Grid Forming Inverters: A Review of the State of the Art of Key Elements for Microgrid Operation

Abstract

In the past decade, inverter-integrated energy sources have experienced rapid growth, which leads to operating challenges associated with reduced system inertia and intermittent power generation, which can cause instability and performance issues of the power system. Improved control schemes for inverters are necessary to ensure the stability and resilience of the power system. Grid-forming inverters dampen frequency fluctuations in the power system, while grid-following inverters can aggravate frequency problems with increased penetration. This paper aims at reviewing the role of grid-forming inverters in the power system, including their topology, control strategies, challenges, sizing, and location. In order to facilitate continued research in this field, a comprehensive literature review and classification of the studies are conducted, followed by research gaps and suggestions for future studies.

1. Introduction

Power electronic interfaced Renewable Energy Sources (RES) continue to replace Synchronous Generators (SG) in the power system. The increase of RES changes the structure and operation mode of electrical power systems due to the fewer SGs and more inverter-based power sources [1]. This change results in a decrease in the system inertia [2,3,4] and an increase in intermittent power generation. In traditional power systems, SGs provide frequency stability via stored kinetic energy, which plays an important role in primary frequency control—increasing the penetration of inverter-interfaced RES results in a reduction of stored mechanical energy. This can result in larger frequency swings which in turn can cause reliability issues, such as tripping of loads and generation [5].

Due to changes in the traditional electric system, increasingly dominated by Distributed Generation (DG) systems based on RES, the concept of microgrids emerges from integrating different kinds of RES [6,7,8]. Depending on the implemented control strategies or operation mode in AC microgrids, inverters can be classified into three groups: Grid-following (GFL) (also called Grid-feeding), Grid-forming (GFM) and Grid-supporting (GS) (also called Grid-conditioning). GFL control regulates the active and reactive output. GFM control is designed for autonomous operation or island mode, represented as ideal AC voltage sources with a fixed frequency. GS control can act both as a voltage and current source, providing basic support [9,10,11,12].

In a 100% inverter-based system, GFM inverters are needed to set the grid voltage and frequency and are mentioned as a critical asset for the power system [13,14,15]. GFM inverters are shown to be able to participate in primary frequency control, which cannot be achieved with GFL inverters [16,17]. For the reliable operation of a GFM inverter, it needs to have access to a dispatchable energy source. As many RES is non-dispatchable, the GFM inverter typically needs to be paired with an Energy Storage Systems (ESS). The sizing and placement of the unit will affect the frequency and voltage regulation capacity of the GFM inverter [18].

Additionally, control systems in power electronic inverters introduce faster dynamics than the conventional (slower) control systems traditionally used for SG [19]. This could be particularly beneficial in islanded power systems with frequency issues where the inverter control can react faster, e.g., help prevent load shedding [16]. On the other hand, faster dynamics can cause issues that need to be addressed. Electromagnetic transients can cause instability in inverter-based power systems [20]. Controller interactions can cause instabilities, e.g., resonance frequency, harmonics etc., several incidents have been reported [21]. In order to mitigate these issues, an increased understanding of grid-connected inverters’ operation, inverter control strategies, and planning, sizing and location are needed for future power system stability.

In the last five years, research of GFM inverters has increased a lot around the world [22,23,24,25,26]. However, this significant increase is still not enough for the large-scale implementation of GFM inverters, once it is a relatively recent concept. Thus, confidence in this field has been gained by operating them in smaller microgrids and island power systems [27,28,29]. Figure 1 illustrates the steps to be studied and the incorporated GFM controls over the years, until this technology is implemented on the main grids.

Due to the expanding interest in GFM technology, many projects and funding have been announced with a big interest in studying the combination of this new technology and old ones; once in the future, the idea is all of them are connected together at the same power system. Some of these GFM projects are summarized in

Table 1. Summary table of GFM inverter projects.

Project	Owner	Location	Year	Voltage Level	Rated Power [MW]/Capacity [MWh]	Applications
Australian BESS [32]	AGL	Australia	2021	MV	250 MW/250 MWh	Electricity Market, Integrated Energy Generation
Dersalloch Wind Farm [33]	SPR	Scotland	2019	MV	69 MW/-MWh	Isoltaed Operation, Integrated Energy Generation
BESS [34]	CBA	Australia	2022	-	150 MW/300 MWh	Electricity Market, Integrated Energy Generation
BESS [35]	Hitachi ABB Power Grids	Australia	2021	-	30 MW/8 MWh	Electricity Market, Integrated Energy Generation
BESS [36]	AEMO and Hitachi ABB	Australia	2020	-	-MW/-MWh	Electricity Market, Mitigate Oscillations
HVDC [36]	-	Scotland	2020	-	1400 MW/-MWh	Black Start

.

Contribution and Organization of the Review

Some reviews on inverter control strategies are already available. In [37] inverter control strategies for parallel operation are reviewed and categorized into master/slave control techniques, current/power sharing control techniques, and frequency/voltage droop control techniques although not based on GFM control [38,39,40].

The present paper, on the other hand, creates a comprehensive picture of the role of the GFM inverter in power systems, including topology, control strategies, current challenges, sizing and location. In order to facilitate continued research in this field, a comprehensive literature review and classification of the studies is conducted, followed by research gaps and suggestions for future research. It is a rapidly growing research field so this paper will focus on the main topics of research.

This investigation is needed not only due to the lack of consistent material in the literature about the topic, but especially considering the growing interest, both academic and industrial, in microgrids, which can be used to emulate larger power systems with high penetration of renewable energy. Therefore, GFM converters have a very important role in smart grid development, and it should be considered that there is still room for research and development within this research topic. In this context, this paper aims at reviewing the role of grid-forming inverters in the power system, including their topology, control strategies, challenges, sizing, and location, in order to facilitate continued research in this field.

The rest of the paper is organized as follows: Section 2 is sub-divided into two parts: describes the operation of power electronics inverters in the connected and island mode of the grid and defines the objectives of the GFM inverters. Section 3 presents different topologies of the GFM inverters. Section 4 describes the control strategies adopted including different layers. Section 5 discusses the island detection used for protection in the system. Section 6 presents GFM inverters in the power system discussed sizing GFM reserve, location, power system stability, load dynamics and grid impedance estimation. Section 7 discusses future directions and challenges for GFM in the power system. Finally, discussion and concluding remarks are presented in Section 8 and Section 9.

2. Background and Definitions

2.1. Categorization of Inverter Operation Mode

Conventional classification of inverters is as: grid-following, grid-forming and grid-supporting [41], as seen in Figure 2.

The GFL inverter operates by exchanging power produced by an energy source, i.e., an RES, to the grid. Most of the time, it has a fast current control, being seen by the AC grid ideally as a controlled current source connected to the grid in parallel with high output impedance. Essentially, the current source should be perfectly synchronized with the AC voltage at the Point of Common Coupling (PCC) requiring a system to estimate the frequency and phase in the PCC, usually, by way of a Phase-Locked Loop (PLL) synchronization technique in order to accurately regulate the active and reactive power exchanged with the grid. The value of the angle of synchronism and the angular frequency of the grid will be used in the control of the system. Reference [42] shows the important state-of-the-art-PLLs algorithms for grid-connected systems.

The GFM inverter, designed for island operation, is controlled to set the voltage amplitude and frequency to form a consistent local grid. This way, it can be represented as an ideal AC voltage source with a low-output impedance. Although synchronization is a characteristic of inverters connected to the grid, GFM power inverters need an extremely accurate synchronization system to operate in parallel with other inverters. Therefore, traditionally, phase reference can be obtained by integrating the set angular frequency. Lastly, GS inverters are designed to provide ancillary services, and control the AC grid voltage amplitude (reactive power) and frequency (active power) of either a stand-alone or inter-connected grid allowing power sharing for power balancing. They support a grid, either alone or with other GS inverters.

Another approach could instead be to consider the services provided to the grid, as it is what is primarily of interest in system analysis. Viewing the inverter from the perspective of the power system, the same can feed the grid, create the grid, provide ancillary services and support the grid, or several of these all at once. In [43] the author differentiates various control strategies based on four criteria: source nature (current or voltage source); grid contribution (e.g., feeding, voltage or frequency support, virtual inertia emulation etc.); synchronization (droop or grid-synchronized); and operation mode (grid-connected or island mode). An important difference between an inverter acting as a Voltage Source (VSI) or a Current Source (CSI) is the transient behaviour. Voltage sources provide power regulation naturally ensuing a disturbance (i.e., fast response time); current sources, on the other hand, react to these disturbances via control dynamics (i.e., longer response time) [16,43].

2.2. Defining Control Objectives for GFM Inverters

As previously discussed, the definitions of various classifications of inverter control strategies are described in the references. Additionally, the operation mode of an inverter can vary depending on the power system. A GFM inverter in a microgrid will operate both in Grid-connected (GC) mode, i.e., in synchronization with the main grid, as well as in island mode. In GC mode, the microgrid voltage vectors will be defined by the main grid and the GFM inverter takes a supporting role in injecting and absorbing power when it can both transition into CSI mode i.e., a GFL inverter [44,45,46] or continue operating as a VSI as in [47], taking on a GS role.

Operating the inverter as a CSI in GC mode is a less complex control structure as it does not require voltage control for the PCC—the voltage is set by the main grid. Although, in GC mode the inverter would still need to inject or absorb the power, either from an RES or to charge/discharge an ESS, which is more convenient as a CSI [46]. On the other hand, the CSI operating mode adds the complexity of having to change operating mode when the microgrid is islanded [48]. If the inverter is operating in a weak grid and needs to provide voltage support, VSI has proven to be more effective in [17].

However, when in island mode, the GFM inverter is responsible for forming the voltage vectors and it is controlled as a VSI in GFM mode [46]. Thus, the GFM inverter will need to have a synchronization system which can both synchronize sufficiently fast with the main grid during re-connection as well as establish the grid frequency in island mode. A general approach towards standardization of the inverters control objectives in a microgrid is presented in [49], where local power-sharing, as well as frequency and voltage control, are proposed for island mode and active/reactive control in GC mode.

For the purpose of this paper the GFM inverter should be able to:

• Form the voltage amplitude and frequency in island operation;
• Operate in synchronization with the main grid in GC mode, either a VSI or CSI GS inverter;
• Be able to detect island and GC operation;
• Remain connected during transient events, i.e.,. have a proper current limiting strategy.

3. Gfm Inverter Topologies

In a microgrid system, to interface RES and ESS to the AC side, an inverter as a power interface is required. On the other hand, the power quality on PCC may be affected as the inverters are operated with Pulse Width Modulation (PWM) techniques. To achieve better power quality, to reduce the size and cost of the output filter, control complexity, reliability and availability, the selection of inverter configuration is the main challenge [50]. In [51], different topologies found in the literature are summarized. The main differences are found according to the number of legs; PWM levels and the type of filters used.

In Figure 3, a general representation of the GFM inverter is shown. It can be applied either in single-phase or three-phase topologies. The most common semiconductor device used in the GFM topologies is the IGBT but Si-MOSFETS could also be an option for some applications [52].

The three-phase inverter has a wide application in systems industries and in the supply of electricity. However, the use of single-phase inverters has grown considerably. One of the advantages of its use is linked to its characteristics and the final cost of production. In [53,54], a Flyback inverter was implemented in an isolated photovoltaic system with a hybrid MPPT method under different environmental conditions.

3.1. Number of Legs

Besides the traditional three legs/three phase inverter [55,56], as can be seen in Figure 4b, other GFM topologies can be found in the literature related to VSI. One of these topologies is the single-phase full-bridge inverter, as seen in Figure 4a, which is the most common single-phase inverter [57,58,59,60,61]. Research on GFM inverters topology with four-leg, Figure 4c, has grown due to their functionalities and advantages in microgrid applications. This configuration is derived from the traditional three legs/three phase inverter, in which the additional leg provides the possibility of managing neutral point currents, which is useful when dealing with unbalanced and nonlinear loads [14,62,63]. Another advantage of the configuration is that you can apply the Space Vector Pulse Width Modulation (SVPWM), which guarantees a lower voltage on the DC-link. On the other hand, the implementation of an additional leg requires additional hardware and more complicated control strategies [63].

3.2. Levels

Inverters can have either two-level (2L) (Figure 4) or three-level inverters, also known as Neutral Point Clamped (3L-NPC), ref. [64], Figure 5. Two-level inverters are the most common [65,66]. In 2L inverters, the two switches on each leg of the inverter must switch complementary, since two semiconductor switch selected on the same leg cannot be connected at the same time, since in this situation the DC source is short-circuited [55]. Each inverter leg, therefore, has only a two-level state. In 3L-NPC the clamping diodes guarantee the current flow resulting in an additional voltage level compared to the 2L inverter [55].

The 3L-NPC inverters achieve a higher power quality performance and a size reduction of filter components for higher power ratings (over 30 kW) compared to 2L H-bridge inverters [64]. The advantage of a multilevel inverter is the smoother waveform and possibility for (several) lower DC-link voltages. There is a trade-off as we increase the complexity of controller circuit and components when we increase the number of levels. Two levels work in most cases, but multilevel inverters could be of interest when low distortion of the output voltage is required.

Inverters able to provide more than two-levels in each phase voltage are named Modular Multilevel Converters (MMC). This technique allows the association of inverters in series and in parallel, which has as its main idea of the division of the total voltage or current of the inverter among other smaller inverters. Furthermore, obtaining intermediate voltage or current levels in certain cases makes it possible to synthesize an alternating waveform with low harmonic distortion. In addition, it is a very used topology when the objective is the application of converters in a high-power system [67].

3.3. Filters

Harmonic constraints in IEEE-519, as well as limitations in size, weight switching frequency, etc., have impacted filter design for grid-connected inverters over the last decade [68]. The three main harmonic filter topologies are L-filter, LC-filters and LCL-filters [69] as can be seen in Figure 6.

One of the earlier filter types is the first-order L filter, shown in Figure 6a. However, besides poor harmonic damping, dynamic performance, and high voltage drop across the filter and bulky design [70], it is not suitable for GFM inverters which require a capacitor filter as they need to be able to supply good power quality for both voltage and current island modes.

An alternative for use with GFM inverters is the LC filter (Figure 6b) a second-order filter that removes high-frequency components from the output voltage of the inverter. To operate as an ideal voltage source the output impedance of the inverter must be kept at zero since there is no additional voltage distortion even under load variation (including non-linear load). To satisfy this condition, the capacitance value should be maximized and the inductance value should be minimized at the selected cut-off frequency of the low-pass filter. However, the higher the capacitance of the filter, the higher the reactive current necessary to establish the output voltage, which increases the required power rating of the inverter switches [71,72]. LC filter is used in island operation in [73,74]. According to [6] the size of an LC filter can be calculated with Equations (1) and (2).

$$L=\frac{V_{DC}}{6f_{sw}\Delta I_{Lmax}},$$

(1)

where $V_{DC}$ is the input DC voltage of the inverter, $f_{sw}$ is the switching frequency of the inverter and $\Delta I_{Lmax}$ is the maximum inductor output current ripple.

$$C=K\frac{S_n}{2\pi f_g{V}_f^2}$$

(2)

where K has an adopted percentage, $S_n$ is rated active power of the inverter, $f_g$ is the grid frequency and $V_f$ is the output phase voltage.

Higher order filters also achieve better harmonic damping at lower switching frequencies with a reduced total inductance [70]. LCL filter (Figure 6c) is used in island operation in [64,75]. Although the LCL filter has a better performance than the L filter and can be manufactured with lower inductance it still introduces resonance to the grid. An algorithm for filter design optimization is proposed in [68]. According to [76,77,78] the design process of an LCL filter depends on parameters of the system such as power rating, inverter input voltage, switching frequency, modulation technique, grid voltage, grid frequency, and other application-dependent factors such as size, cost. $L_1$, C and $L_2$ can be calculated with Equations (3)–(5).

$$L_1=L$$

(3)

$$C=0.05\frac{S_n}{2\pi f_g{E}_n^2},$$

(4)

where $E_n$ is line-to-line RMS voltage output of the inverter.

$$L_2=\frac{\sqrt{\frac{1}{K_a^2}}+1}{{\left(2\pi f_g{E}_n\right)}^{2}C},$$

(5)

where $K_a^2$ is the desired attenuation.

Output filters are adopted to mitigate switching ripples. Besides passive physical components, there are several active filter control strategies. Virtual impedance [79] is implemented to replace coupling inductances which increase the size and weight of the system, it also provides better voltage harmonics compensation compared to passive filters [80]. The virtual resistance (VR) active damping method [81,82] can be adopted instead of a real resistor in the filter to reduce losses while achieving the same advantage in stability. Active damping schemes avoid the use of passive components, which result in reduced losses and size reduction compared to passive damping techniques but it is achieved at the expense of controller complexity.

4. Control Strategies

The control strategy of GFM inverters was developed to keep the system operation stable and efficient. In this way, the control is able to maintain the nominal values of the voltage and frequency and sharing of active and reactive power in the system. When the system is connected to the grid, the voltage and frequency nominal values are imposed by the grid, unlike the islanded mode, in which a control strategy is responsible for voltage and frequency. The hierarchical structure involving the GFM inverters is divided into three levels: current and voltage control, primary, secondary and tertiary control, as seen in Figure 7 [83].

The first level is the inner loop, which includes the voltage control loop and an inner current control loop. This control strategy is known in the literature as cascade control. At this level, the control is responsible for instantaneous tracking of the system’s nominal voltage and power quality issues [85]. At the second level is the primary control with strategies related to system stability, voltage and frequency stability, power sharing in the loads connection (linear and/or non-linear) [28]. The third and fourth levels are the secondary and tertiary controls whose main function is to restore voltage and frequency values. Furthermore, at these levels, the controller determines the ideal operating points of the DG units connected to the system by calculating the values of generation and demand. Furthermore, the design in secondary/tertiary control is based on optimization algorithms [84].

Figure 8 shows a potential island system related to the different layers of control. The normalization stage provides modulation signals. The inner control loop is the device level control related to current and voltage control which aims to stabilize the inverter, e.g., protect from over currents. The primary control provides set-points for the inner controller based on system-level requirements, e.g., ancillary services such as scheduling and dispatch, reactive power and voltage control or providing virtual inertia.

4.1. Linearization

The current control loop generates the modulated voltage to the linearization stage that delivers the modulation signals to the switching stage of the inverter [88]. The modulated voltage is divided to compensate for the inverter voltage gain. The voltage gain depends on the modulation technique used [55]. Among the existing PWM techniques, Sine Pulse Width Modulation (SPWM) and Space Vector Modulation (SVM) have been predominantly used for the efficient operation of the inverter, where SVM has higher voltage gain than SPWM [89].

4.2. Inner Control

An inverter control typically consists of two cascaded control loops, inner current control and an outer voltage control loop. In [15] the inner current loop is excluded for a single voltage control loop to reduce lags/delays and oscillatory response. Although the advantage of the cascaded control structure is the possibility of integrating a current limiter between the voltage and current loop as discussed in [66].

A control strategy that limits and regulates the output current in GFM inverters during faults or load imbalance is needed for the inverter to be able to remain connected and to protect the components in the inverter. The inverter components heat rapidly and thus the current needs to be limited in a short time frame [90]. Transient stability in a highly inverter-interfaced power system is dependent on the inverter remaining connected and synchronized with the grid and when the fault is cleared returning to an appropriate power export. As the GFM inverter from the grid it can not simply disconnect during a fault. Control strategies for voltage support during faults are discussed in [91,92].

Several current limiting methods are proposed in the literature. Instantaneous saturation limits limit the real and imaginary parts of the current separately. It is more appropriate for GFL inverters since when used in a VSI the voltage loop is broken, reducing the two-loop control to a single current control loop [93]. Consequently, the inverter behaves as a constant current source. A disadvantage of the method is that the rated current of the inverter is not used at full capacity since the P/Q ratio remains fixed.

Vector amplitude limitation—also called latched limits—instead limits the absolute value of the current or voltage, as discussed in [66]. This overcomes the drawback of DQ component limiting. Voltage amplitude limitation is used for current limitations in [94]. Static or dynamic limits to the commanded output voltage magnitude and phase within a range around the PCC voltage are compared. Dynamic limits tighten the limits when the current is above the rated value of the inverter and relax them below the rated value. Dynamic limits are shown to significantly reduce fault currents compared to static limits. A current limiting function based on a combination of instantaneous saturation limits and vector amplitude limits for droop-controlled microgrids is proposed in [95].

Another option for current limitation is virtual impedance [96,97,98]. Vector amplitude limitation and non-linear virtual impedance control methods in a GFM inverter are compared in [66]. Vector amplitude limitation is found to work better when the inverter operates in parallel with an SG while the non-linear virtual impedance method provides a smoother transition in stand-alone operation.

A transformation of the controlled parameters is a common strategy to improve a controller’s performance. Therefore, the inner control applied to GFM inverters can be implemented in different reference frames such as:

• Natural reference frame (abc);
• Synchronous reference frame (dq);
• Stationary reference frame ($\alpha$$\beta$).

The abc reference frame is also called a natural frame of stationary reference frame. Linear and non-linear control strategies can be implemented in this frame of reference. Balanced three-phase variables in the natural reference frame can be transformed into two-phase variables in the system rotating reference defined by the d and q axes perpendicular to each other [99]. The synchronous reference frame has an arbitrary position with respect to the stationary system of $abc$ axes. They are related by the angle between the axes a and d. The $dq$ axes rotate in space at an angular speed derived from the angle variation over time. If the stationary vector rotates in space with the same speed as the $dq$ system, the angle between the axes a and d will be constant (the phase angle of the grid voltage should be extracted in this implementation). As a result, the $dq$ components will be DC variables. The stationary reference frame is a type of control scheme where the three-phase electrical quantities are transformed into $\alpha \beta$. The result of this transformation is bi-phase CA quantities (the phase angle information is not necessary) [100].

In [18,63] is presented a classification of voltage and current controllers applied to the inner loop and it is illustrated in

Table 2. Control strategies for inner control in GFM inverter.

Reference Frame	Current Control	Voltage Control
abc	Hysteresis Controller [101]	Repetitive Controller [102]
	Proportional Controller [103]	Proportional Resonant (PR) Controller [103]
	Dead-beat Controller (DB) [104]	DB Controller [105]
		Predictive Controller [106]
		Sliding-mode Controller (SMC) [107]
		Hysteresis Controller [108]
dq	Proportional Integral (PI) Controller [109]	PI Controller [110]
		Linear Quadratic Regulator (LQR) Controller [111]
$\alpha$$\beta$	PR Controller [112]	PR Controller [113]

.

4.3. Primary Control

In a GFM inverter, the primary control strategies have been extensively investigated in the literature. In this paper, the focus will be on decentralized primary control approaches for minimized communication and thus increased robustness of the system. Centralized control approaches introduce more components that can malfunction which entails an increased cost [114]. The most adopted outer control strategies for GFM inverters are discussed in [115]. The most common one is droop control which can achieve island operation as well as power sharing among parallel connected inverters [116,117]. Virtual Synchronous Generator (VSG) has recently emerged and has been explored in several studies [58,118,119,120,121]. It aims at emulating SGs to increase grid inertia. Other new emerging control strategies are, for example, virtual oscillator control [122], dispatchable virtual oscillator control [20,123], and machine matching control [1], which is combining aspects of primary and inner control [19].

4.3.1. Droop Control

Droop control is widely used to enable load sharing in DG networks with parallel-connected inverters, as it does not rely on communication links between the inverters. It is the most common outer control method and is used in nearly all experimentally implemented microgrids [124]. The most common approach for droop control structures is based on regulating the active and reactive power [125]. The conventional droop characteristics are illustrated in Figure 9a,b, where the droop gains ($k_p$ and $k_q$) depend on the properties of the system [126]. Assuming a mainly inductively grid (high voltage grid), the equations for conventional droop control can be written as [18,127]:

$$\left\{\begin{array}{c}\omega ={\omega }_{ref}-k_p(P-P_{ref})\hfill \\ V=V_{ref}-k_q(Q-Q_{ref})\hfill \end{array}\right.$$

(6)

where V and $\omega$ are the amplitude of the output voltage of the inverter, $V_{ref}$ and ${\omega }_{ref}$ are the rated inverter output voltage during no-load conditions, P and Q are the measured feedback signals after they are passed through a low-pass filter (see Figure 9c), $P_{ref}$ and $Q_{ref}$ are the active and reactive power references respectively. According to [88], the low-pass filter in the active power droop and reactive power droop aims to filter the measurement noises. Meanwhile, the active power droop aims to simultaneously filter the measurement noises and emulate the inertia effect of the synchronous machine.

However, another level of complexity is added when the assumption of a purely inductive line is not valid. For example, in distribution networks, the resistive part of the power lines cannot be neglected. An increased R/X ratio also increases the cross-coupling between the P/$\omega$- and Q/V -loops. It also faces other challenges for which various solutions have been proposed in the literature [39,128,129]; the necessity to compromise between load sharing and voltage and frequency regulation [49,130,131,132]; line impedance impact on performance [133,134,135]; difficulty to supply an unbalanced system [136]; harmonic load sharing [75,137]; coupling inductances [79]; dynamic response time [138,139]. In a review of recent studies on droop control techniques, these limitations are addressed and suggestions on how to enhance the droop control design for implementation in a microgrid are presented [128].

4.3.2. Virtual Synchronous Generator

Virtual synchronous generator is an appealing strategy as SG is the dominant frequency regulator in the grid today. The full order model of an SG is a 7th order model which is further described in [140]. This is however deemed unnecessarily complicated [118], as the characteristics of the SG usually sought to emulate is the inertial characteristics and the damping of electromechanical oscillations. The control strategy makes the inverter equivalent to an SG and allows it to have the same frequency droop characteristics as those of an SG.

According to [141] VSG is composed by two parts: electrical part and mechanical part, as can be seen in Figure 10.

Electrical Description of a VSG

The stator windings of the VSG can be regarded as concentrated coils having self-inductance L and mutual inductance M ($M>0$); resistance is $R_s$, as can be seen in Figure 10a. The rotor winding can be regarded as a centralized coil with an inductance value of $L_f$ and a resistance value of $R_t$. The mutual inductance between the field coil and each of the three stator coils varies with the rotor angle $\theta$:

$$\begin{array}{c}{M}_{af}=M_f\mathit{cos}\left(\theta \right)\hfill \\ M_{bf}=M_f\mathit{cos}\left(\theta -\frac{2\pi }{3}\right)\hfill \\ M_{cf}=M_f\mathit{cos}\left(\theta +\frac{2\pi }{3}\right),\hfill \end{array}$$

(7)

where $M_f$ is the maximum mutual inductance between the exciting winding and the three-phase stator winding. The flux linkage of the winding is:

$$\begin{array}{c}{\Phi }_a=L{i}_a-M{i}_b-M{i}_c+M_{af}{i}_f\hfill \\ {\Phi }_b=-M{i}_a+L{i}_b-M{i}_c+M_{bf}{i}_f\hfill \\ {\Phi }_c=-M{i}_a-M{i}_b+L{i}_c+M_{cf}{i}_f\hfill \\ {\Phi }_f=M_{af}{i}_a+M_{bf}{i}_b+M_{cf}{i}_c+L_f{i}_f\hfill \end{array}$$

(8)

where $i_a$, $i_b$, and $i_c$ are the stator phase currents and $i_f$ is the rotor excitation current. Denote:

$$\Phi =\left[\begin{array}{c}{\Phi }_a\\ {\Phi }_b\\ {\Phi }_c\end{array}\right],i=\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$$

$$\left[\widetilde{cos}\theta \right]=\left[\begin{array}{c}\mathit{cos}\theta \\ \mathit{cos}\left(\theta -\frac{2\pi }{3}\right)\\ \mathit{cos}\left(\theta +\frac{2\pi }{3}\right)\end{array}\right],\left[\widetilde{sin}\theta \right]=\left[\begin{array}{c}sin\theta \\ sin\left(\theta -\frac{2\pi }{3}\right)\\ sin\left(\theta +\frac{2\pi }{3}\right).\end{array}\right]$$

Assume for the moment that the neutral line is not connected:

$$i_a+i_b+i_c=0.$$

(9)

It follows that the stator flux linkages can be rewritten:

$$\Phi =L_{s}i+M_f{i}_f\widetilde{cos}\theta ,$$

(10)

where $L_s$ = L + M, and the field flux linkage can be rewritten:

$${\Phi }_f=L_f{i}_f+M_f〈i,\widetilde{cos}\theta 〉,$$

(11)

where $〈.,.〉$ denotes the conventional inner product. The second term $M_f〈i,\widetilde{cos}\theta 〉$ is constant if the three phase currents are sinusoidal (as functions of $\theta$) and balanced.

Assume that the resistance of the stator windings is $R_s$; then, the phase terminal voltages $v={\left[v_a{v}_b{v}_c\right]}^T$ can be obtained from Equation (10):

$$v=-R_{s}i-\frac{d\Phi }{dt}=-R_{s}i-L_s\frac{di}{dt}+e,$$

(12)

where $e={\left[e_a{e}_b{e}_c\right]}^T$ is the back electromotive force due to the rotor movement given by:

$$e=M_f{i}_f\dot{\theta }\widetilde{\mathit{sin}}\theta -M_f\frac{d{i}_f}{dt}\widetilde{cos}\theta .$$

(13)

According to Equation (11) the field terminal voltage is:

$$v_f=-R_f{i}_f-\frac{d{\Phi }_f}{dt}$$

(14)

where $R_f$ is the resistance of the rotor winding.

Mechanical Description of a VSG

The mechanical part of VSG (Figure 10b) is governed by Equation (15), which can be used to provide the voltage phase angle reference for the inverter.

$$J\frac{d\omega }{dt}=T_m-T_e-D(\omega -{\omega }_g),$$

(15)

where J is the inertia of the rotor, $\omega$ is the angular frequency of the VSG, $T_m$ the mechanical torque, $T_e$ the electrical torque, ${\omega }_g$ the angular frequency of the grid, and D a coefficient accounting for the damping torque of the damper windings that occur during transient conditions. $T_e$ can be found from the energy E stored in the machine magnetic field:

$$\begin{array}{cc}\hfill E& =\frac{1}{2}〈i,\Phi 〉+\frac{1}{2}{i}_f{\Phi }_f\hfill \\ \hfill & =\frac{1}{2}〈i,L_{s}i+M_f{i}_f\widetilde{cos}\theta 〉+\frac{1}{2}{i}_f\left(L_f{i}_f+M_f〈i,\widetilde{cos}\theta 〉\right)\hfill \\ \hfill & =\frac{1}{2}〈i,L_{s}i〉+M_f{i}_f〈i,\widetilde{cos}\theta 〉+\frac{1}{2}{L}_f{i}_f^2.\hfill \end{array}$$

(16)

From simple energy considerations (e.g., [143]):

$$T_e={\left.\frac{\partial E}{\partial \theta }\right|}_{\Phi ,{\Phi }_{f}constant}.$$

(17)

Using the formula for the derivative of the inverse of a matrix function:

$$T_e={\left.-\frac{\partial E}{\partial \theta }\right|}_{i,i_{f}constant}.$$

(18)

Thus,

$$T_e=-M_f{i}_f〈i,\frac{\partial }{\partial \theta }\widetilde{cos}\theta 〉=M_f{i}_f〈i,\widetilde{\mathit{sin}}\theta 〉.$$

(19)

Note that if $i=i_0\mathit{sin}\phi$ for some arbitrary angle $\phi$, then:

$$T_e=-M_f{i}_f{i}_0〈\widetilde{\mathit{sin}}\phi ,\widetilde{\mathit{sin}}\theta 〉=\frac{3}{2}{M}_f{i}_f{i}_0\mathit{cos}\left(\theta -\phi \right).$$

(20)

Note also that if $i_f$ is constant (as is usually the case), then Equation (13) with Equation (19) yields:

$$\begin{array}{c}\hfill T_e\dot{\theta }=〈i,e〉.\end{array}$$

(21)

The inertial dynamics of the VSG can be approximated in the Laplace domain by using the p.u. power balance for the SM [140].

$$T_a\ast s\ast {\omega }_{VSG}\approx P_{ref}-P_{out}-k_d({\omega }_{VSG}-{\omega }_g),$$

(22)

where $T_a\left(2H\right)$ is the mechanical time constant which represent the rotor inertia, $P_{ref}$ is the active power reference as in Equation (6), $P_{out}$ is the power output from the VSG, $k_d$ is the damping coefficient. ${\omega }_{VSG}$ is supposed to represent the rotating speed of the VSG and ${\omega }_g$ is the grid angular frequency when the VSG is connected to a strong grid, if it is operating in island mode it will be the frequency reference signal (provided by a secondary controller).

A comparison between droop control and VSG control is performed in [144], showing that the two control strategies present strong similarities and are even equal assuming a constant set-point for the grid angular frequency (${\omega }_g$ in Equation (22)) and a constant reference for the active power ($P_{ref}$ in Equations (6) and (22)). A comparison of the dynamic response of VSG and active power droop control shows better damping and lower overshoot for VSG [145]. Additionally, in [146], VSG shows better frequency stability due to larger inertia compared to droop control which is of interest in low inertia systems such as microgrids. However, the output active power of VSG is more oscillatory. Challenges with VSG are discussed in [120] finding that measurement and computing techniques together with modelling and analysis tools still need to improve for VSG to work on a large scale. The coordination between VSGs and SGs as well as the revision of existing standards is also highlighted as a key issue.

4.3.3. Others

• Dispatchable Virtual Oscillator Control

A recent strategy proposed in the literature is the Dispatchable Virtual Oscillator Control (dVOC) [20], based on Virtual Oscillator Control (VOC) [122]. A GFM control needs to be dispatchable because they are used according to demand, i.e., dispatchable systems do not have a system reference, being necessary for the application of a “Droop” for the generation dispatch, in which the frequency and voltage in the generating units vary according to the generation of active and reactive power [147]. However, in its original form, VOC cannot be dispatched and does not require the explicit calculation of real and reactive power at the inverter terminal [123,148]. dVOC requires only local measurements to induce GFM behaviour with programmable droop characteristics [149]. On the other hand, the VOC does not require frequency as a signal [19]. References [150,151] includes a comparison of droop and VOC. It is a non-linear time-domain controller and differs from droop control as VSG as not rely on phasor approximation [122,152,153]. According to [87,123,154], generating an AC voltage signal based on the pre-defined magnitude and frequency the law of dVOC is given by:

$$\widehat{v}={\omega }^{*}{J}_2\widehat{v}+\eta \left(K(p^{*},q^{*})\widehat{v}-R_2\left(\mathit{k}\right)\mathbf{i}+\alpha \left(1-\frac{\left|\right|\widehat{v}{\left|\right|}^2}{{v^{*}}^2}\right)\widehat{v}\right),$$

(23)

where $\widehat{v}$$={\left[\begin{array}{c}{\widehat{v}}_{\alpha }{\widehat{v}}_{\beta }\end{array}\right]}^{\top }$ is the reference voltage, $\mathbf{i}={\left[\begin{array}{c}{i}_{\alpha }{i}_{\beta }\end{array}\right]}^{\top }$ is the current injection of the inverter, the angle is k: = $ta{n}^{-}1$$\left(\frac{l{\omega }^{*}}{r}\right)$, ($v^{*}$ and $\left|\right|\widehat{v}\left|\right|$ are the reference and measured voltage magnitude), power injection (from its nominal value $p^{*}$) and frequency deviations (from its nominal value ${\omega }^{*}$). Furthermore we have:

$$R_2\left(\mathit{k}\right):=\left[\begin{array}{cc}cos\mathit{k}& -sin\mathit{k}\\ sin\mathit{k}& cos\mathit{k}\end{array}\right],K:=\frac{1}{{v^{*}}^2}{R}_2\left(\mathit{k}\right)\left[\begin{array}{cc}{p}^{*}& -q^{*}\\ q^{*}& p^{*}\end{array}\right].$$

The dVOC does not contain the term of typical oscillator (L,C), in this method a mathematical equation duplicating a conventional oscillator is implemented [154], as can be seen in Figure 11.

• Machine Matching Control

Machine Matching Control [1] is another emerging control technique which aims at creating a coupling between the frequency and active power balance by achieving a crucial coupling between the DC-side voltage and the AC-side frequency. According to [23], these equivalences can be observed through the following equation:

$$\stackrel{SG}{\overbrace{{\dot{\omega }}_{VSG}=\left[\frac{Tm}{{\omega }_{VSG}}-\frac{Te}{{\omega }_{VSG}}-k_d({\omega }_{VSG}-{\omega }_g)\right]\frac{1}{2H}}}\rightleftharpoons \stackrel{2-level-inverter}{\overbrace{{\dot{v}}_{dc}=\frac{i_{dc}}{C_{dc}}-\frac{i_{c_{dc}}}{C_{dc}}-\frac{i_{R_{dc}}}{C_{dc}}}}$$

(24)

In this way, when there is a power imbalance on the AC side of the network; the MC method uses the energy stored in the DC-link bus capacitor to regulate the frequency. On the other hand, the power losses caused by $R_{dc}$ behave as the damping term of the synchronous machine, as can be seen in Figure 12.

• Sliding Mode Control

Sliding Mode Control (SMC) is a non-linear control method. In [13], the robustness to the system parameter variation, fast dynamic response and ability to reject disturbances are obtained applied a control strategy between the inner current loop and a mixed $H_2$/$H_{\infty }$ optimal control in the outer voltage loop.

In this paper, we review six more common grid-forming control methods. The advantages and disadvantages of each strategy are summarized below in

Table 3. Summary of different control methods associated with GFM inverters.

Control Methods	Advantage	Disadvantage
Droop Control [124,156]	Is the simplest implementation of the first order swing equation. Enable several converters to operate in parallel and together to form a consistent local grid. It does not rely on communication links between the parallel-connected inverters.	Higher values of the droop coefficients result in better power-sharing, however, degraded voltage regulation. Conventional Droop control methods have a slow transient response. Inability to handle harmonic load sharing between parallel-connected inverters in the case of non-linear loads.
Virtual Synchronous Generator [118,141]	Is a simple implementation of the second order swing equation. The inertia moment can be modified depending on the operating point of the system.	The traditional VSG control method cannot compensate for the negative sequence component. Therefore, it will cause an unbalanced current and power oscillation.
Dispatchable Virtual Oscillator Control [123,147]	Allows the user to specify the power set point for each inverter, once is dispatchable. In the absence of a set point, dVOC subsumes VOC control, therefore it inherits dynamic characteristics.	Is a recent strategy with complex design.
Virtual Oscillator Control [123,148]	Due to simple design, without conversion between the different reference frame and regulation parameters, the method makes it fast behaviour in the system and acts directly on disturbances.	For not being dispatchable is not required explicit calculation of real and reactive power at the inverter terminal, which makes the method less flexible.
Machine Matching Control [1]	Simple design.	Is a recent strategy and intrinsic switching in the control.
Sliding Mode Control [13]	Robustness to the system parameter variation, used in non-linear system, fast dynamic response and ability to reject disturbances.	Basic SMC configuration produces the chattering phenomenon in control, therefore it is not applicable in real practice. Hence modifications must be applied in order to overcome this problem and improve its performance.

.

4.4. Synchronization System

Synchronization is one of the most important aspects when connecting an inverter to the grid since the control strategies depend on the phase angle of the main voltage to implement the control units [157]. It entails measuring the phase angle of the voltage in real-time and from that input, setting the values for the energy transfer to the grid in order to provide voltage and frequency support even during grid disturbances when the voltage at the PCC is unstable [158]. In the case of the GFM inverters, the frequency is kept at a nominal value by giving a fixed value.

Although synchronization is a characteristic of inverters connected to the grid, it is important to use a synchronization control technique in islanded systems. Even if the GFM inverter follows its own frequency and voltage, in operation transitions there might be a phase jump if a synchronization control technique is not used, causing harmful transients in voltage and current into the system [159]. The GFM inverter must have a system which synchronizes with the main grid in grid-connected mode and a sinusoidal oscillator to generate the voltage reference in island mode [160]. In the past decade, the synchronization methods, Phase-Locked Loop and Frequency-Locked Loop (FLL), which work in the time domain, were the strategies most analyzed and tested [161].

4.4.1. Phase-Locked Loop

Synchronous Reference Frame Phase-Locked Loop (SRF-PLL) [162] is a basic closed-loop synchronization technique and has been used extensively for three-phase systems [163]. The basic features of PLL techniques are described in detail in [164]. SRF-PLL works well in balanced grid conditions, but when the input signal becomes distorted or unbalanced (e.g., during asymmetric grid conditions such as faults or nonlinear loads) the voltage waveform quickly becomes distorted and unstable [165,166]. These disadvantages may be mitigated by different proper modifications of the traditional PLL technique. One example is the Second-Order Generalized Integrator PLL (SOGI-PLL), which generates an orthogonal signal which is filtered without delay and is not affected by frequency changes [167]. Another type of advanced PLL implemented is the Dual Second-Order Generalized Integrator PLL (DSOGI-PLL). To a certain extent, the DSOGI-PLL can be regarded as the combination of both the DSOGI unit and the conventional SRF-PLL unit, which is capable of eliminating both the negative and harmonic distorted components in the grid voltage [157].

4.4.2. Frequency-Locked Loop

The Frequency-Locked Loop (FLL) gives a fast dynamic response with low overshoot. This is beneficial, for example, in the transition between grid-connected and island mode for microgrids. FLL synchronize with the frequency instead of the phase as in the PLL case. Hence, it is less sensitive to phase-angle jumps. As a consequence, it is more stable during transient events such as grid faults and sudden load changes [160]. In the situation of synchronizing the grid frequency and phase when voltage unbalances and frequency variations occur in the three-phase utility grid voltages the alternative is the Dual Second-Order Generalized Integrator—FLL (DSOGI-FLL) [168]. It can be used for three-phase reference voltages—both amplitude and frequency—while also allowing an easy synchronization when re-connecting to the main grid [169,170]. Another type of advanced FLL implemented is the Multiple Second-Order Generalized Integrators—FLL (MSOGI-FLL).

5. Island Detection

Among the necessary protection requirements for the correct functioning of the SEP is the anti-islanding equipment. The interruption or suspension of electricity supply distribution lines is faulty or planned maintenance cases, they form unknown islands due to the difference between the generation of DG units and PCC [171]. The islanding condition, the situation in which part of the system is islanded from the grid and the loads still remain energized by the DG’s local units, is an undesirable situation because it leads to safety hazards for personnel and power quality problems for loads, that can occur in case of unintentional islanding [172]. Due to this, which the islanding operation can cause, IEEE Std 1547-2018 [173] specified a delay of two seconds for the DG unit to detect the islanding situation and isolate itself from the distribution system.

Even though in some countries island operation is not allowed [174], many design and control methods for dual-mode (island and grid-connected mode) inverters have been suggested in the literature [44,45,175]. Although intentional islanding is not common in power distribution networks currently, this operational condition is promising, as can be seen by some proposals in the literature [176,177,178,179]. In this context, if the GDs island operation is allowed, the stability of the system during operation islanding must be guaranteed and the quality indices power requirements must comply with legal limits, besides that, keeping a continuous injection of power and reducing downtime in the electricity supply.

To secure power quality and supply when transitioning to island mode, a fast, precise, and cost-effective island detection method is needed [180]. Islanding detection methods can be classified into two types—a local detection method and a remote detection method [181]. The local method can be divided into passive, active and hybrid methods, where the detection is based on the DG side [182]. On the other hand, the remote methods of detection are based on the utility side [183]. In the passive methods, the system parameters (including voltage, current, impedance, power and frequency) are monitored at the PCC or DG terminals and compared with pre-determined values for islanding detection. The traditional methods are: Rate of Change of Output Power (ROCOP) [174], Rate of Change of Frequency (ROCOF) and Phase jump detection method [184]. Active methods interact with the grid by injecting perturbation signals into the system (including signals variables of voltage, current, harmonic distortion and frequency), and then observing the behaviour of the system. The traditional methods are: Impedance measurement, Active Frequency Drift (AFD), Sliding mode frequency shift, Sandia voltage shift and Sandia frequency shift [185]. Hybrid methods employ two different principles based on active and passive methods, with the aim of removing the limitation of one technique and incorporating the advantages of the other. The traditional methods are: Voltage unbalance and frequency set point [186] and Technique based on voltage and reactive power shift [187]. The traditional remote methods based on communication between utilities and DGs are: Power Line Carrier Communication (PLCC) and Supervisory control and a data acquisition technique [187].

6. Gfm Inverters in the Power System

Sizing, allocation and planning of GFM inverters in the power system are highlighted as one of the main system-level challenges in a future inverter-based low-inertia grid in [155]. In order for a GFM inverter to be able to provide frequency and voltage regulation, a dispatchable energy source is needed. Many of the primary RES are intermittent and thus it is necessary to implement ESS, which can be combined with some kind of RES. System stability is a non-linear phenomenon which depends on the available energy, rate of power and inertia of the component. Due to this, various ESS can have a different impacts on the system stability parameters. For example in [188], ultracapacitors improved the maximum rotor speed deviations better than a Battery Energy Storage System (BESS) while the BESS had a better impact on the oscillation duration compared to the ultracapacitor.

There has been a lot of work undertaken on ESS optimization of placement, sizing, operation and power quality in distribution networks and it has been widely reviewed [189,190,191]. The reviews centre around optimization algorithms, objectives and decision variables as the optimal solution is highly dependent on the investigated system. Attempts at optimization algorithms, such as a genetic algorithm for location and sizing [192,193], have been attempted. A comparison between different works is not feasible as the objectives constraints and decision variables vary [194]. Although high costs are deemed the main obstacle for ESS, it is therefore important to get as many applications as possible from the ESS to justify high investment costs [189,190].

From a GFM perspective, optimization can be based on finding the optimal bus location, power rating and energy capacity. It is shown that the management of storage devices, together with load shedding, is essential for implementing successful control strategies for microgrid operation in island mode [195]. One suggestion is to size the ESS according to the critical loads which can not be shed during unintentional islanding as in [175].

6.1. Sizing of GFM Inverter Reserve

Apart from the power rating of the components in the inverter, the ability of the GFM inverter to provide appropriate frequency support is dependent on the power supply capability (MW rating) and energy storage capacity (MWh rating) of the ESS. Sizing of ESS for frequency regulation is reviewed in [191] and in [196] is discussed the power systems with high shares of RES.

In a more complex power system with a mix of power sources, GFM and GFL inverters and synchronous generators, the reserve allocation is (apart from penetration ratio and per cent droop) also dependent on the load and source location as well as the impedance distribution. Communication would allow for a different distribution of reserves, but the complexity would be enormous in larger systems. Autonomous operation solves the issue of complex communication; however, it depends on the fact that each GFM inverter has the appropriate ESS reserve capacity. An ESS is a large investment and another option which has been discussed in the literature is to unload the RES, i.e., to operate below the available maximum power. This would mean that the RES can participate in frequency control with no ESS or a smaller sized one, which in [197] is shown to be more cost-effective for a photo voltaic system, compared to a BESS for frequency control. Although this would instead increase the power losses as the RES would frequently operate below its maximum capacity.

A case study of the sizing of GFM inverters for transient stability in island mode is discussed in [98]. The sizing of an ESS for synthetic inertial response and primary frequency control is presented in [198], but with a synchronous generator operating in GFM capacity.

6.2. Location of GFM Units

The physical location of DG units can affect the reliability and flexibility in the grid [49,199,200]. There is extensive research carried out on the allocation of Distributed Energy Sources (DERs) and ESS. Common objectives are voltage profiles, reliability and short circuit level. Other important objectives that factor into the decision but fall outside the scope of this paper are energy cost, copper loss and emission reduction [194].

Optimal inertia placement is discussed in [201]. They find that the resilience of the power system is highly dependent on the location of the disturbance and the placement of the virtual inertia unit, not simply the total system inertia. During a fault, the distance between the fault and the GFM inverter (main source) has been shown to affect the transient stability of the system [188]. If the fault occurs close to the main source, the system shows more instability.

One of the differences between inverter-based and traditional generations is that the first one can be interconnected into the transmission system, as well as dispersed and interconnected within medium and low voltage distribution systems. This is not the case with the synchronous generation system which is usually connected to the transmission system. As a result, stability analysis and control requirements are expanded [202].

6.3. Power System Stability

Power system stability is directly related to the physical properties and control responses of large synchronous generators. However, in recent years, with the insertion of renewable sources, the electric power system is changing its characteristics due to the significant fraction of generation with an interface with power electronics [203].

Inverter-based resources do not provide any inertial energy to the power system. Therefore, as synchronous generators are replaced by inverter-based resources, the system inertia and, therefore, damping, are reduced, making the risk of frequency oscillations greater (Figure 13).

Therefore, the way the network operates must be planned and operated differently in order to maintain system reliability. According to [202], a solution to the problems caused by the reduction of synchronous generators is the use of GFM inverters together with a headroom operation, which would allow the neutralization of both the loss of inertia of the system and the control of primary frequency provided by synchronous generation. In this way, GFM inverters would autonomously detect the frequency oscillation and adjust their energy injection during a low-frequency event [202].

The operation of an electrical grid without the presence of synchronous generators requires the use of GFM inverters. In this way, the grid system must have a minimum amount of participation of GFM inverters to make it possible to obtain stability in the electrical grid once the GFM have a limited dynamic regarding the frequency and voltage amplitude variation. The rated power of the GFM inverters will need to be greater than a percentage of the overall rated power of the grid-connected inverters. A reduced version of the Irish system was simulated, and the results showed that the generation mix has to be larger than 30% to keep the system’s stability composed of inverters [29]. No equation was found to calculate the rated power percentage of GFM related to grid-connected inverters in different types of electrical systems, so this value is only valid for the Irish system.

When talking about power stability, the concepts of voltage and frequency are one of the most important, which consist of keeping the voltage and frequency of the system within a limit defined in the norm. Figure 14a shows the control and response scheme associated with frequency dynamics and control. Figure 14b shows future control stability.

6.4. Load Dynamics

The quality in the supply of electricity is basically characterized by the voltage waveform of the components of a three-phase system, which can be affected by the frequency variation, voltage variation (long or short duration), harmonic distortions, voltage fluctuations and unbalanced voltage and current. Many of these phenomena are commonly caused by load dynamics [204].

The use of nonlinear loads causes the appearance of harmonics, which are injected into the electrical system. Even though assuming that the electrical system is linear, it will have voltage drops in each of the harmonic frequencies, causing distortions in the voltage waveform. Furthermore, harmonic circulating in the distribution system increase electrical losses in the system [205]. It is known that the presence of unbalanced three-phase loads connected to a three-phase system causes an unbalanced voltage since the demand currents in the three phases are not symmetrical, i.e., they are not equal in magnitude, nor are they out of phase by 120°. Consequently, when the currents are summed up, they do not cancel out (addition of phasors), and a finite amount of current passes through the neutral conductor [206]. However, with diverse components and uncertain characteristics, it is difficult to accurately model the loads for stability studies [207].

In a stand-alone system, to maintain the stability and performance of the system with imbalances and nonlinearities in loads, compensators are used. In most applications, three-leg inverters are used, but since they are not able to control the zero sequence currents generated by non-linear and unbalanced loads, a $\Delta$-Y transformer is inserted after the inverter, making it possible to obtain a four-way system, wires enabling the supply of single-phase and three-phase loads, balanced and unbalanced load. Another topology of three-leg inverters used is the connection of a fourth wire to the DC link dividing it, making it possible to connect single-phase and three-phase loads, balanced and unbalanced. However, this application produces voltage ripples on the DC link, requiring large capacitors. A fourth leg added to the inverter allows control of the negative sequence current without affects the DC link, as can be seen in Figure 15. In addition, a four-leg inverter also eliminates the need for an output transformer in low voltage systems [206].

7. Future Directions and Challenges for GFM

Different topologies and configurations are being defined in microgrid projects with alternative applications of GFM inverters [114,208,209].

However, several challenges have to be resolved in order to be able to replace synchronous machines with GFM inverters at the transmission level. Among these challenges are: development of hardware, software and controls for network formers, standardization of inverter models, system integration with high penetration of renewables, energy storage, distribution protection, fault path, subtransmission protection, stability analysis, networking capabilities for black-start, dynamic islanding topology solutions, unintentional islanding in distribution classifications, evolution of detection and communication systems, system cost analysis, economic, economic dispatch, etc. [202].

To meet with the loads, the voltages of the support system and, among other challenges, the standards that are relate to inverters connected to the electrical network have to be revised, since the properties of synchronous generators differ from those of inverters. Likewise, the creation of standards for systems in island operation must be rethought, since grid-forming inverters can operate autonomously in isolated networks [202].

8. Discussion

As the structure of the power system changes with increased inverter-based penetration, GFM inverters are considered an important aspect to provide power system stability. The GFM inverter needs to be able to operate in parallel with other GFM inverters using autonomous control which is robust against grid topology and transient events. There are several GFM inverter control strategies proposed in the literature to achieve these targets.

Droop control is the most common control strategy; it can regulate voltage and frequency as well as facilitate the inverter participating in power sharing. VSG is also well studied in the literature. It is similar to droop control under certain conditions and regulates the frequency using virtual inertia, and some studies suggest it provides a better damping and dynamic response compared to droop control. It can, however, not regulate voltage and typically a droop control is implemented for this purpose. Another control strategy, which has recently been proposed, is dVOC, which is a time-domain control strategy and is shown to react faster and with less transient overshoot compared to droop control which is dependant on local measurements. Machine matching control aims to create a coupling between the frequency and active power balance by connecting the DC-side voltage with the AC-side frequency. Sliding mode control is a non-linear control method. In addition to the chosen control strategy, the location and sizing of the GFM inverter is also found to affect the inverter’s impact on the overall power system stability.

In island mode, GFM inverters can form the voltage and frequency of the grid. When the GFM inverter operates in a microgrid it also needs the ability to synchronize with the main grid when the microgrid is connected, therefore many GFM inverters discussed in the literature have dual-operating modes and island detection schemes. Since the GFM inverter operate as a voltage source, it does not have an innate limitation of the output current; it is therefore important to have a current limiting method to prevent over-currents, particularly during transient events. Another challenge with a highly inverter-based power system is the complexity of controlling a large number of inverters.

9. Conclusions

The studies on the operation of GFM inverters so far focus mainly on GFM inverters in microgrid configurations. The response of the GFM inverters to transmission system topology changes (e.g, transmission line dynamics) can have a destabilizing effect on inverter-based power systems and the gains of the inverter control have to be chosen with this in mind. Thus, the operation of GFM inverters in interaction with larger power systems requires more detailed studies. The sizing and location, as well as the control of a GFM’s primary energy source and GFM compatibility, need more research. Additionally, the stability and synchronization of interconnected systems of GFM inverters (e.g., disconnection and re-connection to the main grid, operation under unbalanced and nonlinear load conditions) as well as the filter design for inverters in dual operating modes, need further attention for GFM inverters to be able to replace SM in future power systems.