Frequency and Voltage Control Techniques through Inverter-Interfaced Distributed Energy Resources in Microgrids: A Review

: Microgrids (MG) are small-scale electric grids with local voltage control and power management systems to facilitate the high penetration and grid integration of renewable energy resources (RES). The distributed generation units (DGs), including RESs, are connected to (micro) grids through power electronics-based inverters. Therefore, new paradigms are required for voltage and frequency regulation by inverter-interfaced DGs (IIDGs). Notably, employing effective voltage and frequency regulation methods for establishing power-sharing among parallel inverters in MGs is the most critical issue. This paper provides a comprehensive study, comparison, and classification of control methods including communication-based, decentralized, and construction and compensation control techniques. The development of inverter-dominated MGs has caused limitations in employing classical control techniques due to their defective performance in handling non-linear models of IIDGs. To this end, this article reviews and illustrates advanced controllers that can deal with the challenges that are created due to the uncertain and arbitrary impedance characteristics of IIDGs in dynamics/transients.


Introduction
Electric power generation in conventional power systems includes serious issues such as high energy losses in power generation and transmission, high generation costs, carbon emissions, environmental concerns, and high investment costs for grid expansion [1].Thus, distributed generation units (DGs) that include renewable energy resources the power deficit from the grid and trades the excess power generated in the MG with the grid [8].In the islanded mode, the lack of access to the (stiff) grid has led the MG to perform autonomous voltage and frequency control [9]; moreover, power-sharing among DG units (for load tracking) should be implemented to maintain the productionconsumption balance [10].
The frequency and voltage should be set autonomously in the islanded MG; however, power electronics-based inverters that interface DG units to the (micro) grid are used, which requires new paradigms in voltage and frequency regulations [11].Notably, employing effective voltage and frequency regulation methods for establishing powersharing among parallel grid-forming (GFM) inverters is the most important problem.Since there is a compromise between voltage/frequency regulation and power-sharing that imposes power quality issues and stability challenges, it is vital to ensure the MG's dynamic stability and the desired performance while realizing power-sharing through voltage/frequency regulation.
Therefore, the control architecture of an MG is implemented based on hierarchical control, including the primary, secondary, and tertiary levels [12][13][14][15][16]. Energy management is executed at the highest level, i.e., tertiary control, according to different power generation technologies and power ratings for minimizing operation costs with maximum efficiency and high reliability [17,18].Furthermore, at the tertiary level, optimal setpoints are determined depending on the needs of the host power system grid (e.g., for voltage support, frequency regulation, etc.) [19,20], and this control level is responsible for coordinating the operation of multiple microgrids that interact with each other in the system [21][22][23].The lowest level of hierarchical control is the primary control [24,25].Primary control is responsible for controlling the critical variables of the MG (voltage and frequency), and power-sharing as well as power injection [26][27][28][29].The secondary controller is responsible for power quality and compensates for the voltage and frequency deviations caused by the primary control by restoring their values to nominal values while preserving the power-sharing accuracy [30][31][32][33].
The main focus of this article is on the primary control level, which provides various control methods for voltage and frequency regulation/control and power-sharing.The review of control techniques is based on their dependence on the communication link and is divided into two categories: communication-based and decentralized methods without communication links [34][35][36].In this review, various types of conventional classical control methods based on communication links, without communication links, and also construction and compensation-based techniques are explained, and the advantages/disadvantages of these methods are clarified.
The power system components, such as generators and transmission lines, are modelled by their equivalent impedances, which are used for system and stability analysis.The impedance characteristics of the inverters are also used for modelling, analysis, and design; however, in inverter-dominated MGs, the impedance characteristics of the GFM and grid-feeding (GFD) converters arbitrarily change due to disturbances and are uncertain in transients, e.g., in current limiting and fault ride-through (FRT) transients.Therefore, large disturbances created in the MG cannot be accurately modelled and, in general, the mathematical model for power electronics is highly non-linear and uncertain due to the fast operation and very small time scale.Therefore, using classical controllers in the context of inaccurate models of inverter-dominated MGs would not be effective, and advanced (non-linear) methods are needed for impedance shaping or to deal with uncertainties associated with modelling.This motivated us to review and add some advanced control techniques that can be used in inverter-based MGs.The classification of the control strategies for the inverter-based MGs is illustrated in Figure 1.The remainder of the paper is summarized as follows.Section 2 presents a brief discussion of communication-based control strategies for the parallel inverter.Control strategies based on non-communication, i.e., droop control, are described in Section 3. Construction and compensation control techniques are presented in Section 4 to cover the shortcomings of the droop-based controllers.Section 5 discusses advanced control techniques that can deal with the uncertainties and non-linearities of IIDGs in dynamics/transients.Section 6 discusses future trends related to MGs.Finally, Section 7 concludes the paper.

Communication-Based Control Strategies for Parallel Inverters
The communication-based control methods require a power management platform or supervisory control and data acquisition (SCADA) operation.These control methods are employed to provide power-sharing and voltage control, and their main advantage is eliminating the requirement for a secondary controller.The supervisory control receives information from all inverters and tries to maintain a balance in power-sharing between the inverters.In this regard, several different control techniques based on communication methods, such as the concentrate control method [33,[37][38][39], master-slave control method [40][41][42][43], and current distribution control method [44][45][46], are discussed in the following subsections.

Concentrated Control
This control scheme cannot operate without a centralized controller to acquire the synchronization signals, as shown in Figure 2. The load current can be shared when the phase-locked loop (PLL) is used to ensure synchronization between the grid-feeding (GFD) voltage source converter and the grid [33].This reference current needs to be assigned to all parallel-connected inverters by a high bandwidth communication link (HBWCL).
In [15,22,35,[47][48][49][50], a communication-based control technique is presented so that the current sharing in the transient and steady state can be maintained using this technique; however, the centralized current controller cannot manage harmonics and prevent circulating currents among parallel inverters.To address this problem, high bandwidth communication is necessary; while it reduces reliability and expandability, it provides stable power-sharing in transient and sustained modes and constant voltage and frequency regulation [30,51].
Control schematic of the concentrated/centralized communication-based control [33].

Master-Slave Method
In the master-slave control strategy, one inverter acts as a master and the remaining inverters act as slaves.The master-slave control strategy diagram is illustrated in Figure 3.As suggested in [21,41,52], this technique is mainly based on the oscillating master/dedicated master.In the dedicated master, one inverter works in the voltage control mode and other inverters run in the current control mode.The master unit specifies the reference current for the slave units so that the slave unit follows the reference current.Yet, if the dedicated master suffers a single point of failure, it will significantly affect the stability of the whole system.In [21], the master oscillating technique is suggested to overcome this weakness.The master depends on the maximum inverter active power flow.This proposed technique improves reliability and increases the power-sharing accuracy, but it may lead to synchronization errors [53].
Slave Unit dq abc dq abc Figure 3.The control structure of the master-slave control [33].

Current Distribution Control
Communication-based current distribution control strategies are employed to accomplish voltage regulation and power-sharing among parallel inverters, where power quality is a concern [16,49,54].These techniques do not require a central control unit while keeping the output voltage amplitude and frequency close to the nominal values [35].Hence, these control strategies can limit system reliability, flexibility, and scalability, as well as increase system costs due to the expensive and vulnerable communication link [33].This technique can be further classified as depicted in Figure 4.It can be categorized into current limiting, average current sharing, circular chain control instantaneous current control, one cycle control, and weighted current distribution control techniques.(1) The current limiting control is designed to reduce harmonics and avoid power quality issues while limiting the output current of the inverter.Novel currentlimiting control techniques are suggested to improve power quality and reduce harmonic current [55,56].(2) The average and instantaneous current control techniques are based on inter-unit communication, in contrast to the master-slave control method.This technique requires reference synchronization for the voltage and current at the point of common coupling (PCC) to have better current sharing and voltage regulation.
Figure 5 shows the structure of this control method.Yet, this technique reduces the flexibility and reliability of the system [16].
(3) The one-cycle control method combines a vector and bipolar operation with an extra simple communication link among the parallel inverters.Thus, the circulating current among parallel inverters can be reduced.This control technique has advantages, such as constant switching frequency, no reference calculation, simple system wiring, and lack of need for multipliers, while providing more flexibility [4,57].(4) The circular chain control method, which is also known as the 3C method, is illustrated in Figure 6.In this technique, each unit is connected in a circular configuration that uses internal current control to track the inductor current of consecutive parallel inverter units for achieving equal current distribution among the parallel inverters [31,44].(5) The weighting current distribution control technique has been proposed to achieve current sharing among inverters with different power ratings.It gets a weighted output current by simply adding a simple circuit for each inverter.In this technique, each inverter has current and voltage controllers for a fast dynamic response, stability, and an improved weighted current controller for achieving current sharing among the inverters [45,58].

Summary of Communication-Based Control Strategies
The merits and demerits of communication-based parallel inverter control techniques are summarized in Table 1.• Dependence of the system on the master unit.

Current Distribution Control
• Symmetrical for each unit • Constant voltage and frequency

Non-Communication-Based Control Strategies for IIDGs in Autonomous MGs
The decentralized control techniques used for GFM voltage source inverters are based on the conventional droop control technique known as wireless methods [59].The droop-based GFM inverters are responsible for regulating the fundamental variables of MGs (i.e., voltage and frequency) and controlling the output power of IIDGs.The classification of droop-based control methods is shown in Figure 1.In this section, each of these methods is explained in detail.

𝑓 − 𝑃 and 𝑉 − 𝑄 Droop Controllers
The conventional droop method originates from the principle of the (physical) power balance in synchronous generators in bulk power systems.The imbalance between the prim over mechanical power to the generator and the electromagnetic field (due to output active power) causes a change in the rotor speed, which appears as frequency deviations.Similarly, a change in the output reactive power leads to a change in the voltage magnitude.The frequency-power droop control method is inherent to the operation of conventional DG units, such as synchronous generators, and it can be artificially created for IIDGs.
According to Figure 7, the relationship between frequency − active power and voltage−reactive power can be extracted as follows.The power flow from the inverter to the grid can be mathematically modeled as the following equations [35]. where where  and  represent the line impedance and phase angle;  and  are the inverter's output voltage and phase angle;  and  are the active and reactive power; and  is the AC bus voltage, respectively.
Pcc ∡ =  +  ∡0 ∡ In medium and high-voltage grids,  is dominantly inductive, so the resistive part of Equations ( 1) and ( 2) can be neglected.Therefore,  gives a small phase difference between E and V (sin  ≈  & cos  ≈ 1) [60] and thus Equations ( 1) and ( 2) can be rewritten as According to Equations ( 3) and ( 4), the active power can be controlled by the frequency (as the frequency variation dynamically controls the power angle), and the reactive power is controlled by regulating the voltage magnitude, as shown in Figure 8 [61].Therefore, in droop-based MGs, the active and reactive power of IIDGs can be controlled by adjusting the droop coefficients [62][63][64].Consequently, the voltage and frequency droop control for medium and high-voltage grids can be defined according to Equations ( 5) and ( 6) [65].
The active and reactive droop characteristic values must be obtained with high accuracy because the stability of the system depends on them [66].
Remark 1.The  −  droop reveals an acceptable performance in terms of powersharing accuracy and dynamic response (even in grids with a low X/R ratio where the grid impedance is not purely inductive) since the sensitivity of the power-to-phase angle is very high (proportional to  2  ⁄ ) [67]; however, the problem is with the reactive powersharing via the  −  droop, as the voltage is not a global variable and changes over the power network.Furthermore, the cross-coupling between two  −  and  −  is high when the X/R ≈ 1 , which may make the system unstable if the grid impedance is relatively low regarding the power rating of the IIDGs.

Reverse Droop Control
The conventional droop controller is mainly suitable for high-voltage grids based on pure inductive line impedances.Given this, for low-voltage distribution grids, where the line impedance is dominantly resistive, the conventional droop is not effective.Thus, the reverse droop control technique is used based on pure resistive line impedance at lowvoltage distribution grids.Therefore, the active power is controlled by a voltage magnitude, whereas the reactive power is controlled with the phase angle or frequency [68].Hence, for the low-voltage grids when the inductance is negligible and the line impedance is entirely resistive, bringing Equations ( 1) and (2) into consideration (sin  ≈  & cos  ≈ 1) yields: Equations ( 9) and ( 10) can be displayed as the slope of the line in Figure 9.
Remark 2. The problem with the  −  droop control is that the sensitivity of the power to the voltage difference at the grid is not high (proportional to the voltage magnitude), and thus it reveals a very poor dynamic response; moreover, the voltage is a local variable that is against the accurate active power-sharing in the resistive grids.These two issues are critical for IIDGs to avoid reaching overload/current conditions.Therefore, the inverse droop has not been a popular solution and the power system community prefers to use the conventional  −  and  −  droops by addressing their shortcomings (i.e., stability concerns in low-voltage grids with low X/R ratio and inaccurate reactive power-sharing).Impedance shaping is the most promising solution, which is discussed in this paper in the advanced controller section.
The simplicity of the droop method is the main advantage, where communication isn't necessary among IIDGs.Therefore, high flexibility, plug-and-play, modularity, and reliability can be guaranteed, however, there are challenges for researchers.These challenges include the lack of proper harmonic current sharing, performance dependency on grid impedance, poor power quality due to voltage/frequency deviations, and the problem of circulating a reactive current among IIDGs, voltage regulation, and reactive power-sharing [69,70].In complementing and overcoming the disadvantages of the conventional/reverse droop method, improved droop methods are discussed in detail in the next section.

Modified Droop Control
To solve the shortcomings of conventional droop and inverse droop control mentioned in Sections 3.1 and 3.2, modified droop control is introduced, which can be categorized as follows.

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Power angle droop control

Power Angle Droop Control
This technique shares stable power among inverters without frequency excursions [71].Nevertheless, stability conditions under variable loads have not been studied.In [72], high gain angle droop control ensures proper load sharing, especially in weak system conditions; however, it harms the overall stability of the system.The angle droop control technique has been investigated in detail in [61], namely angle droop without communication to power-sharing between IIDGs, and secondly, angle droop control with minimum communication for enabling the feedback controller to establish economic power-sharing, considering a resistive power grid; however, the angle droop method needs an accurate time frame, e.g., GPS, for synchronization of the inverters, which is the major drawback.

Virtual Flux-Based Technique
Researchers have proposed a novel modified control strategy in [73] and [74] that will act based on the direct virtual flux droop method.The active power, phase angle, and reactive power are proportional to the flux for increasing the controller's ability.Figure 10 shows the expressed control scheme, in which by controlling the flux amplitude and phase angle (instead of the output voltage of the inverter), the appropriate power-sharing can be achieved.Consequently, this control technique is simple and more effective and does not require pulse width modulation modulators and multi-closed loops; however, the fault ride-through of the inverter is questionable and it is not clear how current limiting is implemented.MG performance and stability are mainly based on power control strategies; however, the power control techniques have a slow dynamic response and stability issues.Given this, the VI-based droop characteristics have been proposed in [75,76], wherein this strategy can provide a fast dynamic response and improve system stability under load variation; however, this strategy is valid for small-size inverters with a limited current capacity, mainly because the voltage is not a global variable [77,78].The researchers in [79] have proposed voltage-based droop control techniques, as shown in Figure 11.The  −  droop is categorized into two control loops, namely the droop control loop Vg-Vdc and P-Vg droop and a constant power band control loop.Firstly, power needs to be balanced between the generated power or input DC source, and absorbed power at the AC grid side can be balanced by using the Vg/Vdc droop control loop of the GFM voltage source inverter.AC power changes are based on the Vdc (DC link) voltage changes of power sources.
As for the inverter, the DC side power converter nominal voltage and the grid power converter nominal voltage are  , and  , , respectively, with  > 0.
Secondly, the  −   droop with a constant power band is used to limit the significant deviation of the AC voltage [35,76].
where   ,  , , and b are the power droop gain, rated active power of the converter, and width of the band, respectively.The width of the band is mainly based on the nature of the renewable energy sources.This droop technique adjusts the output power of the IIDG unit [80].The constant power band relies on the characteristics of the generator to avoid frequent changes in the power of given IIDGs.

Complex Droop Control
In distribution grids that contain feeders with a complex impedance, neither the resistance nor the reactance of the line can be neglected relative to each other.In some cases, the line resistance may be equal to or even greater than the line reactance, creating a feeder system with a low X/R ratio.Compared with the L-type or R-type droop, the RLtype droop inherently considers the coupling between the active power and reactive power; however, the power decoupling performance under complex impedances is more difficult [81].Therefore, the inverters are seen as RL-type inverters, and Equations ( 1) and (2), which describe the complex network, are rewritten as follows With small changes in the power angle and voltage magnitude in this control technique, imbalance and instability occurs.The control technique in [82] has been presented and can simplify the equations for active and reactive power coupled with complex impedance and provide an acceptable dynamic performance in low-voltage MGs when   ⁄ ≈ 1.In this case, the droop functions can be expressed as Instability and overcurrent due to large circulating transient currents originate from the oscillatory behavior and the phase angle shift among the inverters.To overcome this challenge, the authors in [83] and [84] presented the droop/gain control technique by adding integral terms and derivatives at the low-voltage distributed droop controller, which resulted in achieving the desired dynamic response.The equations for this control technique are given in Equation ( 17) and (18).
However, this is only suitable for low-voltage MGs.If the distance between the inverters increases, then the characteristics of the line impedance have to be changed from a lowto medium voltage distributed grid, while the current peak could appear due to the initial phase error [79].

Summary of Decentralized Droop-Based Control Techniques
A comparison between conventional and modified droop controllers is given in Table 2, and the merits and demerits of the modified droop control techniques are briefly mentioned in Table 3.

Construction and Compensation Droop Control Method
Modifying some of the droop-based control techniques and taking into account more limitations has led to the creation of construction and compensation droop control techniques, which are among the most effective solutions for IIDGs at the MG level.The classification of the control structure is shown in Figure 1.In this section, the details of each method are explained.

Common Variable
To achieve accurate sharing of active and reactive power among parallel inverters, a common variable-based compensation droop technique is used.This technique works in a short-distance inverter-grid connection.In [104][105][106], a reactive power-sharing scheme is presented, which considers the controller to adjust the common load bus voltage, and the equation for this strategy is represented in Equation (19).
where   is the voltage magnitude of the inverter as the control input,   is the integral gain,   is the reference signal, and   is the common load voltage magnitude at the input.The control input is generated by an integral controller that will regulate the common load voltage to track a reference signal voltage, where the reference signal gives, where  * is the linear function of a local reference signal and reactive power output,   .The steady-state gain is the reciprocal of   , which takes into account the steady-state stability.The     should be near zero to make sure that the injected reactive power is at a minimum.Thus, steady-state Q (MVAr) is calculated as: As in (21), the reactive power control will not be affected by the MG's parameters.
Likewise, [106] has proposed a control technique for improving the active power-sharing control by introducing the integral controller as given in ( 22), but with the addition of the input power,   .

Signal Injection Loop
The signal injection droop compensation technique is mentioned in [23,97,98], and the method of this control approach is displayed in Figure 12.Among the benefits of this approach, the load sharing is suitable for linear, and non-linear loads, and automatic control of system parameters, such as the line impedance mismatch or inverter parameters.Furthermore, this approach has drawbacks, such as having high-frequency components that must be measured and constructed, greater complexity, deviation of the output voltage amplitude, the creation of inter-harmonics, and resonance caused by an injected signal can increase transmission loss and deteriorate the power quality [99].

Power Compensation Loop
A modified control strategy including a power compensation loop, which significantly reduces the reactive power-sharing error, is investigated in [107,108], and the diagram of this control method is presented in Figure 13.In this method, it detects reactive power-sharing faults by injecting real reactive power coupling disturbances that are activated by low bandwidth synchronization flag signals from the central controller.Accurate reactive power-sharing is achieved by manipulating the coupling of the real injected transient reactive power and employing an integrator.The reactive powersharing accuracy could be improved when the reactive power-sharing control error is calculated by inserting an active power transient coupling term and rectifying the errors by using a slow integral, which can be described as, where the integral gain   should be the same for all DG units.Figure 13 shows the diagram of the proposed control strategy, where  0 and  0 are the measured powers before the low pass filter (LPF).When compensation is not active, the conventional  −  and  −  droop methods perform power-sharing.When compensation comes into play, the traditional droop control is replaced by ( 9) and (10).In this diagram, the G unit is the soft compensation gain, and it is proposed for the compensation method, which can avoid excess power fluctuations and overcurrent during the compensation transient.The gain G slowly increases to the nominal value at the beginning of each compensation.After compensation, G slowly returns to zero, meaning that the droop controller slowly returns to a normal droop control mode.

Virtual Impedance Loop
In this section, the virtual impedance loop technique is presented as the latest approach to improve the droop technique and overcome the limitations of line impedance (   ≈ 1) [38,[109][110][111][112][113][114][115][116][117].As a result, in this approach, by adding virtual inductance, a fast droop response has been achieved to decouple active and reactive power coupling, stabilize the frequency adjustment, and maintain the active power balance with minimal physical line losses [51].Consequently, the expected voltage can be modified as, where   ,   ,  * , and   are the virtual impedance, output current, under no-load condition output voltage, and reference generation voltage, respectively.Figure 14 shows the purely inductive virtual impedance technique   =   [49], which proposed the behavior of the controller without considering the steady-state frequency changes and the transient stability issue, so the transient response is not satisfactory.Recently, modified virtual output impedance methods have been proposed to improve transient response and harmonic current sharing [53].In [24], to overcome the limitations and drawbacks of [118], integral terms are added to the conventional virtual impedance loop after the reference signal generator, resulting in an improved transient response.Approaches [24] and [118] are not applicable for online uninterruptible power supply (UPS) due to incorrect current distribution.According to the limitations mentioned in [119], to improve harmonic power-sharing, a decentralized controller with virtual resistive output impedance has been used in both linear and non-linear load conditions.The techniques mentioned so far are classified as classical control techniques.These control techniques are only designed for particular conditions, and these methods use control loops/PI-based controllers or other linear controllers.

Advanced Control Strategies for Inverter-Based IIDGs
Today, MGs have experienced extensive progress in integrating renewable energy resources, energy storage systems, and diverse loads.As a result, classical control techniques are ineffective for dealing with the limitations that develop in MGs and have disadvantages, such as:

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Distorted/imbalanced conditions and weak grid connection: Inefficiency of classical control techniques under these conditions and eliminating/countering the uncertainties generated in the upstream grid.

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The effect of the line impedance on power-sharing accuracy: Ineffectiveness of droopbased control methods and interaction of PI-based control loops under low X/R ratio line impedance conditions.

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Non-linear loads: In MGs, loads are topologically unknown and parametrically uncertain, and can be a source of unknown dynamics that cannot be accurately modeled by classical controllers.

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Lack of flexibility for impedance shaping of IIDGs: The GFM and GFD voltage source converters require different impedance characteristics for stable operation under different grid conditions; however, there is a lack of a sufficient degree of freedom for impedance shaping in conventional methods.
As a result, advanced control methods have been presented to solve the challenges raised, as presented in the sequel.

Robust Control
Conventional controllers based on PID/PI/PR controllers are inefficient for overcoming disturbances caused by internal and external factors, and, as a result, the stability of the MG has been affected [120].Robust control techniques are the best solution for overcoming the uncertainties, disturbances, and non-linear nature of RESs/loads/power electronic equipment.A robust controller should be able to consider all the parameter variations for efficient MG consolidation under different operating conditions.In [121], a robust  ∞ controller is evaluated for AC voltage and frequency regulation in an MG under different loading conditions, and its performance is compared with a droop control method.This method proposed a multi-level control, including a droop control loop, voltage control loop, current control loop, and inductance-capacitorinductance filter control loop and coupling circuit.In [122], a supervisory controller is proposed to control secondary AC voltage and frequency in autonomous AC MGs to overcome possible limitations.In [123], an improved droop-based control scheme is developed to solve the stability problem and increase the power-sharing accuracy in the grid-connected MG that was investigated.A robust MG stabilizer (inspired by the power system stabilizer (PSS)) has been proposed in [124], which dampens low-frequency oscillations (LFO) in MGs that are provoked by the interaction of droop controllers through the power network.
In the grid-connected operating mode, the grid synchronization is performed by a PLL.The basic drawback of PLL is instability following disturbances/faults in the upstream weak grid [125,126].To deal with this defect, a robust PLL is proposed in [127].This controller improves the stability margin of the system under FRT transient conditions and is robust against grid/MG impedance variations, weak grid connections, and distorted grid conditions.Furthermore, the robust PLL reveals a better performance in frequency estimation when being used in the synthesis of virtual inertia and frequency support.The block diagram of this control method is shown in Figure 15.

Fuzzy Control
A fuzzy control system is an approach that applied  − ℎ rules to implement fuzzy logic to the fuzzified inputs (in the (0,1) interval instead of 0/I) to deal with uncertainties in the system parameters.Therefore, this approach is effective for making the controller adaptive by linking the output (system response) to the wide range of input variables [128].In [129], a Takagi-Sugeno (TS) fuzzy control is proposed to regulate the AC voltage and achieve accurate power-sharing in decentralized island microgrids.In [130], fuzzy control is proposed to improve the frequency response of a wind turbine system, which requires an accurate model of the tilt angle control, wind storage system, and wind speed.In [131], a fuzzy controller is applied at the secondary level to reduce voltage and frequency deviations during disturbances.With the development of MGs and the use of multi-bus MGs, droop-based controllers for power-sharing have been affected by line impedance [132,133].Due to the low impedance of power lines, the conventional droop is inefficient; as a result, a fuzzy-based consensus control is introduced in [134] to deal with this inefficiency, see Figure 16.

Sliding Mode Control
Control techniques based on proportional-integral (PI), proportional resonance (PR), and predictive deadbeat (DB) have not performed well in non-linear systems such as microgrids.As a result, sliding mode control (SMC) has been developed in non-linear systems.This control approach has advantages, such as robustness and impermeability against parameter changes and noise, as well as the ability to determine the sliding mode in a limited time [135,136].In [137], an SMC-based control approach is employed to control the AC voltage and frequency in an islanded AC microgrid with an arbitrary topology.In [138], a fractional-order SMC provides terminal voltage and frequency regulation of a DER unit, which also exhibits robustness against unbalanced and/or distorted load currents.A decentralized SMC strategy is proposed in [139] to improve the stability, power-sharing, and robustness to non-linear and unbalanced loads in microgrids.In [140], a robust efficient decentralized voltage/frequency control strategy is presented, which increases power-sharing and system stability under the influence of unbalanced loads.This control strategy includes three separate controllers based on SMC and Lyapunov theory to improve active/reactive power-sharing and voltage regulation.It has been investigated that GFM inverters reveal arbitrary/resistive impedance at current limiting, which makes the MG unstable at FRT transients [141].To address this issue, sliding mode control is proposed in [141] to make the MG system securely pass FRT transients.The proposed controller slides the control system of the GFM inverter on a stable manifold that bypasses unstable modes.

Impedance Shaping
The arbitrary output impedance behavior of each of the GFM/GFD voltage source converters in the islanded/grid-connected conditions and in critical situations, such as disturbances/faults-which leads to instability-cannot be solved by conventional PIbased nested control loops [124,142].In this light, the impedance shaping method is critical for meeting the required impedance characteristics in isolated/grid-connected conditions, and to establish decoupled  −  and  −  loops by avoiding crosscoupling between them, which can highly affect the stability of the MG.The impedance shaping method is a promising solution for identifying and improving the dynamic performance of IIDG units in modern power systems.Yet, only relying on classic control loops in the control system of inverters is not effective for dealing with serious power grid problems.To address this issue and facilitate flexible impedance shaping, a new control structure has been proposed in [143,144], which is called the optimal voltage regulator (OVR), see Figure 17.The proposed controller is based on the optimal state feedback control and optimality refers to the optimal impedance shaping based on the powersharing control target and the grid requirement.Furthermore, the proposed controller is able to work in both the GFD (grid-connected) and GFM (islanded) modes without the requirement of a dedicated PLL in the grid-feeding mode and change in the control structure in the transition from GFD to GFM modes.18-20, to evaluate the importance of impedance shaping and defect performance of the conventional PIbased GFM and GFD power converters in low-voltage and weak grids.In Figure 18, the performance of the GFM power converters in an islanded MG with a low X/R ratio of line impedance (X/R = 1) is shown.After the error/disturbance caused by microgrid islanding, PI-based control techniques are not able to deal with the disturbance.As a result, the MG's variables (frequency and active and reactive powers) have become unstable and unbalanced.Furthermore, in the GFD mode of operation of the converter with high output impedance, this control technique is ineffective in dealing with current limitations, the results of which can be seen in Figure 19.The control structure based on impedance shaping prevents the collapse of network variables thanks to its flexible functionality as the GFM and GFD converter.The results can be seen in Figure 20.

Summary Heuristic/Meta-Heuristic Algorithms
In addition to the advanced methods, heuristic/meta-heuristic algorithms are used according to their advanced features for solving the model in advanced control techniques, which are mentioned in Table 4.

Future Trends in the High-Performance Inverter-Based Grids
Further investigation of the challenges will help to improve the voltage and frequency control strategies of IIDGs in MGs.The views and challenges mentioned below can provide the basis for the design of the AC MGs with advanced control strategies.

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The dynamics of variable loads still affect the stability of IIDGs in two operating modes, connected/islanded, at the MG level; as a result, unsolved challenges remain for achieving voltage and frequency stability at the MG level [151,152].

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The contemplation of sensitivity issues with non-linear droop controller-based strategies [153] is necessary.

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Increased reliability in droop control systems based on robust controllers leads to accurate sharing of active and reactive powers among high penetration levels of IIDGs.With the development of research in this field, more solutions can be obtained [154].

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Droop methods with the aim of cost optimization, in which non-linear control methods and droop gains are variable, are open research fields, and the dynamic stability of the MG system under the influence of variable droop gains should be evaluated.Considering that the droop coefficients are adaptively changed based on the cost function using real-time optimization techniques, different computational and traceable optimization techniques are needed to increase the reliability of microgrids [152].

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The accurate power-sharing from islanded to grid-connected modes has been investigated with hybrid control and non-linear loads [155,156] and using intelligent methods [157].

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The performance and stability of droop controllers in MGs with a networked topology, as stressed in [158][159][160], need further investigation and analysis.

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Impedance shaping has been effective in stability analysis and inverter-based DER control design, including advanced control techniques.Due to the defective performance of virtual inductance loops [143,161], control methods for IIDG units are presented in [143,144].In these methods, a degree of freedom of the optimal impedance-shaping mechanism is considered.Adaptive impedance shaping considering changes in MG structure due to plug-and-play, load changes, grid reconfiguration, and transients from islanded to grid-connected modes are among the open topics in these methods.

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The FRT transients modeling, stability analysis, and stabilization have recently attained significant attention [141,162] and are a future trend.

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Considering the different applications of battery energy storage systems (BESS) in MGs, their impact on MG economic dynamics [163,164], the different time scales of BESS application, and their joint dynamic performances in steady state, modified, and advanced droop mechanisms are needed for BESS control.

Conclusions
In this paper, a technically profound overview of the strategies of communicationbased centralized methods, decentralized droop-based control, construction and compensation techniques, and advanced controllers for voltage and frequency control for power-sharing among parallel inverters in AC MGs was presented.Among the advantages of the communication link-based control techniques is the appropriate powersharing, but they possess low reliability and redundancy.The decentralized droop-based control techniques are another class of control methods that are superior to the communication-based method.Among the advantages and disadvantages of this class of controllers are flexibility, modularity, higher reliability, slow dynamic response, poor power quality, and lack of proper power-sharing due to uncertainty in the output impedance.Given this, to address the problems of droop control techniques based on communication/non-communication links, construction and compensation control techniques have been proposed.Considering the limitations of conventional control techniques in dealing with uncertainty and non-linearities, advanced control methods have been proposed to handle these challenges.Furthermore, in the last section, considering the development of power systems, the future trends in voltage and frequency control-especially in power-sharing control techniques-were discussed.

➢Figure 1 .
Figure 1.Classification of control techniques for parallel inverters.

Figure 4 .
Figure 4. Classification of the communication-based current distribution control strategy.

Figure 7 .
Figure 7. Equivalent circuit of a DG unit connected to the common AC bus.

Figure 15 .
Figure 15.The structure of the robust controller scheme: (a) block diagram representing the control loop of the robust PLL; (b) generalized robust PLL diagram [127].

Figure 18 .Figure 19 .Figure 20 .
Figure 18.Unstable power-sharing performance among three PI-based GFM inverters in a meshed MG with low X/R ratio: (a) frequency; (b) active power; (c) reactive power.

Table 1 .
The merits and demerits of communication-based parallel inverter control techniques.

Table 2 .
Comparison between conventional and modified droop controller.

Table 3 .
Merits and demerits of non-communication-based droop control techniques for parallel inverter.

Table 4 .
[150][148][149]heuristic algorithms used in advanced control techniques.Particle swarm optimization (PSO) is used to solve the design problem of various MG components and controller parameters as an optimization problem formulated to increase MG stability that leads to improved powersharing and voltage and current stability[147][148][149].4.An artificial intelligence-based (Icosφ) controller is proposed for powersharing and power quality improvement in smart MG systems, where various uncertainties caused by load changes, MG battery state of charge, and power tariffs based on power availability in MGs are considered[150].