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A Comprehensive Review of Control Strategies to Overcome Challenges During LVRT in PV Systems

Due to the high penetration of grid-connected photovoltaic (GCPV) systems, the network operators are regularly updating the grid codes to ensure that the operation of GCPV systems will assist in maintaining grid stability. Among these, low-voltage-ride-through (LVRT) is an essential attribute of PV inverters that allows them to remain connected with the grid during short-term disturbances in the grid voltage. Hence, PV inverters are equipped with control strategies that secure their smooth operation through this ride-through period as per the specified grid code. However, during the injection of reactive power under LVRT condition, various challenges have been observed, such as inverter overcurrent, unbalance phase voltages at the point of common coupling (PCC), overvoltage in healthy phases, oscillations in active, reactive power and dc-link voltage, distortion in injected currents and poor dynamic response of the system. Several strategies are found in the literature to overcome these challenges associated with LVRT. This paper critically reviews the recent challenges and the associated strategies under LVRT conditions in GCPV inverters. The drawbacks associated with the conventional current control strategies are investigated in MATLAB/Simulink environment. The advanced LVRT control strategies are categorized and analyzed under different types of grid faults. The work categorizes the state-of-the-art LVRT techniques on the basis of the synchronization methods, current injection techniques and dc-link voltage control strategies. It is found that state-of-the-art control strategies like OVSS/OCCIDGS provides improved voltage support and current limitation, which results in smooth LVRT operation by injecting currents of enhanced power quality.


I. INTRODUCTION
During recent years, the penetration of distributed generation (DG) based grid-connected photovoltaic (GCPV) systems have exponentially increased [1]. This is due to its various advantages such as low generation cost, zero carbon emissions, enhancing the grid reliability and alleviating the network capacity. On the other hand, the sporadic power generation of the DG PV system can jeopardize its normal operation leading to voltage variations, increased energy and reactive power losses. Moreover, these PV systems are operated within a specified voltage range, which helps maintain grid stability [2]. Hence, the network operators continuously The associate editor coordinating the review of this manuscript and approving it for publication was B. Chitti Babu .
develop and update the grid codes to minimize the adverse effects of distributed generating resources, like PV, wind, etc., on the power system [3], [4]. Among these grid codes, LVRT is an essential requirement among grid-connected PV inverters. Fundamentally, LVRT is a control action in GCPV inverters that allows them to stay connected with the utility during a short-term sag in the grid voltage [5]- [8]. Under normal operating conditions, the PV system is operated at maximum power point and injects active power into the grid [9]- [12]. However, during LVRT, the large GCPV systems connected at higher voltages inject reactive power to maintain grid stability [13], [14]. Moreover, small capacity GCPV system is generally connected to a low-voltage network and their inverter control action is designed in such a way to give preference to the injection of active power under FIGURE 1. LVRT Grid codes in different countries [34].
LVRT due to the small X/R ratio of the low-voltage network. To limit the scope of this paper, the authors have reviewed the control strategies that give preference to the injection of reactive power under LVRT.
LVRT requirement is essentially a voltage versus time characteristic, which shows the minimum period required to withstand a voltage drop level. The LVRT of certain grid codes requires an immediate revamping of active and reactive power to the pre-fault values after the voltage has recovered to its nominal value. Other LVRT grid codes require an increased reactive power injection by PVs to provide voltage support to the grid. The operators demand this grid support due to the increasing PV penetration level in the transmission network. Many countries like Germany, China, UK, Italy, Denmark, etc., are continuously updating their LVRT grid codes based on their grid infrastructure to cope with the rapidly expanding use of renewable energy resources, as shown in Figure 1 [15]. According to the German code, the PV inverter should ride through the fault for a maximum of 0.15s under severe faults, i.e., when the grid voltage has dropped to zero. This code allows the PV units to remain connected without any nuisance tripping if the voltage at the point of common coupling (PCC) has been able to recover to 90% of its rated value within 1.5s after a fault. On the other hand, China allows an additional time of 0.475s when the PCC voltage reaches 20% of its rated value. Therefore, the PV units should remain connected for China if the PCC voltage reaches 90% within 2s of its collapse.
Moreover, in German code, if the grid voltage is between 90% -50%, the DG unit should inject reactive current as a function of voltage sag. If the voltage sag is more than 50%, the DG unit should inject 100% of its reactive current [16]. Chinese grid codes are less stringent as compared to German. The former allows a commensurate reactive power injection when the grid voltage is between 90% -20%. If the grid voltage falls below 20%, the PV inverters should inject 100% of their reactive power, as shown in Figure 2. This distinction between the German and Chinese grid codes is apparently due to the difference in penetration levels of PV units within these two countries. The Chinese codes may also need revision as the level of distributed generation is on a constant rise in China. The grid codes for various countries under high PV penetration are reviewed in [17], [18]. Grid codes for reactive power injection [16].
Several methods are present to enhance the fault ridethrough (FRT) capability of PV systems by using additional components like energy storage systems (battery energy storage systems, capacitor energy storage systems), fault current limiters and static synchronous compensator (STATCOM) [19]- [21]. However, the energy storage systems do not consider the injection of reactive current and FACTS devices like STATCOM only inject reactive power to support the grid during fault [22], [23]. Moreover, the overall cost and complexity of the system increase because of the addition of these hardware components. Recently, the researchers have also used computational methods like fuzzy logic control (FLC) and optimization techniques, which help in adjusting the inverter's power references and improve the performance of the inverter controller [24]- [27].
Though these computational methods are efficient and help address the FRT problems, they enhance the system's complexity. However, in light of the issues mentioned above, the modified inverter control techniques are gaining more attention to meet the grid code requirements at a lower cost and better accuracy [28], [29]. Further, the use of these modified inverter control techniques also aids in improving the system speed and its dynamic response [30].
During recent years, several review articles have shone a light on the LVRT capability of GCPV systems [16], [18], [21], [31]- [49]. However, none of the articles have provided a detailed classification and critically reviewed the recently developed modified inverter control techniques for the LVRT capability of PV systems. This paper highlights the differences among the recently published review articles in Table 1 to show the existing research gap clearly.
The proposed work will provide the readers with an exhaustive review of the various control strategies proposed to date that overcome challenges present during LVRT and provide avenues for future work. The key novelty features of the manuscript are: Certain key objectives are identified that are required during the LVRT condition. Finally, recently developed modified control techniques are classified based on these objectives.
The proposed work has provided a critical review of the various inverter control strategies and their advantages and potential shortcomings. VOLUME 9, 2021  Since the outer loop dc-link voltage control plays a vital role during LVRT condition, an exhaustive comparison between the recently developed dc-link voltage control strategies along with their potential demerits is presented.
The rest of the paper is organized as: Section II discusses the challenges associated with LVRT. Section III critically reviews the recently developed current control techniques. Section IV classifies and compares various dc-link voltage control strategies along with their merits and demerits.
Section V provides a discussion on the future aspects of the control strategies during the LVRT condition. Finally, in Section VI, the conclusion of the work is encapsulated.

II. CHALLENGES UNDER LVRT
As previously discussed, appropriate reactive power is injected into the grid based on the specified grid code to ensure grid stability. The LVRT control action is initiated when the grid voltage drops below its rated value [50]- [54].
Hence, a fast and reliable dip detection method is essential under LVRT condition. This dip detection is usually accomplished by a phase-locked loop (PLL).
Synchronous reference frame-based PLL (SRF-PLL) is commonly used for measuring the RMS values of the grid voltage during normal operating and under balanced fault conditions. A major drawback within the SRF-PLL is its inability to accurately detect the grid voltage dip under unbalanced grid faults.
This inability stems from the presence of negative sequence components, which are rich in higher-order harmonics under unbalanced sag conditions. Several researchers have suggested improvements in conventional SRF-PLL by mainly focusing on increasing the noise elimination capability in the conventional SRF PLL, thereby enhancing their filtering capability [55]- [59].
In [55], a double decoupled synchronous reference frame (DDSRF) based PLL is proposed to detect fundamental frequency positive sequence (FFPS) component of grid voltage under polluted grid conditions. The technique employs a double synchronous reference frame (DSRF) with a decoupling cell which enables the decoupling of positive and negative sequence components. In [56], an improved phase-locked loop (EPLL) is proposed, with enhanced frequency flexibility. The EPLL exhibits superior performance even under frequency divergence of the grid voltage from its theoretical value. This EPLL has a high tolerance to noise and harmonics as compared to the conventional PLL. In [57], a moving average filter (MAF) is used to eliminate the ripples caused by negative sequence components for extracting the fundamental frequency positive sequence (FFPS) component in the synchronous domain. Another attractive approach for synchronization, namely, multiple complex coefficient phase-locked loop (MCCF-PLL), which uses complex coefficient filters (CCFs), is presented in [58]. The CCFs have an inherent property of sequence separation, and therefore, these do not require a sequence separation method or decoupling cell. In [59], a dual second-order generalized integrator (DSOGI) based synchronization technique is presented that evaluates the positive sequence component of grid voltage and eradicates the harmonics during polluted conditions. Although, PLLs with enhanced filtering capability possess various advantages in accurately detecting the sag in grid voltage, but at a cost of increasing the overall complexity of the system [68]. To overcome this, researchers have formulated control strategies that eliminate the use of PLL [69]. In [70], a control strategy is proposed to overcome the problems related to power quality. As the control technique does not use a phase-locked loop, the system complexity is significantly reduced thereby improving the dynamic response of the system. Another control strategy is suggested for GCPV inverters without using PLL showing satisfactory performance under symmetrical and asymmetrical voltage sag conditions [71]. The proposed control scheme is relatively simpler and free from jitter. A LVRT technique that uses an arbitrary angle instead of a PLL is proposed in [72].
The positive sequence of this angle is obtained by integrating the angular frequency of the grid.
Once a sag in the RMS value of the grid voltage is detected, efficient current reference generation strategies are formulated based on the grid codes [73]. The use of current control strategy helps in limiting the magnitude of the injected currents, mitigating the double grid frequency oscillations within the injected power, providing voltage support at the PCC and ensuring that the injected currents are of low total harmonic distortion (THD) [74]- [76].
Another important task during LVRT under unbalanced fault is to design an efficient dc-link voltage control strategy to prevent inverter shutdown due to overcurrent and to ensure reliable operation of the inverter. This control strategy also prevents overvoltage in the dc-link capacitor during power imbalance occurring under unbalanced fault conditions [77], [78].
To summarize, under LVRT it is essential to quickly detect the voltage dip, initiate appropriate control action to limit the inverter current amplitude as well as determine precise active/reactive power references to provide voltage support at PCC and to ensure power balance. This entails a carefully designed dc-link voltage controller to avoid overvoltage in the dc-link capacitor. Due to the importance of LVRT in PV inverters which contributes toward grid stability, a broad categorization of LVRT techniques is done, based on the following key objectives: a. Quick dip detection (PLL): Advanced PLLs, notch filters or repetitive controllers are generally used to quickly determine the sag in grid voltage. Several other advanced PLLs have been proposed and reviewed in [60]- [67]. Hence, in this paper, the importance and key attributes of various PLLs which are widely used under LVRT condition, are briefly described in section II.
b. Current control strategy: Formulation of a current control strategy is vital: to limit the amplitude of the injected currents, to provide voltage support and to mitigate double grid-frequency oscillations in injected powers under balanced and unbalanced fault conditions. In this paper, the current control strategies are further classified based on specific objectives that are essential under LVRT.
c. DC-link voltage control: The dc-link voltage control helps in reducing the oscillations in the dc-link capacitor which is detrimental to capacitor life [79]. Moreover, this outer loop control also helps in maintaining the power balance between the dc and ac side. A detailed classification and discussion on the recently developed dc-link voltage control strategies are also carried out ahead.

III. CURRENT REFERENCE GENERATION (CRG)
According to the grid code, a well-designed current reference generation (CRG) must be formulated to deliver the required power components (active and reactive) to the grid [80]. Under normal grid conditions, the objective of the current reference generation strategy is to improve the quality of the power components being injected into the grid VOLUME 9, 2021 that can be easily delivered by conventional CRG strategies. However, the conventional CRG strategies such as instantaneous active-reactive control (IARC), average active-reactive control (AARC), positive-negative sequence control (PNSC) and balanced positive sequence control (BPSC) require modifications to ensure continuous operation under unbalanced grid faults [81]. This is because these conventional CRG strategies do not provide additional support such as current limitation, voltage support, which are necessary during LVRT operation [82]. It can be observed from Figure 3, that all conventional CRG strategies result in high peak current amplitude under unbalanced grid fault as no provision is made for limiting the peak amplitude of the inverter currents. This can trigger the overcurrent protection devices of the inverter and can result in the disconnection of the PV system. Hence, under unbalanced grid voltage conditions, the major task of the CRG technique during LVRT: is to provide voltage support at the point-of-common coupling (PCC) and to limit the amplitude of the injected currents to ensure continuous safe operation of the PV inverter [83], [84].
The importance of the voltage support, current limitation and dc-link voltage control strategies is explained under two types of faults: unbalanced and balanced grid voltage conditions. In the first case, the strategies are tested under an unbalanced grid voltage condition by reducing the grid voltage of phase A to 0.5pu at t = 0.35s. In the second case, a balanced phase drop in the grid voltage is considered by reducing the phase voltages to 0.5pu at t = 0.35pu.
Since this paper focuses on comparing the recently developed CRG strategies under LVRT conditions, therefore, this article majorly classifies these techniques into two categories based on the objectives stated above in Section II. The current reference generation strategies that are discussed in the following sub-sections can be implemented in stationary, synchronously rotating or natural reference frame as shown in Figure 4.

A. VOLTAGE SUPPORT STRATEGIES (VSS)
According to LVRT grid codes, maximum and minimum voltage limits at the PCC must be specified to ensure the stable operation of GCPV systems under fault conditions. By injecting reactive power, the CRG strategies provide voltage support and help PV systems stay connected to the grid. Under balanced grid voltage sag, the voltage support strategies should be designed to equally raise the voltages in all phases. This is achieved by increasing the positive sequence voltage amplitude at the inverter side. Additionally, the phase voltage equalization is another important objective under unbalanced sag conditions. This is so because an equal rise in the phase voltages can trigger overvoltage protection, as the healthy phase voltage can easily surpass the maximum permissible voltage limit. By increasing the amplitude of negative sequence voltage, phase equalization is achieved.
The efficient control of the ratio of positive and negative sequence components in the reference currents helps in providing voltage support at the PCC under both unbalanced and balanced types of faults, as shown in Figure 5 Hence, a current reference generation strategy that provides voltage support at the PCC should be carefully formulated.
The following sub-sections discuss the recently developed voltage support control strategies during LVRT under balanced and unbalanced grid faults. 1) FLEXIBLE VOLTAGE SUPPORT CONTROL (FVSC) [85] In [85], [86], a flexible voltage support current reference generation control strategy is proposed. The voltage support is provided by increasing the positive sequence voltage and minimizing the negative sequence of grid voltage, simultaneously, to reduce the unbalance factor (n) in (1).
where, V + = v + 2 α + v + 2 β ,is the positive sequence and is the negative sequence voltage at PCC evaluated under stationary reference frame.
For flexible voltage support, the proposed strategy injects both positive and negative sequence voltage into the grid by adaptively varying their magnitude, under unbalanced grid conditions. The injected reactive current references are formulated as in (2) and (3).
where, k + and k − are the control parameters to balance the positive and negative sequence voltage components, respectively, and k − = 1 − k + . Taking the value of k + close to 1 will increase the injection of the positive sequence component and result in a constant injection of the negative sequence component. This aids in raising the voltage profile in each phase, under balanced voltage sag. On the other hand, under severe voltage sags, the value of k + is chosen close to zero to achieve injection of a constant positive sequence and to decrease the magnitude of the negative sequence component resulting in voltage equalization at the PCC. The positive and negative sequence voltage amplitudes at PCC, are dependent on the voltage drop due to grid side inductance as in (4) and (5), respectively.
where, ω is the grid angular frequency and Q ref is the reactive power reference. L g is the grid side inductance, whereas, V + g and V − g are the positive and negative sequence component of the grid voltage, respectively.
Although the proposed strategy provides enhanced voltage support, evidently it demands the calculation of grid impedance. Moreover, within this strategy, the maximum allowable inverter current that can be injected into the grid has not been considered.

2) VOLTAGE SUPPORT CAPABILITY IN DISTRIBUTED GENERATED INVERTERS (VSCDGI) [87]
A strategy is proposed in [85] to equally raise the phase voltage without designing a voltage control loop. This is a major drawback as the reference reactive power Q ref and the control parameter k + are calculated without the knowledge of PCC voltage. As previously discussed, for stable operation the maximum and minimum values of phase voltages should be within the limits as per the specified grid codes. To this effect, a method is proposed in [87] which employs a voltage control loop to determine the values of Q ref and k + in (6) and (7), respectively.
where, V * p and V * n are the references for positive and negative sequence voltages at PCC, respectively. V * p and V * n are determined from the type of sag characteristic based on the lower (V * L ) and upper (V * H ) boundary values, where, . V gp and V gn is the positive and negative sequence component of the grid voltage, respectively.
To provide better voltage support, the reactive reference currents are formulated, in αβ reference frame as in (8)- (9).
where, k + is the balancing factor which can take any value between 0 and 1.

3) REACTIVE POWER CONTROL OF DISTRIBUTED GENERATION INVERTERS (RPCDGI) [88]
In [87], the strategy was primarily focused on providing voltage support under symmetrical voltage sags. In [88], this limitation was overcome by proposing a control strategy that works well under unbalanced grid voltage conditions too. The technique increases the positive sequence voltage component by injecting the positive sequence reactive power through the inductor which in turn increases the PCC voltage by a voltage variation of ωL g I + . On the contrary, to reduce the negative sequence component of the PCC voltage, the negative sequence reactive power is injected which reduces the PCC voltage by ωL g I − . By simultaneously, raising and reducing the positive and negative sequence voltage, respectively, the voltage unbalance is minimized. The CRG equations to flexibly regulate the positive and negative reactive power are given in (10) and (11).
Further to ensure the PCC voltages stay within the limit, the positive and negative sequence reactive power references are formulated in (12) and (13), respectively.
where, V + * and V − * are the desired positive and negative sequence voltages, respectively and are further evaluated by carefully determining the maximum and minimum value between phase voltages.

4) FLEXIBLE VOLTAGE SUPPORT WITH IMBALANCE MITIGATION IN DISTRIBUTED GENERATION INVERTERS (FVSDGI) [89]
In [89], the injection of reactive current by using a threelevel T-type inverter for medium switching frequency and low-voltage applications, has been considered. The proposed strategy employed DDSRF-PLL to extract the positive and negative sequence current components at PCC. The reference currents are generated by combining both positive and negative sequence components of PCC currents and are in accordance with the maximum and minimum voltage limits at PCC. Under balanced voltage sags, the PCC voltages are equally raised with the help of a positive sequence regulator.
On the other hand, under unbalanced voltage conditions, two PCC voltage setpoints are determined and flexible control of both positive and negative sequence current regulator helps in achieving voltage equalization. Under deep voltage sag conditions, a current saturation strategy is activated which helps in only injecting the positive sequence current thereby avoiding overcurrent. The active and reactive current references in d-q reference frame are formulated as in (14) and (15), respectively.
As shown in (14)- (15), under severe grid fault conditions the injection of active current is taken as zero, hence only reactive current injection is considered.
In (16)- (17) ,v − d andv − q are the filtered negative sequence voltages in d-q reference frame. I + * and (I − ) * are reference of positive and negative current amplitude, respectively, obtained from voltage control loop, whereas V − is the phasor sum of negative sequence filtered voltages in d-q reference frame.

5) INDIVIDUAL PHASE CURRENT CONTROL TO AVOID OVERVOLTAGE (IPCC) [90]
It is evident that random injection of positive and negative sequence components without monitoring the voltage drop in each phase can result in overvoltage in healthy phases. In [90], a scheme is proposed to avoid overvoltage in healthy phases by independently controlling the current in each phase. Evidently, the injection of balanced reactive currents under unbalanced voltage sags results in overvoltage in healthy phases, hence, the strategy is based on updated European grid code which requires the injection of unbalanced reactive currents to assist towards grid stability [91]. The injection of reactive current is based on the amount of voltage drop in the faulty phase to ensure that the healthy phases remain unaffected. The reactive current is obtained as the output of the droop controller and is given as in (18).
where, droop coefficient is a constant and is evaluated as per the grid codes, de x is the amount of deviation in the phase voltage from the nominal value andÎ n is the nominal current of the inverter as shown in Figure 6.

6) ADVANCE VOLTAGE SUPPORT CONTROL (AVSC) [92]
In [92], a strategy is proposed which is suitable for both inductive and resistive grids and hence injects both active and reactive power into the grid during fault conditions. Under unbalanced grid voltage conditions, the VSS limits the phase voltages at PCC by setting the maximum and minimum voltage limits according to the grid codes. The positive and negative sequence reference currents for active and reactive power for any X/R ratio are given in (19) -(22), respectively.
where, V + ref and V − ref are the positive and negative sequence voltage drop, respectively, due to the grid-side inductance and resistance. X g and R g are the inductance and resistance of grid, respectively. It is evident from (19)- (22), for the inductive grid, there is no contribution from the active current component. For such an instance, this strategy aims to inject maximum active power and regulates the phase voltages, simultaneously. However, the injected active power would suffer from oscillations under severe unbalanced grid conditions.

7) POSITIVE AND NEGATIVE SEQUENCE VOLTAGE SUPPORT STRATEGY (PNSVSS) [93]
In [93], a strategy is designed for both inductive and resistive grids which helps in raising the positive sequence voltage, reducing the negative sequence voltages, and maximizing the difference between these two sequences. The increase in the positive sequence component helps in raising the voltage magnitude and reducing the negative sequence component aids towards phase equalization. The additional objective of maximizing the difference between these two sequences ensures full utilization of inverter capacity as it injects the rated current as well as provides voltage support.
The active and reactive reference currents are formulated as in (23)- (26).
The amplitude of positive and negative sequence voltage at the PCC is obtained as in (27) and (28), respectively. (28) where, I + p , I + q , I − p and I − q are the positive and negative sequence components of active and reactive currents, respectively.

8) MAXIMIZING VOLTAGE SUPPORT IN LOWEST PHASE (MVSLP) [94]
In [94], [95], a voltage support strategy is proposed by maximizing the RMS value of the most sagged phase voltage and reducing the risk of an under-voltage disconnection, during unbalanced grid sag conditions. The scheme works well regardless of the grid impedance and maximizes the inverter's capability by injecting the rated current. The reference currents are formulated as in (29)- (30).
It can be observed from (29)- (30), that balanced currents are injected into the grid, as only the positive sequence component is being considered. Hence, voltage imbalance remains the major drawback of this method.

9) MAXIMIZE REACTIVE CURRENT INJECTION TO AVOID
OVER VOLTAGE (MRCAO) [97] In [96], the strategy ensures simultaneous injection of the maximum value of the positive sequence component of the reactive current to achieve maximum voltage rise in the faulted phase and the injection of negative sequence component of the reactive current to ensure phase equalization. The major demerit of this strategy is that it requires a reliable evaluation of the grid impedance and the controller operates in the open-loop. To overcome this drawback, a voltage control loop is incorporated in [97] to avoid overvoltage in healthy phases. The strategy uses two PI controllers, one to inject the maximum rated current in the disturbed phase, and the other to avoid overvoltage in healthy phases. The current reference generation equations are formulated by using the normalized values of the positive and negative sequence voltages as in (31) and (32).
Here I p , helps in injecting the active power, I + q is used to balance the phase currents and I − q prevents overvoltage in the healthy phase.

10) MULTIPLE OBJECTIVE VOLTAGE SUPPORT STRATEGY (MOVSS) [98]
In [98], a similar VSS is proposed for inductive and resistive grids that minimize the imbalance in voltage by reducing and increasing the negative and positive sequence component of reactive power, respectively as in (33) and (34).
V + and V − determine the voltage support from the utility to the point of common coupling. The positive and negative sequence of active and reactive reference currents are formulated in SRF as in (35)- (38).
The increment in the positive sequence and decrement in the negative sequence component of PCC voltage is achieved by carefully determining the reactive power references as in (39) and (40), respectively.
11) OPTIMAL VOLTAGE SUPPORT STRATEGY (OVSS) [99] Similar to strategies proposed in [93]- [98], the control strategy in [99] is also based on the minimization of voltage unbalance factor (n). However, the optimal solution is obtained based on the knowledge of the impedance angle of the injected current as in (41).
The optimal positive sequence active and reactive current references are given by (42) and (43), respectively.
where, I is a predetermined current value that will limit the amplitude of the inverter current. Based on (42) and (43), the positive and negative sequence components of PCC voltage are determined as in (44) and (45), respectively.
Apart from the above-mentioned VSS, several other improvements have been proposed to provide enhanced voltage support under unbalanced faults [100]- [105]. In [100], the injection of both active and reactive current is based on the severity of voltage sags so that the inverter rating is not exceeded. In [101], the voltage unbalance factor is minimized by employing droop control. The scheme injects the positive and negative sequence components of active and reactive powers to ensure that the PCC voltage remains within specified limits. A symmetric component decoupled control strategy (SCDCS) for a three-phase four-wire system is proposed in [102]. The strategy injects the active power by utilizing the positive sequence component of the inverter current. Moreover, the negative and zero sequence components are utilized to provide local voltage support and unbalance correction. It can be concluded that the knowledge of grid impedance is imperative in deciding the proper VSS i.e., for an inductive grid, the injection of reactive power is preferred which helps in raising the phase voltages as opposed to the preference given to the injection of active power for a resistive grid [103]. In [104], a model predictive current controller (MPCC) is proposed to enhance the VSS under different grid faults. In this controller, the voltage limit targets TABLE 2. Comparison between voltage support strategies under low-voltage-ride-through condition. VOLUME 9, 2021 are achieved by including the zero-sequence component of voltage in the current references. An improved communication-less control strategy for voltage unbalance mitigation is proposed in [105]. In this scheme, the grid impedance estimation is not required and the LV network is imitated by choosing the line impedances to ensure that the X/R ratio is selected close to one. The above-mentioned voltage support strategies are compiled based on certain key performance parameters in Table 2.

B. CURRENT LIMITATION STRATEGIES (CLS)
Another challenge that exists under low-voltage-ride-through condition is to ensure that the peak amplitude of the inverter currents does not exceed beyond the inverter rated capacity. To elaborate on this concept, consider if there is a shortterm voltage sag in one of the grid phases. To ensure power balance between dc and ac network the faulty phase inverter current increases and keeps injecting the same power coming from the dc side. If the amplitude of the faulty phase current exceeds beyond the rating of the inverter, protection devices within the inverter will switch off the inverter for its safety. This interruption in the operation of the inverter will prevent the ride-through operation of the PV inverter. Hence, the current limitation is an important objective under LVRT that limits the amplitude of the injected currents to the rated value, to avoid the operation of overcurrent protection devices. The response of current limitation strategies under unbalanced and balanced grid faults are shown in Figure 7 (a) and (b), respectively. In the following sub-sections various control strategies are discussed that provide over current limitation under balanced and unbalanced grid faults. 1) TWO DISCRETE PARAMETER CONTROL (TDPC) [106] In [106], a current control strategy is proposed which formulates a generalized current reference expression by combining various conventional CRG techniques with the help of two discrete control parameters (α, β). The optimum power quality characteristics can be obtained by carefully choosing the values of α and β in the range of (-1, 1). To obtain the optimum power quality characteristics for a specific condition, values of α and β can be used for the chosen CRG strategy as given in Table 3.
where   to meet future LVRT requirements. Although efficient, this strategy does not provide any regulation on the minimum set point in the reduction of the inverter overcurrent.
2) MINIMUM PEAK GRID INJECTION CURRENT CONTROL (MPGICC) [107] In [107], a strategy is proposed to minimize the power quality problems and help in determining the minimum peak currents during polluted grid conditions. The instantaneous phase currents are obtained as in (49)-(51).
where, P * , is the reference power signal and n is the voltage unbalance factor (VUF) of (1), which can take any value between 0-1. It is evident from (49)-(51) that the peak values of the currents are dependent on the values of α and β. By precisely choosing the values of these two control parameters, the peak currents are minimized. The proposed scheme is extremely useful in balanced conditions, however, during longer periods of voltage sags of more than one second, the injected currents are distorted due to the presence of negative sequence component.

3) REDUCE RISK OF OVERCURRENT PROTECTION (RROCP) [108]
Based on the conventional positive-negative sequence control (PNSC) method, the strategy in [108] injects negative sequence inductive currents to effectively control the peaks in the current waveforms. The peak currents of the three phases are formulated as in (52) -(54). where, and i − q are the positive and negative sequence component of grid currents, respectively. ∅ 1 and ∅ 2 are the phase angles of the positive and negative sequence voltages with respect to the reference axis. ∅ p and ∅ n are the phase angles of the positive and the negative sequence currents, respectively, whereas I p and I n are obtained using (56) and (57), respectively.
It can be observed from (52)- (54), that the peak values of the currents are dependent on ϕ. To limit the peak amplitude, the phase currents should not exceed the maximum value of current I max from (58) and hence I max is set below the threshold value to avoid the operation of overcurrent protection.
4) ZERO SEQUENCE CURRENT CONTROL (ZSCC) [109] In [109], a control strategy is proposed by considering zero-sequence component to ameliorate the power quality issues in a grid-connected distributed generation system. Normally, the conventional current control schemes have four control variables (i + d , i + q , i − d and i − q ) in a three-wire system. The control strategy of [109] has six control variables Re and i 0 Im ) for a four or six-wire converter system to achieve better performance under unbalanced grid conditions. With the injection of the zero-sequence current component, two additional controls of freedom are obtained to improve the power quality characteristics.
The scheme is essentially divided into two objectives: objective 1, in which the oscillations in active and reactive power are removed and objective 2, where the oscillations in active power and negative sequence current are eliminated at the same time. The current references for objective 1 are given as in (59)-(62).
Using (59)-(62), the oscillations in active and reactive power can be eliminated. On the other hand, the reference currents for objective 2 are given as in (63)-(66).
It can be seen from (63)-(66) that, reference currents contain only positive and zero sequence components under unbalanced grid conditions. The proposed control strategy helps in removing the oscillations in active and reactive power for a three-phase four-wire system. Furthermore, it also helps in reducing the current amplitude in the faulty phase.
The proposed strategy is advantageous in terms of power controllability, at the cost of increased computational burden due to two extra control objectives. [110] In [110], [111], a fully flexible current controller is proposed that limits the peak currents to improve the ride through services by injecting positive and negative components of the active and reactive powers, P + , P − , Q + and Q − , respectively. The control scheme ensures that the injected currents do not surpass the inverter rated current and avoid overcurrent tripping of the PV inverter to guarantee its safe and reliable operation. The positive and negative sequence currents are derived in SRF as in (67)- (70).

5) FLEXIBLE PEAK CURRENT LIMITING CONTROL (FPCLC)
From (67)- (70), there are four parameters P + , P − , Q + , Q − , and hence several combinations are possible to limit the peak currents. In [110], the relation among these variables is established and the control gains are defined as in (71)-(73).
where, P = P + + P − and Q = Q + + Q − and k P and k q are the active and reactive control gain, respectively.
It is observed that the phase currents I a , I b and I c correspond to a unique solution of Q a , Q b and Q c , respectively. The maximum value among the phase currents is then determined to ensure safe operation of the inverter as in (74).
A generalized expression is derived, to evaluate the reactive powers for each phase to limit the peak current as in (75)-(78).
And the different values for Q a , Q b and Q C are obtained from the three distinct values ofφ as in (79).
The reactive power reference will be the minimum value among Q a , Q b and Q C and once this reference is determined, the positive and negative sequence of active and reactive powers, i.e., P + , P − , Q + and Q − , respectively can be known.
This strategy is advantageous in terms of its flexibility and capability to balance positive and negative components of the active and reactive power at the same time while restricting the currents to a safe value. It is applicable to all sizes of power converters having different ratings. But the major drawback of this strategy is its increased complexity as compared with other control schemes as it highly depends on the VUF and the phase angle between sequences which may have limited practical applications. Moreover, the proposed strategy does not provide zero active power oscillations. 6) PEAK CURRENT LIMIT CONTROL (PCLC) [112] In [112], a strategy is proposed to avoid overcurrent protection by providing peak current limitation (PCL) of negative sequence current. To guarantee that the highest current does not exceed the pre-defined value (I max ), the maximum amplitude of the negative sequence current injection (I − PCL ) is calculated as in (80).
Symbols have their usual meanings as in [108]. The injection of active and reactive current is flexible; hence the strategy is useful in satisfying the requirements of commonly available grid codes. Moreover, by injecting a specific combination of active and reactive currents, this method eliminates the ripples in active power.

7) LIMIT-THE-CURRENT CONTROL STRATEGY (LCCS) [113]
To overcome the drawback mentioned in [110], a control strategy is proposed in [113], which is independent of VUF and the phase angle. This strategy provides flexible control to ensure proper regulation in the injection of the power components and limits the current to avoid nuisance tripping of the inverters. The peak values of currents during normal and abnormal grid conditions are determined from (81) and (82), respectively.
It can be seen from (81)-(82) that the presence of the negative sequence component under unbalance voltage condition results in higher peaks in current. Hence, minimization of these peaks in current by formulating the current references in the stationary reference frame is obtained as in (83)-(86).
where, I * P and I * q denotes the active and reactive current references, respectively. The reference of the maximum current (I * max ), in (83)-(86) is obtained from (87).
For different values of k p and k q , peak values of currents are obtained, and the proposed scheme reduces the current peaks under polluted grid conditions. The maximum value of current in (87) is determined from the active and reactive current references and the positive and negative sequence components of voltage at PCC. To ensure that the current stays within the permissible limit the current references are formulated in (88), where I rated and I max represents the rated current value of the inverter and the maximum among the three-phase currents, i.e., Here,î * a ,î * b ,î * c are the current references in the natural reference frame. The maximum value of the current reference in (88) is I rated under severe grid fault. As compared to the control strategy in [110], this scheme is simpler as it is independent of the voltage unbalance factor and angle between component sequences which can provide flexible regulation in injected powers and limitation in current amplitudes to avoid overcurrent protection. [114] In [114], positive and negative sequence conductance (G) and susceptance (B) based control method is proposed to achieve multiple objectives like current limitation, minimization of oscillation in active and reactive powers as in (89)- (90).

8) POSITIVE AND NEGATIVE SEQUENCE G AND B CONTROL (PNGBC)
where, k G and k B are the proportional ratio between positive sequence and negative sequence of G and B, respectively and g + , g − , b + and b − are the positive and negative sequence components of susceptance and conductance, which are obtained using (91) and (92), respectively.
where, k G , k B can take any values between -1 to 1. Once g + and b + are calculated (g + cal , b + cal ), the current amplitude of each phase can be easily determined. Further, the maximum phase current (I max ) is calculated as in (93).
where, I amp , I bmp and I cmp are the current amplitude in phase a, b and c, respectively. Then the appropriate value of current is selected based on the converter capacity as I lim . To avoid the operation of overcurrent protection devices the values of g + and b + are determined from (94) (95) If the maximum current I max is less than I lim , the overcurrent control is avoided. On the other hand, when I max is greater than I lim , the current is proportionally decreased based on the ratio of (I lim /I max ) and thus prevents overcurrent with the maximum phase current being limited to I lim .

9) SINUSOIDAL CURRENT INJECTION STRATEGY (SCIS) [115]
A control strategy that eliminates the double grid frequency oscillation in active power and dc-link voltage with the capability of injecting sinusoidal current is proposed in [115]- [117]. The strategy formulates flexible active and reactive current references, based on PNSC strategy, under unbalanced fault. It also limits the injected current to the rated value during faults. Moreover, this scheme involves a non MPPT operating mode under severe faults when the maximum power from the PV array results in overcurrent in the inverter. VOLUME 9, 2021 The reference currents are formulated in the stationary reference frame by taking four key parameters k αp , k βp , k αq and k βq (96)- (99).
where, P * is obtained from the dc-link voltage control loop and Q * is the required reactive power during fault condition. The values of these parameters in (96)-(99) are chosen either +1 or -1 to modify the active and reactive current references according to grid specifications as in Table 4. As evident from (96)-(99), the use of mode 2 is suggested, to utilize the inverter's rated capacity. Once the voltage sag occurs, the controller determines the inverter pseudo power, namely, the new nominal power (NNP) of the inverter which is determined by the voltage sag depth. The NNP is evaluated as in (100).
where, the nominal power is denoted by S, V base is the base voltage and it is equal to the RMS value of line-line grid voltage, Based on the per-unit depth in voltage sag, the reactive power is calculated as per the Chinese grid code as in (101). where, To avoid overcurrent, the new reference power (P max ) to be injected into the grid is P max = NNP 2 − Q 2 . Under severe faults, if (Q > NNP), Q is selected as NNP, and the reference power P max is taken as 0, which means only reactive power is injected. This is because of the low nominal power of the inverter and is not capable of delivering active power to the grid to avoid overcurrent. However, the control strategy allows double grid frequency oscillations within the reactive power. Moreover, the smooth transition from MPPT to de-rated MPPT is not achieved [118]. To remove these oscillations in reactive power, under normal and abnormal grid conditions for a low voltage distribution grid, a robust Kalman filter (RKF) is employed in [119]. A smooth transition from MPPT to de-rated MPPT is achieved with the help of this strategy.
The function of RKF is to calculate the magnitude of the fundamental load component (FLC) from the load current, which enhances the system dynamics under load perturbation. The KF is the mathematical approach, which works through a prediction and correction module.

10) MULTI-OBJECTIVE CONTROL STRATEGY (MOCS) [120]
In [120], the control algorithm simultaneously mitigates the challenges associated with power quality and provides overcurrent limitation. To achieve the control objectives, current references are formulated in the stationary reference frame as given in (102)-(103) [96].
where, k + p , k − p , k + q and k − q are the four variable parameters. P * and Q * are the active power and reactive power references, respectively. By using (102) and (103), the injected reference current can be determined from the positive and negativesequence components of the active and reactive currents (I + p ,I − p , I + q and I − q ), respectively. The current amplitude in each phase is determined as in (104)- (106), as shown at the bottom of the next page.
The maximum values of the phase current (I max ) is evaluated using (107).
where, x = min cos (θ) , cos θ − 2π 3 , cos θ + 2π 3 . It can be observed from (107), that the minimum value of x results in the maximum value of phase currents. To protect the inverter against overcurrent, I max ≤ I rated (108) By using (107) and (108) current limitation is guaranteed. By substituting the value of I + p = I + p max and I max = I rated in (107), the maximum active current (I + p max ) is obtained as in (109).
where, I + qGC represents the positive sequence reactive current, which is defined by the grid code during voltage sag. Under LVRT condition, to prioritize the injection of reactive power the value of I + p is always less than I + pmax . However, in the case of low-power production, if I + p is less than the I + p max , the rated current capacity of the inverter is not fully utilized. Therefore, the amplitude of the reference reactive current is increased to fully utilize the current capacity of the inverter to provide maximum voltage support. By substituting I max = I rated in (107), I + q is determined as in (110).

11) PEAK CURRENT CONTROL WITH RESCALING FACTOR (PCCRF) [121]
In [121], zero oscillations in active power are achieved at the expense of higher peak currents in one or two phases. Hence, to limit these currents, a rescaling factor (k rs ) is used to formulate the current references as in (111).
where, I rms is the rms value of the nominal current of the inverter and I * rms−max is the maximum rms value of the three-phase current references.
The current references are determined as in (112).
where,ī * a ,ī * b andī * c are the current references in natural reference frame, after rescaling. The error and the instantaneous phase current are then tracked using the proportional (PR) controller and the voltage references are generated in stationary (αβ) reference frame.

12) OVER CURRENT CONTROL IN DISTRIBUTED GENERATION SYSTEMS (OCCIDGS) [99]
A strategy to limit the maximum inverter current to avoid overcurrent protection is proposed in [99]. The strategy determines the maximum safe current of the inverter based on the minimum value of the angles among the three phases as in (113).
where, n is the voltage unbalance factor. Also x = min cos (∅) , cos ∅ − 2 3 π , cos ∅ + 2 3 π The proposed strategy also provides maximum voltage support by ensuring that the current injection is based on the chosen injection angle θ inj , for which the amplitudes of the positive-sequence currents i + p and i + q is defined as in (114) and (115), respectively. where, Apart from the above-mentioned strategies, several other improvements have been proposed to provide current limitation under unbalanced grid voltage conditions. A current reference generation strategy is proposed in compliance with the recently developed grid codes (CRGGC) in which the positive and negative sequence reactive currents are injected in proportion with the change in positive and negative sequence voltage [122]. The distribution factors used in the strategy for active power reference and reactive power reference are designed explicitly in accordance with the modern grid codes. The proposed strategy utilizes the converter's full capacity, avoids overvoltage at the PCC, and reduces the unbalance factor. In [123], another strategy is proposed that maximizes the power delivery and provides current limitation. The strategy employs a DDSRF to extract the positive and negative sequence of voltages and currents. The proposed DDSRF based PNS extractor exhibits faster response and lower total harmonic distortion (THD) compared to other techniques. In [124], a CRG scheme is proposed which minimizes the oscillations in active and reactive powers. A FOPI (Fractional-order PI) controller instead of the conventional PI, PR controllers, is employed to obtain the zero steady-state error in the stationary reference frame which improves the response time. In [125], [126], a control strategy is proposed that helps in maximizing the power capability of PV inverter. The flexible current injection strategy is developed by ensuring a proper balance between positive and negative sequence components. The strategy limits the current to its rated value and avoids the oscillations in active power. Table 5 presents a comparison of recently developed current limitation strategies, based on their distinct characteristics.

IV. DC-LINK VOLTAGE CONTROL
The design of an efficient dc-link voltage control loop is essential during LVRT operation. Under normal operating conditions, the power extracted from the PV array is delivered to the grid through a dc-link capacitor to ensure that the power balance is achieved. It is well-known, that the reactive power reference during LVRT under faulty grid conditions is determined from the grid codes, whereas the active power reference is dependent on the inverter power rating. The injected active power to the grid (P inj ), should follow the reference power (P * ) when there is no sag present, i.e., when P * ≥ P inj . The power imbalance occurs in the system when there is inequality between the reference power (P * ) and the injected active power. This usually occurs under unbalanced voltage sag conditions, as the inverter capacity is mostly utilized to inject reactive power, and the MPP power from the PV array cannot be fed to the grid. To overcome this, the MPPT is terminated as the active power injection capability of the inverter is now reduced. If the MPPT is still operating, the power imbalance may give rise to overvoltage across the dc-link capacitor that may result in the deterioration of the capacitor and thus reduce its life. To safeguard the dc-link capacitor from overvoltage, a constant dc-link voltage is achieved, and power balance is ensured by active power curtailment. This is done by reducing the power extracted from the PV array by shifting the point of operation away from the MPP on the P-V curve to a new reduced reference power operating point [127]. Single-stage GCPV systems are self-protected as the operating point shifts to a new point in the I-V curve to curtail down the active power under voltage sag conditions [128]. Nevertheless, in two-stage systems, the MPPT operation is performed by dc-dc converter [129], hence, the system is not self-protected. A separate control loop is required to protect the over voltages in the dc-link capacitor. The response of constant dc-link voltage control strategy under unbalanced and balanced grid faults are shown in Figure 8 (a) and (b), respectively.
On the other hand, there are several challenges associated with providing a constant dc-link voltage under unbalanced sag conditions [130]- [132]. Under deep grid voltage sag conditions, a constant dc-link voltage results in the injection of non-sinusoidal unbalanced currents which is due to a low modulation index [133].
It is well-known that if a fixed reference value of the dc-link voltage is chosen for the worst condition, it results in high switching and inductor losses in two-stage PV systems [134]. In [135], an adaptive dc-link voltage technique is suggested that shows that the PV system may have an increase in the lifetime of 75.76% as compared to the fixed dc-link control strategy. Hence, there exists a trade-off when operating the dc-link capacitor at a fixed or variable voltage. Therefore, the dc-link voltage control strategies are classified into two sub-sections, namely constant and adaptive dc-link voltage control. This paper focuses on discussing the recently developed dc-link voltage control strategies for two-stage PV systems to limit the scope of the proposed study.

A. CONSTANT DC-LINK VOLTAGE CONTROL
This section discusses the recently developed control strategies, to maintain a constant dc-link voltage. These methods mitigate the double grid frequency oscillations within the dclink voltage with improved dynamic response during fault conditions. [127] In [127], three solutions are suggested to limit the dc-link overvoltage by reducing the active power from:  Short-circuiting the PV (P = 0), Open-circuiting the PV (P = 0) and extracting non-MPP power from the PV array (P = 0). In the first two methods, no power is extracted from the PV array, hence, only reactive power is injected into the grid. However, in the third method, less power, as compared to the pre-fault MPP power, is injected into the grid by controlling the dc-dc converter. The controlling of the dcdc converter is done in such a way that the power generated by the PV array matches the injected power to the grid. The operating point moves to a new point to obtain power balance. To ensure that the point of operation moves to the right-side of MPP on the P-V curve, a positive voltage step v pv is added to v mpp as in (117). (117) Faster dynamics are obtained by regulating the energy stored in the dc-link capacitor ( 1 2 CV 2 dc ). In Figure 9, p new_est , v new_est are the estimated power and voltage in the triangle, respectively. From Figure 9, v new_est can be evaluated as in (118). (118) where, p mpp and v mpp are the power and voltage at MPP, respectively before the fault. The new estimated power, p new_est is evaluated from the active current reference as in (119).

1) INJECTION OF LESS POWER DURING SAG (ILPDS)
Simplifying (115) and (117), the new operating point and the voltage difference between the MPP and the new operating can be estimated using (120) and (121) (120) and The v pv_est in (120) is added to the feedforward controller before the limiter as in Figure 10. The limiter gives the positive values for v pv to obtain the v new on the right-side of the PV curve. Moreover, the estimation of duty cycle (d est ) is determined as in (122).
This scheme helps in injecting reduced power to the dc-link capacitor by moving the point of operation away from the MPP of the PV curve and has the advantage of injecting balanced currents even under faulty grid conditions.
2) FEEDBACK LINEARIZING CONTROL WITH SLIDING MODE COMPENSATION (FLCSMC) [136] Several strategies have been proposed that use feedback linearizing control (FLC) in GCPV systems. However, the performance of FLC has not been investigated during the non-MPP mode of operation during grid faults. In [136], a robust FLC strategy is used, which employs sliding mode control to deal with the uncertainties during low-voltage-ridethrough in GCPV systems. The proposed strategy controls the active and reactive power under LVRT and maintains a constant dc-link voltage.
In the case of asymmetrical grid conditions, FLC controls the active and reactive power to fulfill all the LVRT requirements and ensures constant dc-link voltage. The active and reactive power references are given as in (123).
where, S is rated apparent power of the grid. To provide voltage support to the grid I * r is the injected reactive current as per the grid code.
In this mode, the power regulation is done to track reference trajectories given in (123). The proposed feedback sliding control is given as in (124).
where, k v is the positive control gain, e v denotes the tracking error, α v is the sliding gain and s v represents the sliding surface for dc-link voltage control as in (125).
The proposed controller results in a constant dc-link voltage when subjected to external disturbances like irradiance. This is because of the compensation provided by the sliding control within the feedback system. Hence, the proposed controller is superior to a conventional PI controller, which requires its control gains to be adjusted for all the uncertainties to achieve proper tuning.
3) NON-MPPT ALGORITHM WITH MCPC CONTROL (NMMCPCC) [137] In [137], the hybrid control strategy is a combination of model current predictive control (MCPC) algorithm along with a non-MPPT algorithm. The MCPC algorithm minimizes the overcurrent in GCPV inverter and injects symmetrical currents even under faults. To eliminate the dc-link overvoltage problem, the non-MPPT algorithm evaluates the adjusted power for the PV array and a new duty cycle is acquired. The revised duty cycle is then used by the converter controller for proper tuning the output of PV array.
To alleviate the double grid frequency oscillations in dc-link voltage, a feedforward compensation is incorporated. The control diagram for non-MPPT mode is in Figure 11. In non-MPPT mode, the duty ratio under the fault condition (U * g < U N ), is obtained as in (126).
where, U DC denotes the dc-link voltage and U * ref is the reference voltage of non-MPPT mode. U * ref is obtained by the following set of equations given in (127).
Here, the fault voltages in the d-q frame of reference are represented by U * gd , U * gq .
In comparison to the conventional dual-loop control (outer voltage control loop and inner current control loop), this scheme eliminates the use of inner loop PI controller, PWM module and sequence separation techniques which result in balanced injected currents even under unbalanced fault conditions. The dc-link voltage is maintained at a constant level and double harmonics components are removed by using feedforward compensation.
Several other controllers have been proposed that help in maintaining a constant dc-link voltage [138]- [140]. By using the power references in (123) a constant dc-link voltage strategy is proposed in [141]. The strategy for PV inverter is developed based on a robust model predictive control. To achieve robustness, a disturbance compensator is employed in the system, which alleviates the tracking errors in the steady-state. In [142], an improved dynamic voltage regulation (IDVR) method is proposed to regulate the dc-link voltage with the help of a sliding mode controller along with a disturbance observer (SMC + DOB) in dc microgrids. The SMC ensures that the dc-link voltage is kept constant even in the presence of uncertainties and disturbances. To remove the chattering problem due to SMC, a saturation function is employed in place of the signum function. The use of an observer for the dc-link current helped in reducing the cost by removing the dc current sensor which helped in improving the reliability of the controller. In [143], a particle swarm optimization (PSO) based dc-link voltage control of a two-stage PV is proposed. A PI controller is employed to maintain the constant dc-link voltage and the parameters of this PI controller are obtained with the help of the optimization technique which helps in improving the dynamic response of the dc-link voltage. Another metaheuristic approach, namely the whale optimization technique (WOADCVC) is proposed in [144] for optimum tuning of the dc-link PI controller. It was reported that among other meta-heuristic approaches whale optimization algorithm (WOA) is best for tuning the PI controller.

B. ADAPTIVE DC-LINK VOLTAGE CONTROL
Although a constant dc-link voltage helps in enhancing the life of the dc-link capacitor, a variable dc-link voltage controller can assist in maintaining the modulation index within a certain range. By efficiently controlling the modulation index, high-quality current can be injected into the grid. An adaptive dc-link voltage control can also help in injecting more power as compared to a constant dc-link voltage controller. This section discusses the recently developed control methods that adaptively vary the dc-link voltage. [145] In [145], an adaptive dc-link voltage control method is formulated by ensuring that the inverter operates at a high modulation index in the linear region. The use of high modulation index helps in the injection of sinusoidal balanced currents into the grid which improves the output power quality. Under normal operating conditions, using the conventional control strategy, the dc-link voltage is fixed at a constant value. However, even under balanced voltage sag conditions, the proposed strategy follows the variable dc-link voltage reference (V dc ), unlike the conventional strategy in which the dc-link voltage reference is fixed at a constant value. The variation in the update dc-link voltage reference V dc is dependent on the voltage dip as expressed in (128). (128) where, V * dc is the reference value for the dc-link voltage control and λ is the voltage drop ratio tracked by the PLL. Further, the dc-link capacitor voltage is controlled by regulating the input and output current of the capacitor as in (129).

1) VOLTAGE DROP RATIO BASED CONTROL (VDRBC)
where, i i is the input current to the capacitor and i o is the output current. It is worth noting that the output current in (129) is fixed to avoid the nuisance tripping of the inverter. Hence, the current regulation is achieved by the input current. As mentioned earlier, this strategy controls the dc-link voltage which ensures a high modulation index. However, under asymmetrical voltage sag conditions, the modulation index can be in the over modulation region, especially when the dc-link voltage reduces below a certain value. Hence, the operation in the over modulation is avoided by checking the maximum voltage difference between any two phases. Unlike the symmetrical voltage drop, double grid frequency oscillations occur in the case of unsymmetrical voltage drop. Therefore, under two-phase voltage drop conditions, the maximum and minimum values of the dc-link voltage are calculated as in (130).
where, V 1 and V 2 in (128) denote the peak values of output voltages.
The maximum phase difference between phase A and phase B is given by (131), and the minimum value of the dc-link voltage to avoid over modulation can be determined using (132). The circuit diagram of the adaptive dc-link voltage controller is shown in Figure 12. The strategy is applicable for both, balanced and unbalanced grid voltage conditions and a well-designed PIR controller is used for the dc-link voltage control loop. 2) INTERWEAVED DFSOGI CONTROL (IDFSOGI) [146] In [146], the dc-link voltage is adjusted with respect to the variations in PCC voltage. This adjustable dc-link voltage controller: minimizes the switching losses in the power converter devices, helps in reducing high frequency I 2 R losses in the inductor and results in the reduction of ripple current. The reference duty ratio of the converter is evaluated as in (133).
The reference dc-link voltage is determined using (134). where , is the phase voltage amplitude. For an appropriate control action, the dc-link voltage must be about 10% greater than the voltage at the PCC. Hence, in (134) the value of µ is considered as 1.1. Switching losses in the inverter and the boost converter are dependent on the dc-link voltage, hence by keeping the dc-link voltage variable, these losses can be minimized.
The total energy loss (E) is obtained as in (135). Here, P switch on , P switch off are the instantaneous power loss, when switch is on and off, respectively and t on , t off the total on-time and off-time, respectively.
The advantage of variable dc-link voltage is the minimization of high frequency ripple current in the inductor. The ripple current is expressed as in (136).
It can be seen in (136), that the ripple current is dependent on the difference of instantaneous PCC line voltage (V s ) and dc-link voltage (V DC ). The fixed dc-link voltage produces higher ripples in inductor current. As a result, the grid current is also influenced by these ripple currents.
By keeping the dc-link voltage close to the grid line voltage, these ripple currents can be reduced. With the help of the proposed strategy, more power is fed to the grid as compared to the injection of less power using the conventional control strategy with fixed dc-link voltage. The controller also results in a low THD of less than 5% in the presence of nonlinear load.
3) CPI BASED DC-LINK VOLTAGE CONTROL (CPIDCVC) [147] It is clear now that the switching losses are dependent on the value of the dc-link voltage. In the case of fixed dc-link voltage, the switching losses are higher under both, normal and unbalanced grid conditions. Hence, another adaptive dc-link voltage control strategy is proposed in [147]. This strategy reduces the switching losses by adaptively changing the reference dc-link voltage with respect to the PCC voltage. The reference value of the dc-link voltage is obtained as in (137).
To ensure that dc-link voltage remains higher as compared to the PCC voltage, the value of τ is taken as 1.1 as in [146].
Another strategy is proposed in [135] which reduces the dc-link voltage to its minimum possible value to inject more power into the grid. To avoid the operation of the inverter in over modulation region, a linearization strategy is employed which helps in improving the transient and dynamic performance of the system. In [148], another attractive approach is presented, in which an adaptive PI controller is used to obtain different control targets like stability, dynamic response, disturbance rejection and low overshoot. In this scheme, the control gains of the PI controller are adjusted adaptively by employing an anti-wind-up scheme, which effectively reduces the transients in the dc-link voltage. A comparative table on the above-mentioned dc-link voltage control strategies is prepared, based on their distinct characteristics as in Table 6.

V. OTHER MISCELLANEOUS CONTROL STRATEGIES
Apart from the above-discussed control strategies, few additional challenges exist that are addressed by the following control strategies.

A. VOLTAGE COMPENSATION CALCULATION CONTROL STRATEGY (VCCCS)
In [149], a multi-objective strategy implemented in the d-q reference frame is formulated. The strategy performs well under symmetrical and asymmetrical grid voltage conditions. It helps in generating sinusoidal voltage and currents and alleviating the need for a switch for a transition from MPPT to non-MPPT mode. Inverter currents are limited by adjusting the reference dc-link voltage (V * dc ), thereby utilizing the positive sequence of d component. The q-component is utilized to supply the reactive power.  A voltage compensation calculation (VCC) unit is developed to curtail down the active power during voltage sag. A new dc-link reference (V * d ) is obtained by adding a compensating value (V com ) to the optimum value (V opt ).
By taking the tolerance of 10%, the compensating voltage for the positive sequence is obtained as in (138) V com−p = − V dp (V dp − 0.9) (138) Similarly, the compensating voltage for negative sequence is obtained as in (139) Here, V dp and V dn are the positive and negative sequence voltage of d component after fault, respectively. By utilizing (138) and (139) it is ensured that, the V * dc is always less than V oc . where, V oc is the open-circuit voltage of the PV array. The control and calculation unit of the voltage compensation method is shown in Figure 13 and 14, respectively.

B. KRUSH-KUHN-TUCKER BASED CONTROL (KKTBC)
Another optimization strategy in the d-q frame of reference to generate current references by employing Karush-Kuhn-Tucker (KKT) is proposed by [150]. This strategy is designed by considering the X/R ratio of the system which helps in differentiating between the weak and stiff grid. It also provides voltage support by enhancing the positive sequence component and minimizes the negative sequence component. To prevent the activation of overcurrent protection in the inverter, the necessary condition is given in (140).
I max = I +2 + I −2 = max(I a(peak), I b(peak), I c(peak) (140) Although the condition in (140) is necessary, it does not guarantee the prevention of overcurrent protection. Hence, an inequality constraint of (141) is also considered as opposed VOLUME 9, 2021  121826 VOLUME 9, 2021 to the strategy proposed in [54]. (141) where, I oc is the overcurrent protection threshold that the inverter switches can sustain. The optimal solutions by employing KKT are obtained as in (142) - (145).

C. ACTIVE AND REACTIVE CURRENT INJECTION BASED CONTROL (AARCIBC)
The disadvantages of the traditional LVRT control scheme are: 1) It is less effective for low voltage distribution networks (LVDN) as the resistive component is prominent in this type of network.
2) The existing resources are not fully utilized. The dc-link capacitor can be utilized to absorb or release a certain amount of energy in transient voltage event, which has not been pondered in previous works. Considering the drawbacks of conventional strategies, an improved LVRT strategy for LVDN is proposed in [151]. In this, a mathematical analysis is carried out to prove that the active current injection (ACI) in LVDN with a high R/X ratio, is as effective as reactive current injection (RCI) in high X/R ratio networks to provide voltage support. Under normal operating conditions, RCI is employed to support the voltage at PCC. However, under severe grid fault, the ACI supports the PCC voltage in LVDN.
The optimization problem is formulated as in (146) - (150).  (151) where, v is the vector of decision variables, which includes PV output current reference, current references of d and q component and reference dc-link voltage. The main aim is to maximize the ACI during faults and PV energy harvesting. The environmental constraint in (145) ensures that PV reference power should not exceed the PV power at MPP under fault conditions. Using (149), I ref q is determined under LVRT condition, where U g is the RMS phase voltage at PCC. To maximize the ACI, the maximum allowable output current of GCPV inverter is set to be 1.1 pu during unbalanced grid conditions. The maximum injected active power of the GCPV inverter is obtained as in (152). (152) where, P o and U rated are the rated output power and RMS phase voltage of GCPV inverter, respectively. Based on the different PCC voltage and environmental conditions, three modes of operations are proposed. In mode 1, when U g ≥ 0.9 pu, the PV generator works under normal operating conditions with MPPT execution. In mode 2, when U g ≤ 0.9 pu, and P max g ≤ P mpp pv , the PV inverter is operating under LVRT. It fulfills RCI requirements as per grid code and the remaining power capacity of the GCPV inverter is utilized through ACI. During this mode, the dc-link capacitor also stores some extra PV energy.
In mode 3, when U g ≤ 0.9 pu, and P max g ≥ P mpp pv , LVRT control is activated and MPPT is maintained. Moreover, the dc-link voltage is released to fulfill the ACI requirements. In this mode to avoid over-modulation, in a three-phase system, the dc-link voltage is maintained as in (153).

D. REACTIVE POWER SUPPORT WITH APC (RPSWAPC)
A strategy for a LV network with low X/R ratio is presented in [152]. The scheme presents novel reactive power support that works well for under and over voltage conditions by considering the grid impedance. The controller shifts to APC mode if the reactive power support is not sufficient to ensure the PCC voltage does not go beyond the over voltage limits. Injection of active power is given more priority than reactive power for better voltage support. To provide better voltage support, active power is reduced during over voltage conditions. Hence, the scheme also works well under highvoltage-ride-through (HVRT). Unlike conventional peak current limiter, this scheme directly calculates the peak values in injected current and minimizes the active and reactive power references. While minimizing the powers, reactive power is given more priority, however, under severe voltage sag, both power references are minimized. Furthermore, under unbalanced grid conditions, it employs both sequence components for better voltage support. The strategy provides a smooth ride-through operation even for sudden grid faults, without any current overshoots.
The PCC voltage amplitude is given in (154) by assuming a small power angle.
To remove the active oscillations and reducing the ripples of dc-link voltage, the reference currents are formulated in VOLUME 9, 2021 the d-q reference frame as in (155) - (158).
In [153], a control strategy is proposed that reduces the active power backflow in cascaded PV solid-state transformers (SST). As previously discussed, in the case of unbalanced voltage sags, there are three, positive, negative and zero sequence components. The sum of active powers generated by negative sequence voltage component on three-phase inverters is obtained as in (159).
It is to be pointed out that the negative sequence component does not generate any additional active power but redistributes the active power in all three phases. According to (159) the active power generated by negative sequence voltage must be less than zero in a certain phase during LVRT. It is assumed that for phase A, P AN is less than zero. Hence the total active power transmitted by phase A (P A = P AP + P AN ), will be less than zero. This indicates that Phase A will absorb the active power from the grid and is known as active power backflow.
In case of conventional PV inverters, active power generated by negative sequence voltage can return to the common dc bus and have negligible effect on the system. This means that the three level LLC inverter transmits power only in one direction. Hence, the power cannot be returned to the common dc bus and flows through the dc buses of H Bridge which creates overvoltage in phase A and causes shut down of PV SST due to overvoltage protection.
To overcome this power backflow issue in PV SST, two methods have been proposed in [153].
In the first method, the injected current does not contain zero sequence component and only large positive sequence active current is injected. Hence, the active power generated in X phase is greater than the absolute value of that phase which is generated by negative sequence voltage as in (160).
where, X denotes the phases A, B, C and P X = P XP + P XN ≥ 0. The active power generated by positive sequence voltage is given as in (161).
where, V P is the amplitude of positive sequence grid voltages, I g is the amplitude of grid currents, θ is the power factor angle of the PV inverter, I dp is the active current due to positive sequence and P T is the total power of the PV array. It is evident from (161) if I dp increases, P XP will also increase. In the second method for a star-connected system, zerosequence voltage is injected which does not provide excess current and active power and helps in distributing the active powers among the phases. Hence, zero-sequence voltage compensation balances out power redistribution of negativesequence voltages which eliminates the active power backflow issue as in (162).
This method also ensures that the active power flowing in each phase remains the same.

F. RECURRENT WAVELET FUZZY LOGIC NEURAL NETWORK BASED CONTROL (RWFLNNBC)
An improved LVRT technique designed for a weak grid is proposed in [154]. To control the active and reactive powers, recurrent wavelet fuzzy logic neural network (RWFNN) is employed, instead of conventional PI controllers. A threelevel neutral-point clamped (NPC) inverter is employed where active and reactive power references are set according to the grid code.
The active and reactive power references are obtained as in (163)  where, I * r is the reactive current reference, determined from the grid code. S is the maximum apparent power. The short circuit ratio (SCR) is defined as in (165).
where, S AC short circuit capacity of the AC system and S N is the rated power of PV. The strategy considers that the value of SCR in weak grids is less than 3. Since low SCR values highly affect the grid voltage stability and power quality under grid faults, PI controllers are replaced by RWFNN controllers to improve the transient stability. The PI controllers are simple but not robust in terms of tackling the system uncertainties like modeling errors, parametric variations and other external disturbances. On the other hand, the RWFNN achieves superior dynamic modeling behavior, online learning and strong adaptive capability. The online learning algorithm is based on the backpropagation learning rule. The convergence of the tracking errors is determined by using the Lyapunov function. The RWFNN controller ensures smooth tracking responses and helps in reducing oscillations in active and reactive power. In [155], a LVRT technique for reactive power injection is proposed based on instantaneous power theory (IPT). The strategy helps in improving the dynamic response from fault inception to fault clearance. The method also helps in reducing the size of the filter which helps in reducing the overall cost. Two types of controllers have been investigated, PI-IPT and fuzzy logic control (FLC)-IPT and it is found that the FLC-IPT has the better dynamic performance as compared to the PI-IPT. The PI-IPT and FLC-IPT controllers have a superior dynamic response than RWFNN, proposed in [146]. The block diagram of the IPT control strategy is shown in Figure 15. According to IPT, the active and reactive currents are given as in (166) The error signals computed using the reference and actual values of active and reactive currents are passed through a PI controller to obtain active and reactive voltage references (v * p , v * q ), respectively. Using this, the voltage references in αβ reference are obtained as in (170) and (171), respectively.
Another problem faced during LVRT under unbalanced grid conditions is the voltage fluctuations at neutral point (NP) in a transformer-less three-level GCPV inverter. To minimize these fluctuations, a large, middle and zero vector modulation (LMZVM) strategy is utilized [156].
The removal of the transformer causes a ground current between the PV panel and the ground, which injects through the parasitic capacitance.
Moreover, it results in electromagnetic interference and distortion in grid current. By utilizing the LMZVM technique, a low common-mode voltage (neutral point (NP) voltage) is produced which in turn reduces the ground current.
DC-DC Converters are also utilized to balance NP voltage, which increases the overall cost and size of the systems [157]. Using a large dc-link capacitance can be a solution to suppress the NP voltage, however, selecting dc-link capacitance for pure reactive power requires a very high value of capacitance [158]. Another strategy is proposed in [156] which balances the NP voltage by employing four weighing factors to determine the peak-to-peak values of NP voltage.

VI. FUTURE ASPECTS OF CONTROL STRATEGIES UNDER LVRT CONDITION
From the detailed literature survey presented in this study, related to the various challenges associated during LVRT, the following points should be considered while designing the control strategies: 1. There is scope to design a simple low-cost structure to improve the synchronization capability under unbalanced faults. 2. There is further scope in improving the performance of voltage support strategies underlying parameters variation such as X/R ratio. 3. Most researchers have designed control strategies for a single PV system. Much work can be done by considering multiple PV inverters and develop a holistic control strategy that can assist in voltage unbalance from a systemic standpoint 4. There is scope in developing voltage support control strategies that fulfill multiple objectives to mitigate power quality issues, like oscillations in active and reactive power, distortion and high peaks in the inverter currents. 5. The voltage support control strategies devised have mitigated the unbalance factor under constant power generation. Researchers need to consider variable power generation scenarios to practically visualize the performance of these control strategies. 6. More work can be done on designing a flexible current limitation strategy to fulfill the requirements of different available grid codes. 7. The current limitation strategies proposed by most researchers have considered the injection of active power under low generation scenarios. Further improvements can be achieved by considering the maximum injection of both active and reactive power with enhanced power quality. 8. Most researchers have devised dc-link control strategies under constant power generation. Further work can be done on designing dc-link strategies with improved dynamic response under variable power generation. 9. Most strategies have considered the injection of the negative sequence component. More work can be done by considering the zero-sequence component to provide better voltage support. 10. Most researchers have considered a constant dc-link voltage. There is further scope in designing a dc-link control strategy by considering multiple generating sources to analyze a complete system. 11. Further work can be done by providing low-cost solutions to achieve constant or variable dc-link voltage while ensuring low switching losses in the system. 12. More work can be done on developing algorithms to provide active power curtailment by considering variation in irradiance under variable dc-link voltage. 13. Further research can be carried out in reducing the ripples in dc-link voltage to achieve better power balance by using advanced dc-dc converter topologies. In a nutshell, future work should emphasize the design of control strategies from a systemic standpoint. The control strategies should be able to fulfill multiple objectives considering power quality issues under variable power generation. Finally, researchers should also focus on the stability aspects to completely analyze the performance of the system under internal and external disturbances.

VII. CONCLUSION
Several challenges are present during LVRT operation in GCPV inverters. Various strategies are reported in the literature to overcome these challenges. This paper mainly categorizes these strategies and discusses the performance of each strategy. The categorization is based on voltage support, current limitation and dc-link voltage control.
The voltage support control strategies present in the literature are designed based on the type of grid. Some VSS help in providing voltage equalization but results in high THD and poor dynamic response. Other VSSs inject both active and reactive power for enhanced voltage support but have challenges in tuning the controller. Another strategy simultaneously provides voltage support and current limitation but results in sustained oscillations in reactive power. Few other strategies have been discussed that have low THD and improved power factor but results in network losses and suffer from poor dynamic response.
The current limitation strategies discussed help in limiting the overcurrent in the faulty phase to prevent activation of inverter overcurrent protection. A CLS is designed by curtailing the PV power but has large oscillations in the reactive power. Another strategy exploits the maximum rating of the inverter and provides zero oscillations in active power and injects unbalanced currents. Yet another strategy helps in current limitation but provides no regulation on the minimum set point in the reduction of inverter overcurrent and does not exploit the full capability of the inverter. There are other strategies that improve the voltage support at PCC as well as provide current limitation with poor accuracy and result in oscillations in active and reactive power.
The dc-link voltage control strategy is further categorized into constant and adaptive. The constant dc-link strategies help in injecting balanced current within the system but result in oscillations in the dc-link voltage under asymmetrical faults. The adaptive dc-link strategies help in reducing the ripples in the dc-link voltage with low switching and ohmic losses in the inductor but result in large overshoot under external disturbances.
The control strategies present in the literature have only analyzed the performance under constant power generation during LVRT condition. The power quality issues, like oscillations in active, reactive powers and dc-link voltage along with THD in currents, efficiency, accuracy and stability aspects should be simultaneously tackled. Some strategies use the filtering capability of the PLLs to determine the sag under unbalanced grid voltage conditions. However, this additional filtering results in an increased computational burden on the system. Some additional strategies have also been discussed that help in overcoming challenges during LVRT such as active power backflow and voltage fluctuations at NP in transformer-less PV inverter.
Further future avenues for research have been pointed out that can be used to tackle power quality issues under variable power generation conditions. The categorization and comparison of these control strategies would prove to be beneficial for engineers, system operators, and researchers working in this area.