Multi-objective control scheme for operation of parallel inverter-based microgrids during asymmetrical grid faults

: The growing interest in connecting more distributed generation (DG) units to the utility grid, microgrids deal with the various challenges to satisfy a sufficient level of ancillary services such as active power oscillations (APOs), reactive power oscillations (RPOs), fault ride-through (FRT) capability, and overcurrent problem. Hence, for parallel operated grid-connected inverters (GCIs) based MG, this study presents a multi-objective control scheme that simultaneously ensures elimination of the collective APOs/RPOs at point of common coupling (PCC), overcurrent protection and reactive power injection. One of the significant parts of this study compared with similar existing studies is that provides reactive power support capability to fulfil the FRT requirements of the grid-connected multi-DG units and to remain grid-connected during asymmetrical grid faults. A current restraining control is also presented to ensure the safe operation of the MG system and to avoid overcurrent. The cancellation of the collective APOs and RPOs at the PCC for parallel operation of the GCIs has been achieved by using adjustable control coefficients and demonstrated with theoretical analyses in detail. Extensive case studies are presented and discussed to demonstrate the performance of the proposed ideas and to meet the shortcomings of the previous studies.


Nomenclatures
double frequency oscillations +, − positive and negative sequences, respectively ⊥ quadrature p, q active and reactive components, respectively min , max minimum and maximum, respectively

Introduction
Renewable energy sources (RESs) based distributed generations (DGs) become increasingly an attractive solution. Normally, RESs based DG units are integrated with power electronic converters (PECs) to form a large power system as well-known microgrids (MGs). Continuously rising integration of DGs into the utility grid (UG)-connected MGs has brought up crucial reliability and stability concerns to provide a sufficient level of ancillary services under unbalanced network conditions. A multi-MG system includes a cluster of the DGs interconnected for reliable and efficient operation in the grid-tied as well as islanded (disconnected UG) modes (see Fig. 1) [1]. In hybrid MGs, parallel PECs are increasingly used for large capacity DG units [2]. Hybrid MGs have increasingly integrated with PECs interfaced DGs, distributed generators (wind, solar), energy storage elements, and electrical vehicles (smart DC loads) in AC and DC subsystems. Therefore, an advanced power coordination or management strategy is required to coordinate power flow in the grid-connected or islanded power conversion system. In [3], an optimal control has been presented to coordinate the power flow between RES connected to the UG with the energy storage system. In [4], for two MG system predictive active power control has been discussed to control frequency deviation and to provide power balance between generated power and power demand of the system. Optimal frequency deviations control reported in [5] has analysed frequency deviation and tie-line power error between conventional power sources and the RES system. Also, comprehensive power coordination/management approaches have been reviewed for MG applications [6]. An active and reactive energy control scheme discussed in [7] has provided energy flows in the UG-connected fuel cell system. On the other hand, increasing interest in connecting more DG units with sensitive loads to the UG, power quality, and power control issues as a result of unbalanced voltages will be one of the important problems. Hence, the MGs should be properly controlled to overcome voltage unbalances resulting in excessive heat in motor windings, reducing motor life and motor efficiency, deteriorating the operation of electrical equipment, threats to the DC bus capacitor, reducing inverter efficiency, increasing more harmonic injection currents and oscillations [8,9]. In the literature, various methods of symmetrical components have been investigated to simplify the analysis of unbalanced threephase power systems under both balanced and unbalanced conditions [10][11][12].
Especially, power oscillations stemmed from unbalanced voltages can affect the operation of the UG-connected PECs. These oscillations are also reflected as oscillations in the DC-link voltage, which damages the PECs and reduces the lifetime of the PECs [13]. The oscillations on the DC-link cause a reduction of the RES system efficiency. Furthermore, the DC-link voltage oscillations create the third-order current harmonics and instability at the UG side. In many remote areas, AC and DC MGs provide significant ancillary services to solve electric power supply problems with the improvement of more advanced control techniques for the PECs. Among these services, fault ride-through (FRT) capability, overcurrent restraining control (ORC), and elimination of active power oscillation (APO) and reactive power oscillation (RPO) are fundamentally necessary [14].
The FRT of the UG connected MGs is of great importance. The RES-based DG systems are required to disconnect during grid faults, but sudden disconnection can affect the stability and reliability of the system because of the increased penetration of the RESs such as photovoltaic and wind power. Therefore, new standards and grid codes are enforced with large-scale photovoltaic and wind power plants to meet low-voltage ride-through (LVRT) requirements and to support the grid voltage recovery [15][16][17]. The FRT of the MGs requires increased reactive power during grid faults.
Extensive studies have been conducted to present various control schemes for the FRT of the MG applications in the grid-tied or islanded modes. Control strategies are addressed in [16,18,19] to enhance the voltage of the point of common coupling (PCC) with reactive power injection for large-scale grid-connected photovoltaic power plants during voltage sags. In [20], the FRT of three-phase three-wire (3P3W) inverter-based distributed energy sources has been presented. A fault detection method presented in [21] analyses the fault component characteristics of an MG under high-and low-impedance faults. A droop control loop-based LVRT strategy proposed in [22] to improve power-angle stability and provide reactive power support. Piya et al. [23] have presented an auxiliary voltage controller based on positive/negative sequences for the FRT of inverters used in the RESs in the case of unbalanced voltage sags. In [24], a control strategy based on improving the functionality of energy storage by providing islanded operation capability has been proposed for small-scale low-voltage active networks. Except for a few studies, all these methods study control strategies for single DG units. In [15], the LVRT scheme-based droop control has been proposed for three-phase four-wire (3P4W) grid-connected MG. Zhao et al. [25] present a positive/negative sequence-based droop control strategy to meet FRT operation of grid-interactive MG. Liu et al. [26] have suggested a fault current limitation strategy to suppress fault current during the FRT of the UG connected MG. In [27], an autonomous control scheme was presented to achieve LVRT and grid voltage support with multiple DG units. In [28], a distributed hierarchical control scheme was discussed for islanded MGs.
Elimination of APOs, RPOs, and the ORC are other important issues for parallel grid-connected inverter (GCI) of the MGs. A control strategy proposed in [2,13,29] cancels out the APOs for the operation of the GCI in hybrid MGs to enhance both AC and DC sub-grids power quality. Sadeghkhani et al. [30] conduct a current and voltage limiting strategy to improve FRT capability of 3P4W inverter-based islanded MGs. A reference current generation scheme with multi-objectives for DG operation reported in [31] to eliminate DC-link oscillations, enhance AC system stability, and comply with stringent grid codes. In [32], overcurrent control mechanism and regulation of the APOs and RPOs are addressed for a single GCI unit. Coordinated control of the parallel operation of two single-phase DG systems is considered in [33]. Another similar study proposed in [34] to develop a dual functional controller for single-phase fuel cell-based GCI. A flexible control strategy is proposed to fulfil new grid code requirements for asymmetrical FRT of the GCI in [35]. Shuai et al. [36] investigate the fault current characteristics of the 3P4W inverter and present a new overcurrent protection based on the estimation of the maximum phase current amplitude. The above-mentioned control strategies have been proposed for a single GCI operation under unbalanced grid faults. However, these control strategies cannot provide reduction and elimination of the adverse effects for parallel GCI and cannot guarantee their optimal operation. The FRT capability, ORC, and elimination of the APOs and RPOs for parallel GCI have not been systematically studied yet. Therefore, research studies on the parallel operation of the GCI under unbalanced grid faults are quite limited.
This paper presents a multi-objective control scheme for parallel operation of 3P3W inverters in the UG connected MG during asymmetrical grid faults. The proposed control scheme focuses on the following aspects: (i) to cancel out collective APOs or collective RPOs of parallel GCI at PCC, (ii) to meet the FRT requirements of parallel operation of the UG connected inverterbased MGs during grid faults, and (iii) to restrain overcurrent for parallel inverter at the same time. To provide reactive power support, reactive current sequences are developed based on voltage sequence and line impedance and incorporated into the proposed control structure using a detailed mathematical formulation. Adjustable control coefficients are designed to eliminate collective APOs and RPOs at PCC, which improve the power quality of both AC and DC sub-grids. Besides, the overcurrent protection method is addressed to provide the safe operation of each parallel inverter and to avoid overcurrent. The proposed control scheme is examined in parallel operation of the GCI-based practical test system. A comprehensive of case studies demonstrate the performance of the proposed ideas and meet the shortcomings of the previous studies.
The organisation of this paper is given as follows: Section 2 analyses the parallel operation of multiple GCI in MGs under asymmetrical grid faults. The mathematical equations of the collective APOs and RPOs are deduced by using control constraints. Section 3 introduces the proposed control scheme. The effectiveness of the proposed control scheme is validated by selected test cases in Section 4. Conclusions are presented in Section 5.

Operation of the UG connected MG under asymmetrical grid faults
This section analyses the operation of multiple parallel inverter based-MG under asymmetrical grid faults. The topology of the MGs and derivation of the cancellation of the collective APOs and RPOs are introduced.

Topology of the MGs
Considering Fig. 1, the MGs can be connected to the distributed systems via 3P3W or 3P4W GCI topologies (closing sw 1 and sw 2 , simultaneously). The performance of the GCI is considerably affected by zero-sequence voltage during unbalanced grid faults in the 3P4W. Hence, additional control is required for zero-sequence elimination. Zero-sequence components can be removed by using four-leg inverter topologies. In the proposed system, 3P3W GCI topologies are used, thus, positive and negative sequence components are only considered. Three-phase voltages at the PCC are calculated depending on the amplitude and phase angle by the following expressions for the kth parallel GCI as: The instantaneous PCC voltages can be converted in the stationary α − β coordinate system based on the Clarke transformation. For any unbalanced conditions, UG and PCC voltages v are separated into symmetric components using a sequence detection method as [37] v α where v PCC where γ = γ + − γ − is the phase angle between positive and negative sequences. The instantaneous active and reactive power can be written for the kth parallel GCI as where p and q indices in current components are related to active and reactive power, respectively. The magnitude of positive and negative sequence currents is respectively. The APOs and RPOs terms of the kth parallel GCI is calculated depending on the instantaneous power theory as: Considering (4) and (5), for unity power factor, Q k * is zero. APOs and RPOs for the kth parallel GCI are compensated using adjustable coefficients, μ p, k since v PCC

Elimination of the collective APOs for parallel inverters
Oscillatory of active power is directly reflected in the DC-link voltage, and variation of high-DC voltage can cause overvoltage problems and output distortion. Therefore, the APOs are required to eliminate. Considering (4), (5), and (8), the instantaneous active power comprising oscillations may be arranged for the kth parallel GCI [13].
where k = 1, 2, …, m. m is the number of parallel GCI. P k * and Q k * are references of active and reactive powers, respectively. When reference of reactive power for each parallel inverter is selected as zero, the amplitudes of active and RPOs are only controlled by the parameter μ p . Expression of (9) is rearranged as is the voltage unbalance factor. Considering m-parallel GCI, total APOs can be calculated as [2] p 2ω, 1 + p 2ω, 2 + p 2ω, 3 3 , and μ p, m are adjustable coefficients of first, second, third, and mth GCI, respectively. Assuming ∥ v PCC Considering (12) to provide oscillation-free of active power, p 2ω, 1 + p 2ω, 2 + p 2ω, 3 + ⋯ + p 2ω, m = 0 (see (13)) . Expression of (13) is rearranged as (see (14)) . For the collective APOs injected from parallel inverters to be zero in (14), μ p, 1 = μ p, 2 = μ p, 3 = ⋯ = μ p, m = − 1 or complement adjustable coefficients should be as IET Renew. Power Gener., 2020, Vol. 14 Iss. 13, pp. 2487-2498 © The Institution of Engineering and Technology 2020 1 a + μ p, 1 Constraint coefficients are extended for m-parallel GCI as

Elimination of the collective RPOs for parallel inverters
The oscillating in reactive power lead to power losses, control instability, and operating current rise, and thus, it is required to mitigate. Similar procedures for analysing APOs can be performed for the elimination of the RPOs for parallel inverters. Considering (4), (5), and (8), the instantaneous reactive power including oscillations can be expressed for the kth parallel GCI as [13] Flexible coefficient, μ p, k , has an impact on the RPOs. The RPOs are expressed as Considering the m-parallel GCI, total RPOs at PCC can be calculated as follows: Expression of (19) is rearranged as (see (20)) . Considering the above equations, oscillation-free of reactive power should be q 2ω, 1 + q 2ω, 2 + q 2ω, 3 + ⋯ + q 2ω, m = 0. To provide oscillation free of reactive power, constraint coefficients should be μ p, 1 = μ p, 2 = μ p, 3 = ⋯ = μ p, m = + 1 or can be expressed as Expression of (20) can be generalised for m-parallel GCI as

Design of adjustable control parameters
The unbalanced grid voltages result in double-frequency oscillating terms in active and reactive powers, which are directly reflected at the DC-side as oscillations and at the AC side as harmonics and instability [38]. Considering the unity power factor with the proposed control strategy, there is only one adjustable coefficient for each parallel inverter. The APOs are eliminated when the amplitude of p 2ω is controlled to be zero. Thus, the coefficients requirement of the APOs can be derived as The RPOs can affect the performance of the reactive power injection, which provides voltage support. Therefore, the oscillations in reactive power should be suppressed. To cancel out the RPOs for m-parallel GCI, the adjustable coefficient is selected as

Proposed control scheme
Parallel 3P3W inverters with common DC and AC-links are shown in Fig. 2a. These parallel inverters can be the connection path between the subsystems of the DC-AC MGs or the converter interfaces between the DG and the storage elements. Each parallel inverter is controlled separately and overcurrent protection is provided. Elimination of the APOs and RPOs for parallel inverters is performed by the proposed control scheme. According to the previous control strategies used in single three-phase inverters, one of the major contributions of the proposed control strategy used in parallel inverters is to eliminate the oscillations in the total power at the PCC even if each inverter out power has oscillations. Fig. 2b illustrates the proposed control scheme that focuses on the following aspects: (i) FRT of the UG connected inverter-based MG, (ii) overcurrent protection for parallel inverters, (iii) generation of reference currents for control of the GCI, and (iv) cancellation of the collective APOs and RPOs for parallel GCI.

FRT of the UG connected MG
Conventionally, inverters interfaced RES disconnect from the UG during grid faults and connect to the UG after clearing faults. However, all inverters interfaced RES located inside MG should be kept connected to the UG during FRT of the MG. Amplitude and phase angle are two controllable elements for the FRT of the UG connected MG. The PCC voltages are calculated depending on the amplitude and phase angle by using (25) and (26) q 2ω, 1 + q 2ω, 2 + q 2ω, 3 where sin min and sin max can be derived by the following functions as [41]: sin min, k = min sin γ k , sin γ k − 2π/3 , sin γ k + 2π/3 sin max, k = max sin γ k , sin γ k − 2π/3 , sin γ k + 2π/3 During grid fault conditions, to fulfil grid code requirements, minimum amplitude of three-phase voltages at the PCC should be the set value which is min V a, PCC , V b, PCC , V c, PCC ≥ 0.9 p . u . and maximum amplitude of three-phase voltage at the PCC should be the set value, which is max V a, PCC , V b, PCC , V c, PCC ≤ 1.1 p . u . In the proposed control scheme, the minimum and maximum voltage values, V min set , V max set are set to 0.9 and 1.1 p.u., respectively [42].
After determining the reference of minimum and maximum voltages in (27), the references of the positive and negative sequence PCC voltages for the grid code requirements are derived considering the shape of the grid voltages with (28) [39] v ref, k where To meet the FRT of the UG connected MG, the positive/negative sequence reactive current injected by m-parallel GCI is expressed based on (28) and line impedance as where I q, k * , + and I q, k * , − are the reference of positive/negative reactive current, respectively. The rate of reactive power flow is dependent on the occurrence of sag/swell and this in turn affects the power factor. Reactive power support is mainly dependent on voltage sequence and system impedance. Estimation of line impedance is an open research topic. It can be estimated by various methods [43] (see (33))

ORC for parallel inverters
Overcurrent issue is another important concern for reliability and stability of parallel GCI used in the MG. Restraining overcurrent faults are major challenges for the RES connected MG during unbalanced grid faults. Overcurrent also affects the lifetime of the power converter devices. Therefore, overcurrent restraining based schemes is required to provide AC and DC MG protection. A strong voltage sag as a result of the UG faults results in the inverter current to increase above the acceptable current limits of the GCI. Therefore, injected active power for each parallel inverter is adjusted to prevent this overcurrent. The phase currents are limited to the maximum current, I max for each parallel inverter, which can be obtained by (33) using (32). The reference current is updated and limited to maximum current to prevent overcurrent as

Generation of reference currents and operation of the system
In this section, the reference currents for the m-parallel inverters connected UG are calculated separately under unbalanced grid conditions. The calculated reference current can be used to easily control and eliminate oscillations. The reference current for the kth parallel inverters can be written by (32) or (34). I p, k * is the reference of active current and I q, k * = I q, k * , + + I q, k * , − is the reference of reactive current and obtained in the previous section. The generation of reference current and the switching signal for each parallel GCI is shown as step-by-step in Fig. 3. The reference currents which are used as input current control loops are obtained by using voltage sequence components, adjustable control parameter, and active and reactive current references. Then, the switching signals are obtained to drive the three-phase inverter.

Performance verification of the proposed control scheme
In this section, considering Fig. 2a, the proposed control scheme is examined on a practical test system based on parallel inverter topologies used in the UG connected MG. The performance and effectiveness of the proposed control scheme are confirmed by PSCAD/EMDTC based on various faults consisting of single lineto-ground (SLG) and line-line-to-ground (LLG) network faults. Along with case studies, while SLG fault occurs between phase A and ground, the LLG fault occurs between phase B, phase C, and ground. Under the SLG fault test, the amplitude of phase A is decreased as 50%. Under the LLG fault test amplitude of phase B and phase C is decreased as 35%. The main parameters used for parallel GCI topologies are given in Table 1.

Elimination of the collective APOs and RPOs using different control coefficients for parallel inverters
In this subsection, elimination of the APOs and RPOs for parallel GCI is discussed under various adjustable control parameters. The SLG fault is applied to the UG. In the following, first, the elimination of the APOs is considered for three parallel inverters (inverter#1, inverter#2, and inverter#3). The amplitudes of the APOs and RPOs are flexibly adjusted by the control coefficients.
Based on (23), there are two options to eliminate APOs, complementary control coefficients, and constant control coefficient ' −1 '. As is observed in Fig. 4a, except for the values of the control coefficients as chosen μ p, 1 = μ p, 2 = μ p, 3 = − 1, the active power signal has oscillations with other values of the control coefficients as a result of unbalanced grid faults. Also, when the control coefficients of parallel inverters are selected different from '−1', there are phase differences and different amplitudes between the output APOs. To demonstrate this case, three cases as shown in Figs. 4b-d are addressed. Considering, first, no oscillations in the output active power of inverter#1, the oscillations in the output active power of other inverters (inverter#2 and inverter#3) have the same amplitude but 180° phase differences. However, collective (total) oscillations of the active power are eliminated at the PCC since oscillations of the powers are complementing each other to cancel out.
IET Renew. Power Gener., 2020, Vol. 14 Iss. 13, pp. 2487-2498 © The Institution of Engineering and Technology 2020 Considering oscillations at the output active powers of three parallel inverters, the collective oscillations of active power are also eliminated at the PCC using different control coefficients. In Figs. 4c and d, although the output power of each inverter has oscillated, the collective oscillations of active power are eliminated using control coefficients as μ p, 1 = 0, μ p, 2 = 0, and μ p, 3 = − 2.75 and μ p, 1 = − 1.6, μ p, 2 = − 1.2, and μ p, 3 = 0. On the other hand, while APOs are eliminated, the oscillations of total reactive power are higher at the PCC. Due to not use the ORC, total phase currents (I abc, T ) of parallel inverters exceed the maximum current.
Similar to the elimination of the APOs, the RPOs can also be eliminated. The presence of the RPOs affects the voltage stability of the PCC. Unlike single three-phase inverters, in multiple parallel inverters, even if there are oscillations at the reactive power provided by each inverter, the collective oscillations of reactive power are cancelled out at the PCC. In this case study, three inverters are selected as inverter#1, inverter#2, and inverter#3 and the RPOs of inverter#1 are kept constant. Based on (24), there are two options to eliminate RPOs, complementary control coefficients and constant control coefficient '1'. When control coefficients are chosen as μ p, 1 = μ p, 2 = μ p, 3 = 1, the RPOs of all inverters are eliminated (see Fig. 5a), but in other control coefficient values, the RPOs oscillations occur. When control coefficients are chosen as μ p, 1 = 1, μ p, 2 = 1.5, and μ p, 3 = 0.5, there are no oscillations at the output reactive power of inverter#1, while there are oscillations in the output reactive power of other inverters (inverter#2 and inverter#3). As clearly shown in Fig. 5b, there is a 180° phase difference with the same amplitude between the output RPOs of inverter#1 and inverter#2. Therefore, the collective oscillations of reactive power at the PCC are eliminated.
In this case study, the output reactive powers of parallel operated three inverters have oscillations. The collective oscillations of reactive power can be eliminated at the PCC by using different control coefficients. In Fig. 6, when control coefficients are chosen as μ p, 1 = 0.3, μ p, 2 = 0.7, and μ p, 3 = 1.85 (see Fig. 6a) and μ p, 1 = 0.2, μ p, 2 = 0.5, and μ p, 3 = 2.3 (see Fig. 6b). Although the output reactive power of each inverter has the oscillations, the collective RPOs are eliminated at PCC. Likewise, in cases where RPOs are eliminated, oscillations in active power are present and oscillations in total active power are higher.

Overcurrent protection of each parallel inverter
Overcurrent protection of parallel operation of the GCI is quite limited in literature studies. Therefore, the ORC has been integrated into the proposed control scheme to satisfy the safe operation of the MG system. Over-current is prevented by applying ORC to each inverter. The collective output phase currents, (I abc, T ), of the parallel inverters are limited to maximum currents, (I max ). An LLG fault occurs at t = 0.4 s. To eliminate APOs, control coefficient is chosen as μ p, 1 = − 0.2, μ p, 2 = − 1.4, and μ p, 3 = − 1.2, while to eliminate RPOs, the control coefficient is chosen as μ p, 1 = 0.7, μ p, 2 = 0.6, and μ p, 3 = 1.7. As seen in Fig. 7a, with the ORC, the amount of active power injected by each inverter has changed due to using different control constraints for each inverter. Although there are oscillations at different active power levels, collective oscillations of active power are cancelled out at the PCC. Furthermore, compared to the existing methods, the collective RPOs are eliminated by the proposed control scheme (see Fig. 7b).

FRT for parallel operation of the GCI in MG
In this scenario, multi-objectives have been performed, simultaneously such elimination of the RPOs, FRT capability and avoiding overcurrent. As shown in Fig. 8, when LLG grid fault occurs at t = 0.4 s, the performance of the proposed control scheme is examined in case of reactive power support with and without ORC. Before the LLG fault, reactive power is not delivered by inverters (sw FRT is open). After closing switch sw FRT , the FRT control of two parallel inverters (inverter#1 and inverter#2) based-MG is activated (see Fig. 2b). A certain amount of reactive power, 46 kVAR for each parallel inverter is injected with large positivesequence current amplitude to meet FRT requirements of the GCI. At the bottom of Figs. 8a and b, about 92 kVAR for two parallel inverters, oscillations-free reactive power is injected to support the UG. Due to overcurrent; the maximum currents of each parallel inverter are injected to prevent damages or their disconnection. While the ORC is applied to each parallel inverter to restrain overcurrent in Fig. 8b, overcurrent has not been prevented in Fig. 8a. There are differences between amount injections of reactive currents since different control coefficients are used for each inverter. At the bottom of Figs. 8a and b, oscillations of the reactive power are cancelled out each other using control coefficient as μ p, 1 = 0.5 and μ p, 2 = 1.45.

Discussion for existing state-of-the-art controllers
In Table 2, different control strategies have been chosen to provide a comprehensive comparison with the proposed control scheme. The first merit factor is to cancel out collective APOs and RPOs of parallel GCI at the PCC. One of the main advantages of the proposed control scheme is to mitigate oscillations in the active and reactive powers at the PCC for parallel GCI. The collective APOs and RPOs of parallel GCI are dependent on the control coefficients. In [2,13], the total APOs have been removed from multi-DG units, but the elimination of the RPOs is not considered. The second merit factor is to provide a certain amount of reactive power injection for the FRT of the MG during asymmetric faults.
While some studies proposed in [22,23,25] have injected reactive power, but other issues (such as overcurrent protection and reducing oscillations from active and reactive powers) are not discussed. Another important factor is the overcurrent, which threatens the safety of the inverter under the asymmetrical grid fault. The ORC is quite limited for the operation of the parallel inverters. Except for some previous studies [2,26,27], the ORC is not introduced to prevent the risk of overcurrent over the inverter. Generally, the existing studies have addressed the above-mentioned issues for single inverter based-DG units. In this sense, the proposed control scheme provides multi-objectives, simultaneously to meet shortcomings of previous control schemes.

Conclusions
This paper presents a multi-objective control scheme for parallel operation of the GCI in MGs under asymmetrical grid faults. The proposed control scheme provides three important features for the different parallel GCI topologies, simultaneously: (i) elimination of the APOs/RPOs, (ii) protection of overcurrent, and (iii) supporting reactive power to meet FRT requirements. Even if there is oscillation at the power provided by each inverter, the proposed control scheme has the capability to cancel out collectively the APOs and RPOs of both individual and multi-parallel GCI. The cancellation of the collective APOs and RPOs for m-parallel GCI in MGs has been demonstrated by adjustable control coefficients as mathematically in detail. Elimination of the collective APOs and RPOs has been performed under the selection of different control coefficient scenarios. Reactive current sequences based on voltage sequence and line impedance have been incorporated into the   [2] no yes no yes no yes [13] yes yes no no no yes [15] yes no no no yes yes [22] yes no no no yes no [23] yes no no no yes no [25] yes no no no yes yes [26] yes no no yes yes yes [27] yes yes no yes yes yes [29] no yes no no no yes [33] yes no no no yes yes proposed control scheme yes yes yes yes yes yes IET Renew. Power Gener., 2020, Vol. 14 Iss. 13, pp. 2487-2498 © The Institution of Engineering and Technology 2020 proposed control structure using a detailed mathematical formulation to provide reactive power support during grid faults. A certain amount of reactive power about 46 kVAR for each parallel inverter is injected to fulfil FRT requirements of the parallel operated GCI units. Another major contribution of this paper is to keep all inverter peak currents in safe operation using the ORC. Extensive test results have confirmed the performance of the proposed control scheme and fulfilled the shortcomings of the existing studies. Besides, state-of-the-art existing methods have been compared to the proposed control scheme in Table 2. The proposed control scheme has the capability to be applied to both individual and multiple parallel GCI in MGs. Future study will consider an optimal control strategy (using Lagrange's theorem) for minimisation of the APOs and RPOs for parallel operation of single and multiple inverters based MGs.