A Grid-Supporting Photovoltaic System Implemented by a VSG with Energy Storage

: Conventional photovoltaic (PV) systems interfaced by grid-connected inverters fail to support the grid and participate in frequency regulation. Furthermore, reduced system inertia as a result of the integration of conventional PV systems may lead to an increased frequency deviation of the grid for contingencies. In this paper, a grid-supporting PV system, which can provide inertia and participate in frequency regulation through virtual synchronous generator (VSG) technology and an energy storage unit, is proposed. The function of supporting the grid is implemented in a practical PV system through using the presented control scheme and topology. Compared with the conventional PV system, the grid-supporting PV system, behaving as an inertial voltage source like synchronous generators, has the capability of participating in frequency regulation and providing inertia. Moreover, the proposed PV system can mitigate autonomously the power imbalance between generation and consumption, ﬁlter the PV power, and operate without the phase-locked loop after initial synchronization. Performance analysis is conducted and the stability constraint is theoretically formulated. The novel PV system is validated on a modiﬁed CIGRE benchmark under different cases, being compared with the conventional PV system. The veriﬁcations demonstrate the grid support functions of the proposed PV system.


Introduction
This paper proposes a grid-supporting photovoltaic system, including implementation and performance analysis. In this section, the background, literature review, formulation of the problem of interest for this investigation, scope and contribution of this study, and organization of the paper are presented.

Background and Significance
Synchronous generators (SGs), which take responsibility for frequency regulation in electric power systems (EPS), operate as inertial voltage sources, providing the inertia to slow down frequency dynamics and moderate the power imbalance between generation and consumption in an autonomous fashion. Driven by issues such as potential exhaustion of conventional fossil fuel based energies (e.g., coal, oil, and natural gas) and increasing environmental concerns, the quantity of renewable energy sources (RES) integrated into EPS is escalating [1,2]. In consequence, SGs are gradually being replaced by inverters with high penetration of RES.
Among RES, solar energy via photovoltaic (PV) systems is one of the most promising, and has largely penetrated the global energy market [3,4]. A decrease of investment costs, technological

Organization of the Paper
The content of this paper is organized as follows: Section 2 introduces the topology and control scheme. In Section 3, performance analysis is conducted, and the stability constraint is obtained through the established small-signal model. Results of case studies conducted on a modified CIGRE LV network benchmark are presented and discussed in Section 4. Section 5 draws the conclusions of this paper and discusses future research directions. Figure 1 shows the topology and control scheme of the grid-supporting PV system. In order to mimic the kinetic energy stored in the rotating rotors of SGs, an energy storage (ES) unit equipped with a bidirectional DC-DC converter was installed in the conventional PV system. Accordingly, the hardware consists of an ES unit, a bidirectional DC-DC converter, an inverter, and a PV array. The PV array was tied directly to the dc link, sharing the same dc bus with the DC-DC converter and the inverter. A buck/boost converter is adopted in this paper.

Scope and Contribution of This Study
Motivated by the above observations, this paper presents a novel grid-supporting PV system, achieving emulation of SG characteristics. Consequently, the grid-supporting PV system, behaving as SGs, contributes to supporting the grid by autonomously mitigating the power imbalance between generation and consumption, and slowing down frequency dynamics with virtual inertia. Accordingly, the proposed grid-supporting PV system is superior to the conventional PV system, while the conventional PV system cannot moderate the deficits and surplus of power in the grid, and is unable to provide inertia.

Organization of the Paper
The content of this paper is organized as follows: Section 2 introduces the topology and control scheme. In Section 3, performance analysis is conducted, and the stability constraint is obtained through the established small-signal model. Results of case studies conducted on a modified CIGRE LV network benchmark are presented and discussed in Section 4. Section 5 draws the conclusions of this paper and discusses future research directions. Figure 1 shows the topology and control scheme of the grid-supporting PV system. In order to mimic the kinetic energy stored in the rotating rotors of SGs, an energy storage (ES) unit equipped with a bidirectional DC-DC converter was installed in the conventional PV system. Accordingly, the hardware consists of an ES unit, a bidirectional DC-DC converter, an inverter, and a PV array. The PV array was tied directly to the dc link, sharing the same dc bus with the DC-DC converter and the inverter. A buck/boost converter is adopted in this paper. As Figure 1 depicts, the overall control scheme of the grid-supporting PV system comprises three strategies: DC-DC control, VSG control, and coordination control. The coordination control is designed to attune the system with two tasks: (1) One is to ascertain the value of the dc link voltage reference Udc_ref, utilizing a maximum power point tracking (MPPT) algorithm to draw maximum power from the PV array. Udc_ref is provided for DC-DC control, which performs the regulation of dc link voltage udc. (2) Another is to constrain the state of charge (SOC) of the ES unit through regulating As Figure 1 depicts, the overall control scheme of the grid-supporting PV system comprises three strategies: DC-DC control, VSG control, and coordination control. The coordination control is designed to attune the system with two tasks: (1) One is to ascertain the value of the dc link voltage reference U dc_ref , utilizing a maximum power point tracking (MPPT) algorithm to draw maximum power from the PV array. U dc_ref is provided for DC-DC control, which performs the regulation of dc link voltage u dc . (2) Another is to constrain the state of charge (SOC) of the ES unit through regulating the inverter active power reference P ref , which capacitates the buck/boost to control u dc for the inverter The conventional PV system is only energized by PV input, and its interface inverter is controlled by a voltage-oriented control method, with an outer dc link voltage control loop and an inner current control loop [29]. As shown in Figure 1, the proposed grid-supporting PV system however, is energized by a PV array and ES unit, and the interface inverter is driven by the VSG control. Benefiting from the topology and control scheme, which are different from those of the conventional PV system, the grid-supporting PV system is able to provide inertia and participate in frequency regulation as SGs.

Coordination Control
To behave as an energy buffer like a rotating rotor, the ES unit must have not only energy to release, but also capacity to store absorbed energy. Therefore, the SOC of the ES unit must be kept within a proper range. Meanwhile, it is necessary to constrain the SOC to control the dc link voltage u dc , so that the ES unit can release energy when u dc falls, and store the absorbed energy when u dc rises.
To constrain the SOC, the exchanged power P ES (positive for discharge and negative for charge) between the ES unit and the dc link must be regulated. However, P ES cannot be directly controlled by the buck/boost converter, which is resulted from that the DC-DC control performs the regulation of u dc .
According to the law of conservation of energy, the following equation is obtained when the energy change of the capacitor at the dc link is ignored: where P pv is the power generated by the PV array, and P e is the output active power of the inverter in the system. Since the PV array operates at the maximum power point, P pv in Equation (1) fails to adjust. Thus, regulating P e is the only way to control P ES . Due to the emulated SG characteristics of the inverter, P e can be controlled with coordination control through regulating the inverter active power reference P ref . To track the exchanged power reference P ES_ref , a proportional-integral (PI) regulator, whose input is the error between P ES_ref and P ES , is used for generating P ref . Then, P ref can be expressed as where G PI (s) = K p + K i /s is the transfer function of the PI regulator, K p and K i are the proportional coefficient and integral coefficient of the PI regulator, respectively, and s is the Laplace operator. The relationship of exchanged power reference P ES_ref with respect to the SOC is designed as shown in Figure 2, where SOC M is the mean of lower limit SOC L and higher limit SOC H , and P 0 is the absolute value of the charge power and the discharge power. The ES unit starts charging once the SOC is less than SOC L , and discharging when the SOC is more than SOC H . Both charging and discharging are terminated when the SOC reaches SOC M . Applying the curve shown in Figure 2 to specify P ES_ref , frequent operations of charge/discharge near SOC L /SOC H can be avoided by the coordination control. As the charge power and the discharge power of the ES unit depend on P 0 , the rated power of the inverter and the charge-discharge rate (C-rate) of the ES unit need to be taken into account when determining P 0 . First, the charge power and the discharge power of the ES unit should not be more than the rated power of the inverter to protect the inverter from over-current. Second, P 0 should ensure the charge current and the discharge current do not exceed the maximum C-rate so that the cycling life and the capacity of the ES unit are not significantly affected.
The dc link voltage reference U dc_ref is generally equal to U MPP , which is calculated by a maximum power point tracking (MPPT) algorithm, to ensure that the PV array operates at the point where it can output maximum power. Incremental Conductance [30,31], a classical MPPT algorithm, is employed in this paper.  The dc link voltage reference Udc_ref is generally equal to UMPP, which is calculated by a maximum power point tracking (MPPT) algorithm, to ensure that the PV array operates at the point where it can output maximum power. Incremental Conductance [30,31], a classical MPPT algorithm, is employed in this paper.

VSG Control
The VSG control aims to equip the inverter with the characteristics of a SG so that the inverter is capable of behaving like the SG. To realize the inverter emulating the characteristics of the SG, there are three sub-processes to implement during one carrier cycle, as illustrated in Figure 1. The voltages of the filter capacitors, ua, ub and uc, are measured in real time, and virtualize the phase terminal voltages of the stator windings and serve as the input variables of a SG model. Through solving the model, the stator currents of the SG, ia_ref, ib_ref, and ic_ref, are obtained as the reference currents for the inverter. To complete the emulation of the SG characteristics, the inverter output currents should be driven to track the reference currents. Thus, proportional-integral (PI) regulators in the rotating frame are employed to control the inverter.
The SG model adopted in this work comprises third-order electrical equations and second-order mechanical equations. The electrical equation set, which reproduces the stator circuit of the SG, is given by The electromechanical characteristics of the SG, neglecting the mechanical losses and considering the effect of damper windings, can be described as where H is the inertia constant, Pm is the mechanical power, D is the damping coefficient, ω and ω0 are the actual and the nominal angular frequency, respectively, and θ is the electrical rotation angle.
To emulate the droop characteristics of the primary frequency control (PFC) and primary voltage control (PVC), Pm and E can be expressed as

VSG Control
The VSG control aims to equip the inverter with the characteristics of a SG so that the inverter is capable of behaving like the SG. To realize the inverter emulating the characteristics of the SG, there are three sub-processes to implement during one carrier cycle, as illustrated in Figure 1. The voltages of the filter capacitors, u a , u b and u c , are measured in real time, and virtualize the phase terminal voltages of the stator windings and serve as the input variables of a SG model. Through solving the model, the stator currents of the SG, i a_ref , i b_ref , and i c_ref , are obtained as the reference currents for the inverter. To complete the emulation of the SG characteristics, the inverter output currents should be driven to track the reference currents. Thus, proportional-integral (PI) regulators in the rotating frame are employed to control the inverter.
The SG model adopted in this work comprises third-order electrical equations and second-order mechanical equations. The electrical equation set, which reproduces the stator circuit of the SG, is given by where u abc = [u a , u b , u c ] T denotes the phase terminal voltages of the stator windings; R s and L s are respectively the stator resistance and the stator inductance; i abc_ref = [i a_ref , i b_ref , i c_ref ] T represents the currents of the stator windings, which serve as reference currents for the inverter; and e abc = [e a , e b , e c ] T = E[sinθ, sin(θ − 2π/3), sin(θ + 2π/3)] T denotes the induced phase electromotive forces in the stator windings. The electromechanical characteristics of the SG, neglecting the mechanical losses and considering the effect of damper windings, can be described as where H is the inertia constant, P m is the mechanical power, D is the damping coefficient, ω and ω 0 are the actual and the nominal angular frequency, respectively, and θ is the electrical rotation angle.
To emulate the droop characteristics of the primary frequency control (PFC) and primary voltage control (PVC), P m and E can be expressed as where K ω is the unit power regulation, E 0 is the no-load electromotive force (EMF), Q ref and Q are the reference value and the actual value of the inverter output reactive power, respectively, and K Q is the voltage droop coefficient.

DC-DC Control
The objective of the DC-DC control is to keep the actual value of the dc link voltage u dc equal to the voltage reference U dc_ref provided by the MPPT algorithm of the coordination control. Regulating u dc to track u dc_ref enables the PV array to operate at the maximum power point. The DC-DC control strategy incorporates an outer voltage loop with an inner current loop, as depicted in Figure 1. Through DC-DC control, a stiff dc link voltage, which is required to emulate the inertia, is provided for the inverter.
The buck/boost converter works in BUCK mode and charges the ES unit to prevent u dc from rising when P pv > P e . Under the condition of P pv < P e , the buck/boost converter operates in BOOST mode and discharges the ES unit to stop u dc from dropping. This indicates that the ES unit behaves as an energy buffer, emulating a rotating rotor through complementing the deficit, or absorbing the surplus, of PV production.

Performance Analysis and Stability Constraint Formulation
In this section, a small signal per unit (pu) model that considers the Q-E droop control is established. Utilizing the model, performance analysis is conducted, the impact of the Q-E droop control on stability is investigated, and the stability constraint is obtained. δ is the power angle; U g is the amplitude of the grid voltage; R s + jX s is the virtual stator impedance implemented by the VSG control; R g + jX g is the grid impedance, which includes the line impedance; and the grid-side filter impedance jωL 2 and P e + jQ is the apparent power measured for the control scheme.

Small-Signal Modelling
where Kω is the unit power regulation, E0 is the no-load electromotive force (EMF), Qref and Q are the reference value and the actual value of the inverter output reactive power, respectively, and KQ is the voltage droop coefficient.

DC-DC Control
The objective of the DC-DC control is to keep the actual value of the dc link voltage udc equal to the voltage reference Udc_ref provided by the MPPT algorithm of the coordination control. Regulating udc to track udc_ref enables the PV array to operate at the maximum power point. The DC-DC control strategy incorporates an outer voltage loop with an inner current loop, as depicted in Figure 1. Through DC-DC control, a stiff dc link voltage, which is required to emulate the inertia, is provided for the inverter.
The buck/boost converter works in BUCK mode and charges the ES unit to prevent udc from rising when Ppv > Pe. Under the condition of Ppv < Pe, the buck/boost converter operates in BOOST mode and discharges the ES unit to stop udc from dropping. This indicates that the ES unit behaves as an energy buffer, emulating a rotating rotor through complementing the deficit, or absorbing the surplus, of PV production.

Performance Analysis and Stability Constraint Formulation
In this section, a small signal per unit (pu) model that considers the Q-E droop control is established. Utilizing the model, performance analysis is conducted, the impact of the Q-E droop control on stability is investigated, and the stability constraint is obtained. Figure 3 depicts the equivalent circuit of the inverter when connected to the grid. In this figure, δ is the power angle; Ug is the amplitude of the grid voltage; Rs + jXs is the virtual stator impedance implemented by the VSG control; Rg + jXg is the grid impedance, which includes the line impedance; and the grid-side filter impedance jωL2 and Pe + jQ is the apparent power measured for the control scheme. When Rs and Rg are neglected due to Xs ⪢ Rs and Xg ⪢ Rg, Pe and Q can be expressed according to Figure 3 as follows:

Small-Signal Modelling
Linearizing Pe and Q with respect to E and δ, the deviations of Pe and Q are given by  When R s and R g are neglected due to X s R s and X g R g , P e and Q can be expressed according to Figure 3 as follows: Linearizing P e and Q with respect to E and δ, the deviations of P e and Q are given by where ∆x (x = P e , Q, E, and δ) represents the deviation of x, and The small signal model of the Q-E droop control described by Equation (7) is given by Solving Equations (10), (11), and (16), ∆P e and ∆Q can be further derived as Normalizing and linearizing Equations (4) and (5) yields [32] d∆ω where ∆ω is the angular frequency deviation, ∆P m is the deviation of P m , D is the damping coefficient, H is the inertia constant in seconds, and ω 0 is the nominal angular frequency in rad/s. The incremental Equations of (1), (2) and (6) are By combining Equations (17)-(24), the small-signal model considering the Q-E droop control is established in Figure 4, and ∆ω is correspondingly derived as Equation (25).
where the transfer function G(s) is given by  (25) where the transfer function G(s) is given by The expected performance of the grid-supporting PV system can be achieved if H, D + Kω, Kp, and Ki are properly selected in such a way that the poles of Equation (26) are located at desired locations.

Performance Analysis
The root loci family of the proposed PV system is shown in Figure 5a, where 2H = 1 s, 3 s, and 15 s, and D + Kω changes from 10 pu to 200 pu. It is clear that H plays an important role in determining The expected performance of the grid-supporting PV system can be achieved if H, D + K ω , K p , and K i are properly selected in such a way that the poles of Equation (26) are located at desired locations.

Performance Analysis
The root loci family of the proposed PV system is shown in Figure 5a, where 2H = 1 s, 3 s, and 15 s, and D + K ω changes from 10 pu to 200 pu. It is clear that H plays an important role in determining the settling time of the proposed PV system. As D + K ω increases, the damping of the system rises and the stability is improved.

Impact of Q-E Droop Control on Stability
As Figure 5c illustrates, KS is a factor that affects the stability of the grid-supporting PV system. According to Equation (17), Ks consists of two parts, kPδ and ΔKS. It is indicated in Equation (19) that Figure 5b depicts the root loci family considering variations of K i from 0.1 pu to 50 pu, and K p = 0.3 pu, 1.1 pu, and 2 pu. As Figure 5b shows, the damping drops, the overshoot rises, and the undamped natural frequency increases when K p becomes larger. The damped frequency and the stability margin mainly depend on K i . Instability may happen with an excessively large value of K i . To ensure the stability of the system, it is necessary to formulate the constraint explicitly on H, D + K ω , K p , and K i to guide the tuning of parameters. Figure 5c depicts the root locus where K S varies from 0.5 pu to 2 pu. Among the three poles depicted in the plane, s 3 is the real root and its position depends on K p and K i . As K S increases, the conjugate complex roots s 1 and s 2 evolve in the direction of the arrows. A larger K S increases the real parts of s 1 and s 2 , which improves the stability.

Impact of Q-E Droop Control on Stability
As Figure 5c illustrates, K S is a factor that affects the stability of the grid-supporting PV system. According to Equation (17), K s consists of two parts, k Pδ and ∆K S . It is indicated in Equation (19) that ∆K S is related to the coefficient K Q of the Q-E droop control and embodies the impact of the Q-E droop control on the stability. When the Q-E droop control is invalidated (i.e., K Q = 0) and only P-ω is considered, ∆K S vanishes identically, and K S in Equation (17) is equal to k Pδ .
By substituting Equations (13)-(15) into Equation (19), ∆K S can be obtained as Equation (27), where r = X g /X S . On the condition that the Q-E droop control works, K Q is set to be a positive number. The power angle δ lies in the range from 0 • to 90 • , and E is generally larger than U g . Thus, k Pδ , k PE , and k QE are all positive. Accordingly, the curve of ∆K S with respect to the ratio X g /X S is shown in Figure 6.
Energies 2018, 11, x FOR PEER REVIEW 10 of 20 The power angle δ lies in the range from 0° to 90°, and E is generally larger than Ug. Thus, kPδ, kPE, and kQE are all positive. Accordingly, the curve of ΔKS with respect to the ratio Xg/XS is shown in Figure 6.
As Figure 6 illustrates, ΔKS is positive if the ratio Xg/XS is less than 1, while ΔKS is negative if the ratio Xg/XS is greater than 1. Accordingly, KS is greater than kPδ under the condition of Xg < XS, which means the Q-E droop control improves the stability, since a larger KS improves the stability. Conversely, KS is less than kPδ when Xg > XS, which indicates that the Q-E droop control worsens the stability in the weak grid. Besides, KS is zero in the case of Xg = XS, implying that the Q-E droop control has no effect on the stability.

Stability Constraint Formulation
The closed-loop system of Equation (26) is a third-order linear time-invariant. To analyze the stability, the Routh-Hurwitz stability criterion is used. The system characteristic equation is obtained from Equation (26) where a0 = 2H, a1 = D + Kω, a2 = ω0KS(Kp + 1), and a3 = ω0KSKi. Through applying the Routh-Hurwitz stability criterion to Equation (28), the system stability discriminant is yielded as Since H, D + Kω, Kp, and Ki are positive real numbers, the discriminant can be simplified as Xg/Xs ΔKS Figure 6. Curve of ∆K S with respect to the ratio X g /X S .
As Figure 6 illustrates, ∆K S is positive if the ratio X g /X S is less than 1, while ∆K S is negative if the ratio X g /X S is greater than 1. Accordingly, K S is greater than k Pδ under the condition of X g < X S , which means the Q-E droop control improves the stability, since a larger K S improves the stability. Conversely, K S is less than k Pδ when X g > X S , which indicates that the Q-E droop control worsens the stability in the weak grid. Besides, K S is zero in the case of X g = X S , implying that the Q-E droop control has no effect on the stability.

Stability Constraint Formulation
The closed-loop system of Equation (26) is a third-order linear time-invariant. To analyze the stability, the Routh-Hurwitz stability criterion is used. The system characteristic equation is obtained from Equation (26) as D(s) = a 0 s 3 + a 1 s 2 + a 2 s + a 3 = 0 where a 0 = 2H, a 1 = D + K ω , a 2 = ω 0 K S (K p + 1), and a 3 = ω 0 K S K i . Through applying the Routh-Hurwitz stability criterion to Equation (28), the system stability discriminant is yielded as Since H, D + K ω , K p , and K i are positive real numbers, the discriminant can be simplified as Substituting a i into Equation (30) gives Equation (31) presents the stability constraint for the grid-supporting PV system, which H, D + K ω , K p , K i , and K S must satisfy to guarantee the stability of the system.

Results and Discussion
The proposed grid-supporting PV system was verified on the CIGRE benchmark of the European LV distribution network elaborated in Reference [33]. The topology of the benchmark is shown in Figure 7, and the line parameters of the benchmark are given in Table 1. All loads were configured to be balanced for simplicity. The apparent power and power factor (PF) of the loads are described in Figure 7. The 20 kV medium voltage grid in this benchmark was equated with a SG system with inertia constant of H = 9 s [32]. The PFC of the SG system reacts in 5 s when there is a frequency deviation, and the speed regulation of the PFC is 3.33%. Six cases were considered when disturbances occur, as listed in Table 2.

Results and Discussion
The proposed grid-supporting PV system was verified on the CIGRE benchmark of the European LV distribution network elaborated in Reference [33]. The topology of the benchmark is shown in Figure 7, and the line parameters of the benchmark are given in Table 1. All loads were configured to be balanced for simplicity. The apparent power and power factor (PF) of the loads are described in Figure 7. The 20 kV medium voltage grid in this benchmark was equated with a SG system with inertia constant of H = 9 s [32]. The PFC of the SG system reacts in 5 s when there is a frequency deviation, and the speed regulation of the PFC is 3.33%. Six cases were considered when disturbances occur, as listed in Table 2.   Figure 7. Modified benchmark of the European LV distribution network. Case A and Case B considered sudden load variation by switching a load of 25 kW in R11 at 2 s. Case C and Case D considered a three-phase short circuit fault occurring at 2 s, the fault in each case was located at R17 and was cleared at 3 s. A step of solar irradiance from 1000 W/m 2 to 1050 W/m 2 was exerted on the PV array of DG3 at 2 s in Case E and Case F. After the disturbance occurred at 2 s in each case, the PFC was activated in 5 s; that is, at 7 s.
In Case A, Case C, and Case E, three conventional single-stage PV systems were applied to the benchmark as DG1−DG3. In comparison with the conventional PV system, three proposed grid-supporting PV systems, with parameters listed in Table 3, were connected to the feeder as DG1−DG3 in Case B, Case D, and Case F, and each ES unit was comprised of 25 Powersonic PS-121100 batteries in series. The SOC of each ES unit was set to 50%, which leads to P ES_ref = 0. To verify the functions of smoothing the power and tracking the maximum power point of the conventional PV system and the proposed grid-supporting PV system, solar irradiance steps were used in Case E and Case F to provide the most severe condition, although there is little possibility that the solar irradiance step would occur in a real case. Figure 8a gives the resultant frequency of the grid, DG1, DG2, and DG3, respectively. All frequencies decrease consistently between 2 s and 5 s. With the phase-lock loop, the conventional PV system tracks the grid frequency (i.e., the LV distribution network frequency), but fails to provide the inertia due to operating as a grid-following unit. As depicted in Figure 8b, the output power of the conventional PV system injects power into the LV distribution network without change after the load variation, and thus is incapable of mitigating the power imbalance between generation and consumption. Figure 8c illustrates the dc link voltages, which are always regulated by the inverter of the conventional PV systems to perform MPPT. consumption. Figure 8c illustrates the dc link voltages, which are always regulated by the inverter of the conventional PV systems to perform MPPT.  Figure 9 presents the responses when three proposed PV systems are integrated into the LV distribution network as DG1−DG3. As depicted in Figure 9a, all frequencies decrease between 2 s and 5 s, with a smaller rate of change of frequency (ROCOF) and higher frequency nadir when compared with Figure 8a of Case A. Through emulating the inertia of SGs, the proposed PV system is able to slow down frequency response and allow decent time for frequency control. Figure 9b shows that the proposed PV system mitigates the power imbalance between generation and consumption by increasing the output active power Pe autonomously, and thus supports the grid, mimicking the SG. Figure 9c plots the dc link voltage of the interface inverter, which is maintained at UMPP by the buck/boost converter with the ES unit, even if there is an imbalance between Ppv and Pe. It is demonstrated that a stiff dc link voltage can be provided in the proposed PV system for the inverter to emulate the inertia. Figure 9d illustrates the exchanged power PES between the ES unit and the dc link. After the sudden load variation, the incremental of PES is consistent with that of Pe shown in Figure 9b. It is indicated that the ES unit balances the power between the PV array and the inverter, which emulates the behavior of a rotating rotor releasing kinetic energy when it's frequency drops. After PFC activation, the exchanged power PES, regulated by coordination control, gradually converges to PES_ref to constrain the SOC.  Figure 9 presents the responses when three proposed PV systems are integrated into the LV distribution network as DG1−DG3. As depicted in Figure 9a, all frequencies decrease between 2 s and 5 s, with a smaller rate of change of frequency (ROCOF) and higher frequency nadir when compared with Figure 8a of Case A. Through emulating the inertia of SGs, the proposed PV system is able to slow down frequency response and allow decent time for frequency control. Figure 9b shows that the proposed PV system mitigates the power imbalance between generation and consumption by increasing the output active power P e autonomously, and thus supports the grid, mimicking the SG. Figure 9c plots the dc link voltage of the interface inverter, which is maintained at U MPP by the buck/boost converter with the ES unit, even if there is an imbalance between P pv and P e . It is demonstrated that a stiff dc link voltage can be provided in the proposed PV system for the inverter to emulate the inertia. Figure 9d illustrates the exchanged power P ES between the ES unit and the dc link. After the sudden load variation, the incremental of P ES is consistent with that of P e shown in Figure 9b. It is indicated that the ES unit balances the power between the PV array and the inverter, which emulates the behavior of a rotating rotor releasing kinetic energy when it's frequency drops. After PFC activation, the exchanged power P ES , regulated by coordination control, gradually converges to P ES_ref to constrain the SOC.

Case C: Short Circuit Fault-Conventional PV System
As Figure 10a depicts, the grid frequency, which is tracked by the conventional PV system, decreases until the fault is cleared and reaches the nadir of 49.82 Hz at 3 s. However, after the clearance of the fault, frequencies of the grid, DG1, DG2, and DG3 hardly change until the PFC is activated at 5 s. This shows that the conventional PV system fails to participate in frequency regulation. As Figure 10b depicts, the power imbalance resulting from the fault is counteracted only by the grid, while the conventional PV system is incapable of responding to the power imbalance, and outputs power without change after the fault occurs. The dc link voltage, illustrated in Figure  10c, is regulated during the fault to draw maximum power from the PV array.

Case D: Short Circuit Fault-Proposed PV System
System responses to a three-phase short circuit fault, where three proposed PV systems are integrated as DG1−DG3, are studied in this case, and given in Figure 11.

Case C: Short Circuit Fault-Conventional PV System
As Figure 10a depicts, the grid frequency, which is tracked by the conventional PV system, decreases until the fault is cleared and reaches the nadir of 49.82 Hz at 3 s. However, after the clearance of the fault, frequencies of the grid, DG1, DG2, and DG3 hardly change until the PFC is activated at 5 s. This shows that the conventional PV system fails to participate in frequency regulation. As Figure 10b depicts, the power imbalance resulting from the fault is counteracted only by the grid, while the conventional PV system is incapable of responding to the power imbalance, and outputs power without change after the fault occurs. The dc link voltage, illustrated in Figure 10c, is regulated during the fault to draw maximum power from the PV array.

Case C: Short Circuit Fault-Conventional PV System
As Figure 10a depicts, the grid frequency, which is tracked by the conventional PV system, decreases until the fault is cleared and reaches the nadir of 49.82 Hz at 3 s. However, after the clearance of the fault, frequencies of the grid, DG1, DG2, and DG3 hardly change until the PFC is activated at 5 s. This shows that the conventional PV system fails to participate in frequency regulation. As Figure 10b depicts, the power imbalance resulting from the fault is counteracted only by the grid, while the conventional PV system is incapable of responding to the power imbalance, and outputs power without change after the fault occurs. The dc link voltage, illustrated in Figure  10c, is regulated during the fault to draw maximum power from the PV array.

Case D: Short Circuit Fault-Proposed PV System
System responses to a three-phase short circuit fault, where three proposed PV systems are integrated as DG1−DG3, are studied in this case, and given in Figure 11.

Case D: Short Circuit Fault-Proposed PV System
System responses to a three-phase short circuit fault, where three proposed PV systems are integrated as DG1−DG3, are studied in this case, and given in Figure 11. The grid frequency, as shown in Figure 11a, decreases from the normal value of 50 Hz to the nadir of 49.87 Hz lasting from 2 s to 3 s. In comparison with Case C, a smaller ROCOF and slighter frequency deviation are caused by the fault in this case. It is perceived in Figure 11a that the grid frequency is regulated by the proposed PV system in the absence of PFC action during 3-7 s. As depicted in Figure 11b, the proposed PV system increases its output active power and moderates the power imbalance, while the conventional PV system fails to implement this function, as shown in Figure 10b. Figure 11c illustrates the dc link voltage of the proposed PV system, which indicates that the proposed PV system is able to provide a stiff dc link voltage to emulate the inertia and perform MPPT. As depicted in Figure 11d, the incremental of PES is consistent with that of Pe shown in Figure 11b, verifying that the ES unit balances the power between the PV array and the inverter, which emulates the behavior of a rotor releasing kinetic energy when it's frequency declines.

Case E: Step of Solar Irradiance-Conventional PV System
As Figure 12a shows, the step of solar irradiance exerted on the PV array of DG 3 causes a sudden change of the power generated from the PV array in DG3. The dc link voltage of the inverter in DG 3 increases, as depicted in Figure 12b, to track UMPP specified by the MPPT algorithm in the coordination control. Due to the lack of an energy buffer in the conventional PV system, DG3 injects the fluctuant PV power resulting from the solar irradiance step into the LV distribution network, and the output active power rises suddenly, as shown in Figure 12c. Figure 12d shows that the grid frequency deviates after the solar irradiance step until the PFC is activated. The grid frequency, as shown in Figure 11a, decreases from the normal value of 50 Hz to the nadir of 49.87 Hz lasting from 2 s to 3 s. In comparison with Case C, a smaller ROCOF and slighter frequency deviation are caused by the fault in this case. It is perceived in Figure 11a that the grid frequency is regulated by the proposed PV system in the absence of PFC action during 3-7 s. As depicted in Figure 11b, the proposed PV system increases its output active power and moderates the power imbalance, while the conventional PV system fails to implement this function, as shown in Figure 10b. Figure 11c illustrates the dc link voltage of the proposed PV system, which indicates that the proposed PV system is able to provide a stiff dc link voltage to emulate the inertia and perform MPPT. As depicted in Figure 11d, the incremental of P ES is consistent with that of P e shown in Figure 11b, verifying that the ES unit balances the power between the PV array and the inverter, which emulates the behavior of a rotor releasing kinetic energy when it's frequency declines.

Case E: Step of Solar Irradiance-Conventional PV System
As Figure 12a shows, the step of solar irradiance exerted on the PV array of DG 3 causes a sudden change of the power generated from the PV array in DG3. The dc link voltage of the inverter in DG 3 increases, as depicted in Figure 12b, to track U MPP specified by the MPPT algorithm in the coordination control. Due to the lack of an energy buffer in the conventional PV system, DG3 injects the fluctuant PV power resulting from the solar irradiance step into the LV distribution network, and the output active power rises suddenly, as shown in Figure 12c. Figure 12d shows that the grid frequency deviates after the solar irradiance step until the PFC is activated.

Case F: Step of Solar Irradiance-Proposed PV System
Responses to the step of solar irradiance exerted on DG3 are studied in Figure 13 when three proposed PV systems are applied as DG1−DG3. After the solar irradiance steps, the power generated from the PV array in DG3 rises suddenly, as shown in Figure 13a, and the dc link voltage of DG3 increases to perform MPPT, as shown in Figure 13b. In comparison with Case E, the active power that DG3 feeds to the LV distribution network is filtered and rises smoothly, as depicted in Figure 13c, and the grid frequency deviates with a smaller ROCOF and lower zenith, as depicted in Figure 13d. Figure 13e shows that the exchanged power PES between the ES unit and the dc link decreases suddenly, and the ES unit of DG3 absorbs the surplus of PV production after the solar irradiance steps. PES eventually returns to zero, tracking the reference PES_ref to constrain the SOC, and the output active power Pe is finally equal to the power generated by the PV array Ppv.
It is demonstrated that the proposed PV system is able to smooth the power fed to the LV distribution network, even if the power generated by the PV array fluctuates suddenly.
Combining with the results in Cases A-F, Table 4 shows the following advantageous features of the proposed grid-supporting PV system as compared with the conventional PV system: (1) The grid-supporting PV system, presenting as SGs from the point-of-view of the grid by mimicking SG characteristics with VSG control, can support the grid through mitigating the power imbalance between generation and consumption, and slowing down frequency dynamics with virtual inertia. (2) Through emulating the droop characteristics of PFC and PVC, the grid-supporting PV system can participate in frequency regulation and voltage regulation. (3) The proposed PV system has the functions of filtering the PV power and smoothing the power fed to the grid, which leads to a reduced impact of PV fluctuation on the grid. (4) The grid-supporting PV system synchronizes with the grid through mimicking the synchronization mechanism of SGs, and thus the PLL, in which the delay may cause instability [34], is discarded in the proposed PV system.

Case F: Step of Solar Irradiance-Proposed PV System
Responses to the step of solar irradiance exerted on DG3 are studied in Figure 13 when three proposed PV systems are applied as DG1−DG3. After the solar irradiance steps, the power generated from the PV array in DG3 rises suddenly, as shown in Figure 13a, and the dc link voltage of DG3 increases to perform MPPT, as shown in Figure 13b. In comparison with Case E, the active power that DG3 feeds to the LV distribution network is filtered and rises smoothly, as depicted in Figure 13c, and the grid frequency deviates with a smaller ROCOF and lower zenith, as depicted in Figure 13d. Figure 13e shows that the exchanged power P ES between the ES unit and the dc link decreases suddenly, and the ES unit of DG3 absorbs the surplus of PV production after the solar irradiance steps. P ES eventually returns to zero, tracking the reference P ES_ref to constrain the SOC, and the output active power P e is finally equal to the power generated by the PV array P pv .
It is demonstrated that the proposed PV system is able to smooth the power fed to the LV distribution network, even if the power generated by the PV array fluctuates suddenly.
Combining with the results in Cases A-F, Table 4 shows the following advantageous features of the proposed grid-supporting PV system as compared with the conventional PV system: (1) The grid-supporting PV system, presenting as SGs from the point-of-view of the grid by mimicking SG characteristics with VSG control, can support the grid through mitigating the power imbalance between generation and consumption, and slowing down frequency dynamics with virtual inertia. (2) Through emulating the droop characteristics of PFC and PVC, the grid-supporting PV system can participate in frequency regulation and voltage regulation. (3) The proposed PV system has the functions of filtering the PV power and smoothing the power fed to the grid, which leads to a reduced impact of PV fluctuation on the grid. (4) The grid-supporting PV system synchronizes with the grid through mimicking the synchronization mechanism of SGs, and thus the PLL, in which the delay may cause instability [34], is discarded in the proposed PV system.

Conclusions
A novel grid-supporting PV system, which operates as an inertia voltage source by emulating the characteristics of SGs, is proposed in this paper.
To present the PV system as a SG from the point-of-view of the grid, both the topology and the control scheme were investigated. An ES unit equipped with a bidirectional DC-DC converter was installed, which can mimic the function of a rotating rotor for kinetic energy and buffer the imbalance of the PV power. On the other hand, the coordination control, DC-DC control, and VSG control were employed in the proposed system. The coordination control is able to constrain the SOC of the ES unit and calculate the voltage at the maximum power point of the PV array. The DC-DC control can perform the regulation of the dc link voltage to realize MPPT, and the VSG control is capable of equipping the interface inverter with SG characteristics.
To guide the tuning of the parameters, the system performance was analyzed with the variation parameter values. It was found that the inertia constant H plays an important role in determining the settling time, and that the system damping mainly depends on D + Kω. Furthermore, the stability constraint was formulated as Equation (31), which should be satisfied to guarantee the stability of the system.  Table 4. Advantages of the proposed grid-supporting PV system as compared with the conventional PV system.

Conventional PV System Proposed PV System
Emulating the characteristics of SGs to support the grid × √ Primary frequency control and primary voltage control × √ Smoothing the fluctuation of the power fed to the grid × √ PLL-less operation after initial synchronization × √ ×: operating without the feature; √ : operating with the feature.

Conclusions
A novel grid-supporting PV system, which operates as an inertia voltage source by emulating the characteristics of SGs, is proposed in this paper.
To present the PV system as a SG from the point-of-view of the grid, both the topology and the control scheme were investigated. An ES unit equipped with a bidirectional DC-DC converter was installed, which can mimic the function of a rotating rotor for kinetic energy and buffer the imbalance of the PV power. On the other hand, the coordination control, DC-DC control, and VSG control were employed in the proposed system. The coordination control is able to constrain the SOC of the ES unit and calculate the voltage at the maximum power point of the PV array. The DC-DC control can perform the regulation of the dc link voltage to realize MPPT, and the VSG control is capable of equipping the interface inverter with SG characteristics.
To guide the tuning of the parameters, the system performance was analyzed with the variation parameter values. It was found that the inertia constant H plays an important role in determining the settling time, and that the system damping mainly depends on D + K ω . Furthermore, the stability constraint was formulated as Equation (31), which should be satisfied to guarantee the stability of the system.
Results of case studies conducted on the modified CIGRE LV network benchmark verify the grid-supporting PV system. Compared with the conventional PV system, the grid-supporting PV system is advantageous in the following areas: (1) The VSG control and the ES unit capacitate the interface inverter of the proposed inverter to mimic SG characteristics, slowing down frequency response with inertia, and moderating the power imbalance between generation and consumption. (2) The emulation of the droop characteristics of PFC and PVC capacitates the grid-supporting PV system to contribute to frequency regulation and voltage regulation of EPS. (3) In the conventional PV system, the power fed to the grid must be equal to the power generated from the PV array. However, the installation of the ES unit in the grid-supporting PV system spares this embarrassment. Through the installed ES unit and the control scheme, the function of filtering the PV power and smoothing the PV system output power, which reduces the impact of PV fluctuations on the grid, is implemented in the proposed grid-supporting PV system. (4) With the VSG control, the interface inverter of the grid-supporting PV system mimics not only the inertia and frequency damping of SGs, but also the synchronization mechanism of SGs. Beneficially, the impact of the PLL on the stability is eliminated, which leads to the proposed PV system being more compatible with EPS than the conventional PV system that employs the PLL.
The topology, the control scheme, and the stability constraint for parameters are presented in this paper. In future, the method for optimizing the capacity of the ES unit under different conditions, where the values of H, D, and K ω , and the capacity of the PV array vary, need to be obtained in order to reduce costs. As the analysis indicates, the grid impedance has impacts on the stability of the system with the Q-E droop control. How to reduce or avoid these impacts is also set as one of our future research directions.
Author Contributions: H.X. and J.S. provided the original idea for this paper. H.X., N.L., and Y.S. organized the manuscript and attended the discussions when analysis and verification were carried out. All the authors gave comments and suggestions on the writing and descriptions of the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: