, grid-supporting, and self-synchronization with grids. The general structure of the PSL-based GFM control is shown in

Fig. 7 Basic structure of PSL-based GFM control [
According to different structures of PSL, the common PSL-based GFM control includes droop control, power synchronization control (PSC), VSG, synchronverter, synchronous power controller (SPC), etc. Specifically, the structures of these control structures are shown in

Fig. 8 Different control structures of the PSL-based GFM control. (a) Droop control. (b) PSC. (c) Low-pass filter (LPF) droop control. (d) VSG. (e) Synchronverter. (f) SPC.
In
In the steady state, the droop characteristics of SGs can be obtained from (2) by letting . Replacing with the converter power , the PSL can be designed as:
(3) |
where the droop coefficient of PSL is . The design of the QCL refers to the Q-V droop characteristics of SGs, which is:
(4) |
where is the droop coefficient of QCL. With the PSL designed from (3) and (4), the GFM converter can mimic the droop characteristics of SG and share the load power change with other voltage sources (SGs and droop-controlled GFM converter).
Comparing (3) with (2), the inertia term in (3) is missing, which also means that the droop control lacks inertia support capability.
As can be observed from
In practical projects, to eliminate the sampling ripple in power measurements, the LPFs are commonly added to the droop control, which is shown in
(5) |
where K is the gain coefficient; and is the desired cut-off frequency, which is represented by and in
(6) |
It can be found that due to the existence of LPFs, the inertia term exists in (6), which introduces an inertia simulation to the converter dynamic. Thus, the LPF droop control can provide inertia support to suppress the frequency fluctuation of the power grid.
Similar to the principle of current-controlled VSG control shown in
Based on the VSG, the excitation characteristics of SGs have been further considered in the design of synchronverter. Therefore, the synchronverter mimics the operation characteristics of SGs more comprehensively. As shown in
(7) |
(8) |
(9) |
(10) |
where ; denotes the conventional inner product; is the mutual inductance between the rotor coils and the stator coils; and is the excitation current in the rotor.
The structure of the SPC is shown in
(11) |
where is the maximum output power of the converter; and . Assuming is the first-order transfer function, the closed-loop active power control shown in

Fig. 9 Closed-loop structure of active power control.
Thus, the closed-loop transfer function of the active power control is second-order and can be expressed as:
(12) |
(13) |
According to (13), the damping coefficient and the un-damped natural oscillation angular frequency of the second-order system can be pre-set by adjusting and of , respectively. Thus, the closed-loop active power control can be further designed as an overdamped system to attenuate the inherent power oscillations of SGs. The has many other forms, such as PI controller (additional droop control is required) [
According to inertia support capability, the PSL-based GFM control can be further divided into non-inertia control (
Unlike PSL-based GFM control, VOC is proposed to make use of the inherent synchronization characteristics of the coupled oscillator network. The VOC converter can generate sinusoidal voltage independently by emulating the dynamic characteristics of the weakly nonlinear oscillator [

Fig. 10 Structure of VOC based on Van der Pol oscillator.
References [
However, the VOC shown in

Fig. 11 Structure of dVOC.
In
(14) |
where , ; and are the positive gain constants; ; and , , and the real number are expressed as:
(15) |
where is the Euclidean norm of matrix v, which means the amplitude of v, represented by ; and is selected according to the line parameters. For inductive lines, ; for resistive lines, . Moreover, choosing , the steady-state droop characteristics of dVOC can be expressed as:
(16) |
Reference [
(17) |

Fig. 12 Hopf-type oscillator based dVOC.
According to (16) and (17), ignoring the voltage dynamics, it can be found that the closed-loop active power control of dVOC is also a first-order system, which is a non-inertia control like droop control.
Due to the voltage source characteristic, the GFM converter may encounter overcurrent problems under large grid disturbances, such as AC faults. To ensure the safety of power semiconductors, the current limiting strategies for AC fault are necessary for GFM converter. There are two classic fault current limiting strategies, i.e., the instantaneous saturation limiter and the latched limiter. They are both realized by adding the current limiter block between voltage and current control [
The instantaneous saturation limiter of the current reference is expressed as:
(18) |
where is the output of the voltage control; Ith is the threshold of the current limiter; and is the limited current reference. Moreover, the instantaneous saturation limiter can be applied in the stationary reference frame (STRF), the synchronous reference frame (SYRF), and the natural reference frame (NARF), which are depicted in

Fig. 13 Instantaneous saturation limiter in different reference frames. (a) NARF. (b) SYRF. (c) STRF.

Fig. 14 Sine signal limiter in NARF and STRF. (a) NARF. (b) STRF.
The latched limit strategy means that the current reference will be switched to their pre-defined value once the magnitude exceeds the threshold. Thus, the clipping of the signal can be avoided. The latched limiters in different reference frames are shown in

Fig. 15 Latched limiter in different reference frames. (a) NARF. (b) SYRF. (c) STRF.
However, for the limiters in SYRF and STRF, all current reference coordinates will be switched to pre-defined values once the magnitude exceeds the threshold, which will cause the same injected current in three phases. As a result, there will be a large converter current injected into healthy phase under asymmetric faults, which may cause overvoltage in healthy phases.
Regarding the overvoltage issue of the limiters in SYRF and STRF, the limiter in NARF shows the merits in controlling each phase current independently. Since the current reference of healthy phases will not be switched to the pre-defined value when the phase fault current exceeds the threshold, the overvoltage issue of healthy phases is avoided. However, this conclusion only applies to three-phase four-leg converters. For the common three-phase three-leg converters in three-wire AC power grids, the sum of three-phase output currents is always zero due to the absence of neutral lines. Thus, there will be no zero-sequence fault current in this system under any faults. However, under asymmetric non-ground faults, the current reference may contain a zero-sequence component due to the separate phase current limit of the NARF limiter.
This zero-sequence current reference may cause the control error of the current controller. Under this circumstance, the outer voltage control of each phase will be saturated. And the current reference will increase to its maximum limit. The overvoltage issue of healthy phases still exists.
To further overcome the overvoltage issue of the common three-phase three-leg converters, some improvement methods have been proposed. The first method is the parallel virtual impedance method [

Fig. 16 Current limiting strategies in HBRF [
Most existing studies on current limiting strategies of GFM converters only focus on the performance of current limiting function, and rarely involves the analysis of impact on the transient stability of the converter. In fact, when the fault current exceeds the limiter threshold, the current reference is saturated, which will change the operation mode of GFM converters from voltage source mode to current source mode.
Under this circumstance, a large input error of the PSL during faults may cause a large output frequency deviation. Meanwhile, the power angle of converters will increase continuously, leading to the loss of synchronization. The detailed impact of the current limiting strategies on transient stability will be presented in Section V-B.
Stability analysis is another factor to evaluate the performance of GFM control strategies. Thus, the small-signal and transient stability of GFM converters need to be investigated.
The small-signal stability of converters is defined as the ability of the converters to automatically return to the initial operating state without spontaneous oscillation or aperiodic out-of-step when subjected to small disturbances.
In strong active power grids, it is difficult for GFM converters to regulate the point of common coupling (PCC) voltage, which can easily cause oscillation and small-signal instability. According to the oscillation frequency, the instability phenomenon of GFM converters can be divided into sideband oscillations (low-frequency oscillation) and synchronous oscillations (near nominal frequency oscillation) [
In weak active power grids with large integration of RESs, it can be proven that GFM converters have robust small-signal stability [
In particular, for extremely weak active power grids, e.g., 100% GFM converter based network, the control parameters of the power control loop are regarded as the key factors affecting the small-signal stability of the overall system [
The aforementioned state-space and impedance analysis methods are the commonly-used stability analysis methods. The state-space method is detailed but suffers from high complexity with the increase of system size. Compared with the state-space method, the impedance analysis method only requires the output voltage and current measurements, which has stronger practicability. The impedance analysis method also contains sequence-impedance modeling [
As analyzed in Section IV, when subjected to a large disturbance (i.e., AC fault), the current limiter of GFM converters may saturate and the operation mode of converters will change from the voltage source mode to the current source mode. Therefore, to comprehensively study the transient stability of the GFM converters, both operation modes should be considered.
Under a slight AC grid fault, the converter current will not exceed the threshold and the converters remain in voltage source mode. Thus, the power control loop of GFM converters is still available. According to the analysis in Section III, the active power control loop of non-inertia GFM control is a first-order system. While for inertia control, it is a second-order one. According to the dynamic characteristics of the second-order system, power oscillations may occur if there is no sufficient damping, which will deteriorate the stability of inertia GFM converters [
References [

Fig. 17 Phase portrait of inertia and non-inertia GFM control [
In conclusion, non-inertia control converters have stronger transient stability than inertia control converters. However, due to the absence of inertia support, the non-inertia GFM converters can endanger the frequency stability of the power system. Therefore, the inertia GFM converters are still required in the power system.
To enhance the transient stability of the inertia GFM converters, [
Notably, the above transient stability analysis is performed in a strong active power grid. For weak active power grids, e.g., RESs dominated grid, the system frequency is mainly dominated by the output frequency of converters. During the transient process, the frequency of the PCC will vary following the output frequency of the connected converter. The difference between PCC frequency and converter frequency may be negligible, and the phase angle difference is approximately constant. In this case, the conventional transient stability analysis methods based on the change of to evaluate transient stability are no longer applicable, e.g., the phase portrait method in
To solve this issue, referring to the concept of the center of inertia (COI) in the conventional power system introduced by [
When a serious AC fault occurs, e.g., a three-phase fault, the current limiter will be saturated and the converter will work in current source mode. To analyze the transient stability in current source mode, [

Fig. 18 Virtual power curve of non-inertia control.
Before the saturation of the current limiter, the GFM converter still operates in the voltage source mode. Thus, the power angle curves of the converter during normal operation and faults are similar to those of SGs, which are shown as curves 1 and 2 in
As analyzed above, the essential reasons for the transient stability issues caused by the current limiter can be concluded as: ① the saturation of current limiter reduces the critical clearing angle ; ② the input error of PSL causes the power angle to increase continuously and exceed the critical clearing angle in the power-angle curve.
To overcome these issues, existing improved current limiting strategies have three main methods: ① the method of switching control mode; ② the method of avoiding operating mode change; ③ the method based on power-angle curve [
The method of switching control mode is to switch the GFM control to GFL control mode when the fault is detected, as shown in

Fig. 19 Mode of switching control method.
To avoid the saturation of current limiters, the virtual impedance based voltage limiting strategy and the power limiting strategy have been proposed to reduce the current reference during AC faults.
The virtual impedance based voltage limiting strategy is designed to add a virtual output impedance to reduce the AC voltage reference when the current exceeds the threshold. Thus, the voltage control loop will not wind up and the current reference will decrease, which can avoid the saturation of current limiters [
For the power limiting strategy, the current is limited by reducing the power reference during faults [
In summary, the basic idea behind the methods of avoiding operation mode change lies in reducing the references of active quantity () and reactive quantity ( and ) to maintain the outer loop control available and avoid the saturation of the current control loop.
The method based on the modified power-angle curve is to modify the power-angle curve to satisfy the equal-area criterion through additional control. Reference [
In summary, the grid-tied GFM control can be summarized and compared in terms of control structures, operation characteristics, small-signal stability, and transient stability, etc., as concluded in
In AC microgrids, distributed generators (DGs) are commonly connected to power grids via the GFL converters. Under grid disturbances, the frequency fluctuation caused by low-inertia is the major stability issue in microgrids. To improve the stability of the microgrids, GFM control is promising for grid-tied converters [
Although the GFM converters have superior performance, there are still some noteworthy problems, e.g., the reactive power sharing error between parallel converters caused by the mismatch of output impedance or line impedance, and the power decoupling error caused by the resistive lines in low-voltage microgrids.
Regarding the power-sharing between parallel converters, the converters require sharing load power change according to their respective capacity to avoid overload [

Fig. 20 Illustration of reactive power-sharing. (a) Topology of parallel converters. (b) Q-V droop control of converters.
Assuming there are two parallel GFM converters GFM1 and GFM2 with capacities of and , respectively, the output voltage of two converters can be obtained from the Q-V droop control shown in
(19) |
where and are the output voltages of GFM1 and GFM2, respectively; and and are the droop coefficients. According to
(20) |
Substituting (20) into (19), we can obtain:
(21) |
To share the reactive power according to the converter capacity, the droop coefficients are commonly set as:
(22) |
Referring to (21), the line impedances XL1 and XL2 should satisfy:
(23) |
In fact, owing to different distances from converters to PCC, the line impedance may not meet (23), which will cause reactive power sharing error (). The large power error may result in a large circulating current between converters and even damage the converters. While for active power sharing, since the frequency cannot be affected by the line impedance, active power can be shared according to the converter capacity without error [
To eliminate the reactive power sharing error, the virtual impedance control is regarded as a promising solution [101]-[103]. By introducing large matched virtual impedances in parallel converters, the mismatched line impedance issues can be overcome. The virtual impedance control is shown in

Fig. 21 Illustration of virtual impedance control.
For the power decoupling error, it arouses from the resistive lines, especially in the low-voltage microgrids. According to
To overcome the power decoupling error, the virtual impedance control technology is still effective. By introducing a large virtual inductance, the effect of resistive lines can be ignored [105]-[107]. However, the virtual inductance should be selected appropriately. A large virtual inductance will cause a large output voltage sag, which requires compensation [
The topology of a typical point-to-point HVDC system integrating OWFs is shown in

Fig. 22 Topology of OWF-HVDC system.
Due to different technical requirements of various application scenarios, the adopted GFM controls in OWF-HVDC systems are different from those in AC microgrids. Thus, there are some variants of GFM control in OWF-HVDC systems.
Since the grid-side converter (GSC) of wind turbine (WT) adopts GFL control, the offshore AC grid is equivalent to a passive grid [
With the increasing integration of RESs via HVDC systems, the onshore AC grid has potential instability problems, such as low inertia and low short-circuit ratio (SCR). To overcome these issues, the GFM control can be applied in onshore HVDC converters [
(24) |

Fig. 23 Principle of matching control.
where is the equivalent capacitor of the DC system; and T is the damping coefficient in the DC system.
It can be observed that the DC voltage can reflect the unbalance of power, which is like frequency . Thus, by coupling with , the block diagram of self-synchronization control based on the DC capacitor is shown in

Fig. 24 Matching control coupling Vdc and ωm.
The transfer function G(s) in
(25) |
By coupling and , [

Fig. 25 Matching control coupling and ωm.
In
(26) |
where KJ is the virtual inertia constant; KD is the damping coefficient; and KT is the tracking coefficient of the DC link voltage. The relationship between power deviation and frequency deviation is illustrated in

Fig. 26 Block diagram of power-angle control.
As mentioned above, the WT GSC commonly adopts the GFL control. However, the offshore AC grid may lose its AC voltage sources in some scenarios. Firstly, the offshore HVDC converter may be blocked or tripped under some accidents, e.g., DC cable faults [
In the first scenario, once the offshore converter is blocked, the large power deviation in the offshore grid will cause the saturation of the current integral loop in GSC. And the overvoltage and over-frequency phenomena will occur [
In the second scenario, since the DRU cannot control the offshore grid, the WT GSC should have the ability to form AC voltage independently [
In previous research works, the GFM control is simply implemented by an ideal DC voltage source connected to the DC side of converters. Actually, energy storage systems (ESSs) should be involved in GFM converters to self-synchronize with grids and provide grid support. Thus, the implementation and coordination control of ESSs in GFM converter are the technical focuses in future applications.
Currently, ESSs can be realized through different approaches, such as flywheel ESSs, superconducting magnetic energy storage, battery energy storage (BES), and energy capacitor storage. So far, the promising ESS topology is the hybrid energy storage system (HESS) [
In summary, the selection of energy storage units in an ESS is the first challenge during the design of ESSs, which requires a trade-off among performance, complexity, costs, etc. Then, the coordination of GFM control and ESSs is the other challenge, such as the lack of guidance for parameter design.
In a conventional SG-dominated power system, the main AC line protection strategies are designed according to the fault characteristics of SGs, such as overcurrent-based protection, distance protection, zero-/negative-sequence protections and so on. With the large-scale integration of GFM converters, the fault characteristics will be depended on the converter control, which is quite different from SGs. Thus, conventional protection methods may lose their reliability. For example, the unique current limiting control may cause the malfunction of overcurrent protection schemes during AC faults [
In conclusion, with the increasing proportion of renewable energy, conventional AC line protections are not reliable. It is necessary to construct new AC protection schemes considering the cooperation of converter control and relay protection elements.
In RESs dominated power systems, common GFL control shows poor stability and dynamic performance due to its current source characteristics. As a promising alternative, the GFM control has grid-friendly features, which can work as a voltage source to provide grid support. Considering the control structures, the state-of-the-art GFM control can be divided into VF control, PSL-based GFM control, and VOC-based GFM control.
1) Comparing the small-signal stability of GFM control in different application scenarios, it shows poorer small-signal stability in strong active grids than those in weak active grids. Especially for the GFM converter-based network, the control parameters of the power control loop are the key ones affecting the small-signal stability of the overall system.
2) Considering the saturation of the current limiter, the transient stability of GFM converters in voltage source mode and current source mode are both analyzed. For the converter in voltage source mode, the inertia control shows weaker stability than non-inertia control due to the overshoot of the second-order system. For the converter in current source mode, the saturation of the current limiter reduces the stability margin.
3) By analyzing the applications of GFM control, this paper points out the reactive power sharing error and power decoupling error in AC microgrids. Comparing the variants of GFM control applied in OWF-HVDC systems (includes GSC of WTs, offshore and onshore HVDC converters), these GFM control strategies also show their advantages in VF control, autonomous operation, and strong stability.
4) Nowadays, ESSs with high energy and power densities and accurate coordination control strategies are urgently required for GFM converters. Moreover, due to different fault characteristics of GFM converters, conventional AC line protection methods may be unavailable. These two issues should be handled for the wide applications of GFM converters in the future.
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