Additional Compound Damping Control to Suppress Low-Frequency Oscillations in a Photovoltaic Plant with a Hybrid Energy Storage System

: The use of the conventional dual closed-loop control strategy by photovoltaic (PV) plants with grid-connected inverters may weaken the damping of a power system, which may aggravate low-frequency oscillations (LFOs). This inﬂuence will become more severe as the penetration of PV plants increases. Therefore, it is necessary to incorporate damping controls into PV plants to suppress LFOs. This paper proposed an additional compound damping control (ACDC) system that combines additional damping control (ADC) for the inverter with ADC-based dynamic power compensation control (DPCC), allowing hybrid energy storage systems (HESSs) to suppress LFOs. First, the feasibility of suppressing low-frequency oscillations in PV plants is demonstrated by the torque method and a small signal model. Then, an additional damping controller is added to the active power control link of the PV inverter to enhance the damping abilities of the system. However, given that the damping performance of PV plants with only ADC is limited by the compensated power, PV plants require devices that can rapidly compensate for the damping power. Therefore, we added the HESS to the DC bus and proposed DPCC. Finally, a three-machine nine-node system for a PV plant was modeled and simulated in the PSCAD platform. The simulation results showed that the proposed control strategy could provide effective damping for interarea oscillation.


Introduction
Globally, due to the rapid consumption of fossil fuels and the continuous deterioration of the environment, renewable and clean energy sources have become a research focus.These include energies such as wind and solar energy.Wind and solar energy are expected to meet 50% of the global energy demand by 2050 [1].Photovoltaic generation systems have been developed especially rapidly, and the installation of large-scale photovoltaic plants is increasing in scale year by year [2].PV plants differ from traditional power plants and are classified as inverter-based power plants (IBPP) [3].Since PV plants have no rotating mechanical components, they have no inherent inertia, which increases the risk of LFOs [4].Low-frequency oscillations can be triggered by a lack of damping or by the system being in a negative damping state, which can cause new electromechanical oscillation modes in severe cases [5,6].These LFOs are in the frequency range between 0.1 and 2 Hz [7]: the frequency range is 0.1-0.7 Hz for interarea oscillations and 0.7-2 Hz for local oscillations [8].The problem of how to reduce the interarea oscillations caused by large-scale PV plants has attracted widespread attention.
The most common method for suppressing LFOs in power systems is to install a power system stabilizer (PSS) in the generator, which can offset the negative damping torque generated by the automatic voltage regulator (AVR) and enhance the system's damping Energies 2022, 15, 9044 2 of 13 performance [9,10].PSSs are mainly used to suppress local oscillations, and they are not effective for interarea oscillations [11].In PV plants, the damping is mainly controlled by altering the power flow of the system, and the lack of a damping control link may have a negative impact on the damping of a system [12].Adjusting the power output of a PV plant can indirectly change the electromagnetic power of the generator, which enables the PV plant to provide a damping torque to the generator that is sometimes positive and sometimes negative [13][14][15].The production of positive damping torque by PV plants is the key to enhancing the oscillation damping of the power system [16].The location of PV plants can have either positive or negative effects on the low-frequency oscillations [17].However, PV plants are positioned according to geographic factors and cannot be placed in ideal locations that have little effect on the LFOs; thus, it is essential to design damping controllers for PV plants.
In recent years, wide-area damping control (WADC) has been extensively used to suppress interarea LFOs.In [11], several practical problems and design methods related to WADC are described.In order to reduce the risk posed by the increasing penetration level of PV plants, some PV plants suppress LFOs through power oscillation damping controllers (PODCs) [18].An optimal damping controller (ODC) was proposed in [19], and the particle swarm optimization (PSO) algorithm was used to determine the controller parameters in order to maximize the damping performance during low-frequency oscillation.The controller mentioned above can be regarded as having the structure of a PSS, which is widely used because of its easy adjustability.
In this paper, an additional damping controller consisting of gain, filter, and phase compensation was used to suppress low-frequency oscillations by combining it with the active reference of the PV inverter.The damping performance of the ADC depends on whether the damping power can be compensated for quickly.To avoid wasting solar energy, PV plants working at the maximum power point at all times cannot provide quick and sufficient power compensation.When there is a margin for PV power output, the margin can compensate for the damping power, and the damping performance depends on the magnitude of the margin at this time.However, the greater the margin, the more solar energy is wasted.Therefore, this paper proposes an additional compound damping control system combining ADC for the inverter and ADC-based DPCC for the HESS to suppress LFOs, with the required damping power of the inverter being provided by the HESS.
The rest of this paper is organized as follows.Section 2 establishes the mathematical model of the SG and analyzes the damping performance of a single-machine infinite-bus system for a PV plant by the torque method.Section 3 demonstrates the feasibility of ADC for the inverter using a small signal model.Section 4 proposes the DPCC system for the HESS.Sections 5 and 6 present the simulation verification and the conclusions, respectively.

Single-Machine Infinite-Bus System for a PV Plant
The structure of the single-machine infinite-bus system for a PV plant is shown in Figure 1.The synchronous generator (SG) is connected to the infinite bus through a transmission line with the PV plant.Meanwhile, the PV arrays and the hybrid energy storage system are connected to the inverter through the DC bus.The hybrid energy storage system consists of a super capacitor and a battery, which are safer and more efficient because they only need to perform the functions for which they are suitable.E q is the transient electromotive force of the q-axis of the synchronous generator.U v is the bus voltage of the grid-connection point of the PV plant.U s is the infinite-bus voltage.δ is the phase-angle difference between E q and U s .θ is the phase-angle difference between E q and U v .P e is the electromagnetic power of the synchronous generator, which can be regarded as the active output power when copper loss is ignored.P v is the active power of the PV plant, P s is the sum of the active power of the synchronous generator and the PV plant.X 1 is the sum of the transient reactance of the synchronous generator and the line reactance.In addition, X 2 is the line reactance on the side of the infinite-bus system.output power when copper loss is ignored.Pv is the active power of the PV plant, Ps is the sum of the active power of the synchronous generator and the PV plant.X1 is the sum of the transient reactance of the synchronous generator and the line reactance.In addition, X2 is the line reactance on the side of the infinite-bus system.
Structure of single-machine infinite-bus system for a PV plant.

Modeling of the SG
The rotor equations of the classical second-order model of the SG are shown in Equation (1).
1 m e dω H P P D ω dt dδ ω dt (1) H is the inertia time constant of the SG, Pm is the mechanical power of the SG, D is the damping coefficient, and ω is the rotor angular velocity.Linearizing Equation (1) at the equilibrium point, the resulting equation is given by the following: (2)

Damping Performance Analysis of a Single-Machine Infinite-Bus System for a PV Plant
According to the power angle characteristic, the electromagnetic power of the SG can be described as the following: The power balance relationship at node A in Figure 1 is shown in Equation ( 5).
Figure 1.Structure of single-machine infinite-bus system for a PV plant.

Modeling of the SG
The rotor equations of the classical second-order model of the SG are shown in Equation (1).
H dω dt = P m − P e − D(ω − 1) H is the inertia time constant of the SG, P m is the mechanical power of the SG, D is the damping coefficient, and ω is the rotor angular velocity.Linearizing Equation (1) at the equilibrium point, the resulting equation is given by the following: 2.2.Damping Performance Analysis of a Single-Machine Infinite-Bus System for a PV Plant According to the power angle characteristic, the electromagnetic power of the SG can be described as the following: The power balance relationship at node A in Figure 1 is shown in Equation (5).
Linearizing Equations (3)-( 5) at the equilibrium point, the resulting equations are shown as follows: ) Energies 2022, 15, 9044 4 of 13 Substituting Equation (7) into Equation (8), the resulting equation is as the following: Furthermore, Equation ( 6) can also be expressed as Substituting Equation (10) into Equation ( 9), the resulting equation is as the following: where . Analyzing Equation ( 11) by the torque method, it can be found that ∆P e can be composed of three parts.The first part (K 0 ∆δ) is called synchronous torque and is in phase with ∆δ, where K 0 is the synchronous torque coefficient.The second part (K 1 ∆U v ) is proportional to ∆U v and the third part (−K 2 ∆P v ) is inversely proportional to ∆P v .Consequently, when LFOs occur in the system, the electromagnetic power of the SG can be adjusted through both the bus voltage of the grid-connection point and the active power output of the PV plant.The second and third parts are called damping torque, and the damping performance of the system depends on their phase relationship with ∆ω.Therefore, it is necessary to propose an effective additional damping control for the PV inverter to suppress LFOs.

Basic Principle of ADC for the PV Inverter
During the LFOs, the rotor angular velocity (ω) of SG swings up and down at the steady-state operating point (ω 0 ), and the schematic of rotor speed is shown in Figure 2. When ω is in the upper half-cycle of the oscillation (ω0 < ω), dω/dt should be reduced in order to quickly return to the steady-state operating point.According to Equation (1), since Pm is constant, Pe can be increased to reduce dω/dt.Conversely, when ω is in the lower half cycle of the oscillation (ω0 > ω), Pe can be reduced to increase dω/dt.Based on the analysis of Equation ( 11) in Section 2.2, the expected relationships between ΔUv, ΔPv and ΔPe are shown in the following table.
As can be seen from Table 1, the optimal damping performance of the system depends on whether both active and reactive damping play a positive damping role, which requires that ΔUv should be in the same phase with Δω and ΔPv should be in opposite phase with Δω.When ω is in the upper half-cycle of the oscillation (ω 0 < ω), dω/dt should be reduced in order to quickly return to the steady-state operating point.According to Equation (1), since P m is constant, P e can be increased to reduce dω/dt.Conversely, when ω is in the lower half cycle of the oscillation (ω 0 > ω), P e can be reduced to increase dω/dt.Based on the analysis of Equation ( 11) in Section 2.2, the expected relationships between ∆U v , ∆P v and ∆P e are shown in the following table.
As can be seen from Table 1, the optimal damping performance of the system depends on whether both active and reactive damping play a positive damping role, which requires that ∆U v should be in the same phase with ∆ω and ∆P v should be in opposite phase with ∆ω.

Additional Damping Controller
In order to suppress LFOs, this paper proposed the incorporation of an active additional damping controller into the PV inverter.The additional damping controller can be considered as a common structure of PSS, which is widely used due to its simple structure and principles.The local frequency deviation (∆ω) is used as the input signal of the controller, and then the DC voltage reference of the PV inverter is obtained through the amplifier, the band-pass filter, the phase compensator and the amplitude-limiting link.The structure of the additional damping controller is shown in Figure 3.
in order to quickly return to the steady-state operating point.According to Equation (1), since Pm is constant, Pe can be increased to reduce dω/dt.Conversely, when ω is in the lower half cycle of the oscillation (ω0 > ω), Pe can be reduced to increase dω/dt.Based on the analysis of Equation ( 11) in Section 2.2, the expected relationships between ΔUv, ΔPv and ΔPe are shown in the following table.
As can be seen from Table 1, the optimal damping performance of the system depends on whether both active and reactive damping play a positive damping role, which requires that ΔUv should be in the same phase with Δω and ΔPv should be in opposite phase with Δω.

Additional Damping Controller
In order to suppress LFOs, this paper proposed the incorporation of an active additional damping controller into the PV inverter.The additional damping controller can be considered as a common structure of PSS, which is widely used due to its simple structure and principles.The local frequency deviation (Δω) is used as the input signal of the controller, and then the DC voltage reference of the PV inverter is obtained through the amplifier, the band-pass filter, the phase compensator and the amplitude-limiting link.The structure of the additional damping controller is shown in Figure 3. Amplifier: The gain coefficient (K) directly affects the damping performance of the additional damping controller.And the value of K is constrained by some conditions.The capacity of the energy storage device needs to be considered in active additional damping control, as does the margin of PV output and the allowed fluctuation range of the DC bus Amplifier: The gain coefficient (K) directly affects the damping performance of the additional damping controller.And the value of K is constrained by some conditions.The capacity of the energy storage device needs to be considered in active additional damping control, as does the margin of PV output and the allowed fluctuation range of the DC bus voltage.Conversely, the allowed fluctuation range of the AC bus voltage needs to be considered in reactive additional damping control.
Band-pass filter: Butterworth filter is used to attenuate DC and high-frequency components, only allowing the low-frequency components to pass.
Phase compensator: The angle to be compensated is the phase shift of the transfer function of the frequency measurement link and band-pass filtering link at the low-frequency oscillation point f i .The phase compensator ensures that the additional damping controller can provide positive damping.The time constants T 1 and T 2 are given by Equation (12), θ is the angle to be compensated, and it is worth noting that the angle of compensation for each phase compensation link does not exceed 60

Small-Signal Modeling and Analysis of ADC for the PV Inverter
When the PV inverter adopts traditional control strategy, the following equations can be obtained.
Energies 2022, 15, 9044 6 of 13 Substituting Equation ( 13) into Equation (11), the resulting equation is as follows: Substituting Equation ( 14) into Equation ( 2), the resulting equation is as follows: From the above equation, it can be seen that the damping factor of the system is not changed.In other words, the PV plant fails to enhance the damping performance of the system.
When an additional damping controller is added to the active control link of PV inverter, the damping performance of the system will be enhanced.The block diagram of additional damping control is shown in Figure 4, where K ω is the gain coefficient of additional damping controller.

Small-Signal Modeling and Analysis of ADC for the PV Inverter
When the PV inverter adopts traditional control strategy, the following equations can be obtained.Δ 0,Δ 0 Substituting Equation ( 13) into Equation (11), the resulting equation is as follows: Substituting Equation ( 14) into Equation ( 2), the resulting equation is as follows: From the above equation, it can be seen that the damping factor of the system is not changed.In other words, the PV plant fails to enhance the damping performance of the system.
When an additional damping controller is added to the active control link of PV inverter, the damping performance of the system will be enhanced.The block diagram of additional damping control is shown in Figure 4, where Kω is the gain coefficient of additional damping controller.It can be seen from Figure 4 that: where Udc_damp is the new DC bus voltage reference.According to the decoupling characteristics of active power and reactive power, ΔUv caused by active power is tiny which can be ignored.So, the following equations are obtained.It can be seen from Figure 4 that: where U dc_damp is the new DC bus voltage reference.According to the decoupling characteristics of active power and reactive power, ∆U v caused by active power is tiny which can be ignored.So, the following equations are obtained.
The power stored in the DC capacitor is: Linearizing Equation ( 18) at the equilibrium point, the resulting equation is given by the following: where C dc is the DC side capacitance value, U dc0 is the DC bus voltage at steady state, A = C dc U dc0 , in the case of ignoring the loss of PV inverter, ∆P v and ∆P dc are the same in size but opposite in direction.Therefore, ∆P v can be expressed as Substituting Equations ( 17) and (20) into Equation (11), the resulting equation is as follows: Substituting Equation (21) into Equation ( 2), the resulting equation is as the following: Energies 2022, 15, 9044 7 of 13 From Equation ( 22), the new damping coefficient of the system is It is effectively proved that the active additional damping control for the PV inverter can increase the damping coefficient of the system and enhance the ability to suppress LFOs.

HESS
For the PV plant without energy storage device, the damping performance is limited by the following three problems: 1.
According to Equation ( 23), the damping effect is enhanced with the increase in K ω .However, according to Equation ( 16), the deviation of the new reference value of DC bus voltage from the original reference value increases as K ω increases.So the allowed fluctuation range of the reference value of DC bus voltage should be considered when setting the value of K ω ; 2.
When the PV works at the maximum power point, the PV plant can only damp the upper half wave of the LFOs, which is because the PV inverter cannot increase the output power but only decrease it; 3.
When the PV does not work at the maximum power point, the PV plant can damp the full wave of the LFOs, which is because the PV inverter can increase and decrease the output power.Additionally, the damping performance depends on the magnitude of power that the PV can adjust.Inevitably, a large amount of solar energy will be wasted.
Accordingly, configuring energy storage devices for PV plants is undoubtedly an effective solution to the above problems.
At the moment of LFOs or drastic changes in the external environment, the system suffers a short-term shock.At this time, the power to be compensated by the energy storage system is composed of high-frequency components and low-frequency components.Due to the battery having the characteristics of low power density and slow charging and discharging, it does not meet the requirements of charging and discharging with high power and fast speed.If only battery is used for power compensation, not only is the compensation effect not satisfactory, but also the service life of battery will be shortened.The super capacitor has the characteristics of high power density and fast charging and discharging, which can be used as a supplement to the energy storage system.A hybrid energy storage system composed of battery and super capacitor can better complete various power compensation tasks, and its equivalent mathematical model for hybrid energy storage can use the model proposed in [20].

ADC-Based DPCC
It is shown in Figure 1, the battery and the super capacitor are, respectively, connected to the DC bus through the Buck/Boost bidirectional converter.If the energy loss of the inverter is ignored, the power flow relationships of the PV plant are shown in Figure 5.Where P v_ref is the active power reference value when the inverter does not add ADC.P v_damp is the active power reference value when the inverter adds ADC.P sto_ref is the active power reference value of the HESS.P pv is the output power of the PV arrays; ∆P v is the damping power provided by the HESS.∆P pv is the output power fluctuation of the PV array.P bat_ref is the output power reference value of the battery.P sc_ref is the output power reference value of the super capacitor.the inverter is ignored, the power flow relationships of the PV plant are shown in Figure 5.Where Pv_ref is the active power reference value when the inverter does not add ADC.Pv_damp is the active power reference value when the inverter adds ADC.Psto_ref is the active power reference value of the HESS.Ppv is the output power of the PV arrays; ΔPv is the damping power provided by the HESS.ΔPpv is the output power fluctuation of the PV array.Pbat_ref is the output power reference value of the battery.Psc_ref is the output power reference value of the super capacitor.Additionally, they should also satisfy the following equations.(28) 1/(1 + sT) is the low-pass filter link and T is time constant.The HESS has two power compensation goals: one is to compensate the output power of the PV arrays, and the other is to compensate the damping power required by ADC.In order for ΔPv to be in opposite phase with Δω, the compensation power provided by the HESS should also be in opposite phase with Δω.Therefore, this paper proposed a DPCC based on ADC for HESS, where K is equal to AKω.Since both DPCC and ADC use Δω as Additionally, they should also satisfy the following equations.
P v_re f = P pv + ∆P pv (24) P sc_re f = P sto_re f − P bat_re f (28) 1/(1 + sT) is the low-pass filter link and T is time constant.The HESS has two power compensation goals: one is to compensate the output power of the PV arrays, and the other is to compensate the damping power required by ADC.In order for ∆P v to be in opposite phase with ∆ω, the compensation power provided by the HESS should also be in opposite phase with ∆ω.Therefore, this paper proposed a DPCC based on ADC for HESS, where K is equal to AK ω .Since both DPCC and ADC use ∆ω as the input signal, it ensures that the compensation power provided by the HESS is in phase with the damping power required by the inverter.The block diagram of proposed ACDC, combining the ADC for the inverter with the DPCC for the HESS, is shown in Figure 6.
x FOR PEER REVIEW 9 of 14 the input signal, it ensures that the compensation power provided by the HESS is in phase with the damping power required by the inverter.The block diagram of proposed ACDC, combining the ADC for the inverter with the DPCC for the HESS, is shown in Figure 6.
The block diagram of ACDC.
When the system does not generate LFOs, the HESS only compensates the power fluctuation of the PV arrays (ΔPpv), and the power reference value of the HESS is given by Equation (29).When the LFOs occurs in the system, the HESS also needs to compensate the damping power required by the inverter (ΔPv), and the power reference value of the HESS is given by Equation (30) at this time.
Psto_ref is divided into Pbat_ref and Psc_ref by the Butterworth low-pass filter, where Pbat_ref When the system does not generate LFOs, the HESS only compensates the power fluctuation of the PV arrays (∆P pv ), and the power reference value of the HESS is given by Equation (29).When the LFOs occurs in the system, the HESS also needs to compensate the damping power required by the inverter (∆P v ), and the power reference value of the HESS is given by Equation (30) at this time.
Energies 2022, 15, 9044 9 of 13 P sto_ref is divided into P bat_ref and P sc_ref by the Butterworth low-pass filter, where P bat_ref is the low-frequency components and P sc_ref represents the high-frequency components.According to the energy complementary characteristics of the battery and super capacitor, they can respond quickly to power commands.HESS can effectively suppress the power fluctuation, improve power quality, and enhance the reliability and stability of the system.

Simulation Verification
In order to verify the effectiveness of the proposed damping control strategy in this paper, a simulation model of a three-machine nine-node system with a PV plant is built in PSCAD/EMTDC.At 8 s, a three-phase fault lasting 0.1 s will occur at bus 8, at which time there is an obvious LFO in the system.
The simulation topology is shown in Figure 7, and the ratings of the main parameters of the system are given in Table 2. U dc is the DC bus voltage of the PV plant, P pv is the output power of a PV array, P vsc is the output power of a inverter (ignoring power loss), Scale is the number of PV arrays, and P v is the output power of the PV plant.

DPCC for HESS
Figure 8a shows that the active power output of a PV array has a variation of about 0.06 MW as the irradiation intensity decreases from 1200 W/m 2 to 1000 W/m 2 at 5 s and returns to 1200 W/m 2 at 15 s.According to Section 4.2, whether the damping power can be compensated quickly will directly influence the effect on suppressing the LFOs.It can be seen from Figure 8b that DPCC for HESS can quickly compensate the fluctuating power of PV output and the damping power required by the inverter.Psto is the output power of HESS and DeltaPv + DeltaPpv is the compensation power required by the system.Figure 8c shows the power sharing link of the HESS, where Pstoref, Pscref and Pbatref are the power reference values for the HESS, super capacitor, and battery, respectively.It can be seen that the super capacitor is responsible for compensating high-frequency power, while the battery is responsible for compensating low-frequency power and providing long-term power support.

W W
7. Topology of three-machine nine-node system with a PV plant.

DPCC for HESS
Figure 8a shows that the active power output of a PV array has a variation of about 0.06 MW as the irradiation intensity decreases from 1200 W/m 2 to 1000 W/m 2 at 5 s and returns to 1200 W/m 2 at 15 s.According to Section 4.2, whether the damping power can be compensated quickly will directly influence the effect on suppressing the LFOs.It can be seen from Figure 8b that DPCC for HESS can quickly compensate the fluctuating power of PV output and the damping power required by the inverter.P sto is the output power of HESS and DeltaP v + DeltaP pv is the compensation power required by the system.Figure 8c shows the power sharing link of the HESS, where P storef , P scref and P batref are the power reference values for the HESS, super capacitor, and battery, respectively.It can seen that the super capacitor is responsible for compensating high-frequency power, while the battery is responsible for compensating low-frequency power and providing long-term power support.

DPCC for HESS
Figure 8a shows that the active power output of a PV array has a variation of about 0.06 MW as the irradiation intensity decreases from 1200 W/m 2 to 1000 W/m 2 at 5 s and returns to 1200 W/m 2 at 15 s.According to Section 4.2, whether the damping power can be compensated quickly will directly influence the effect on suppressing the LFOs.It can be seen from Figure 8b that DPCC for HESS can quickly compensate the fluctuating power of PV output and the damping power required by the inverter.Psto is the output power of HESS and DeltaPv + DeltaPpv is the compensation power required by the system.Figure 8c shows the power sharing link of the HESS, where Pstoref, Pscref and Pbatref are the power reference values for the HESS, super capacitor, and battery, respectively.It can be seen that the super capacitor is responsible for compensating high-frequency power, while the battery is responsible for compensating low-frequency power and providing long-term power support.

ACDC Combining ADC with DPCC
This paper lists the following four damping control modes for the PV plant and compares their suppression effects on LFOs.


NDC: The inverter adopts a traditional control strategy.The PV plant is not configured with HESS and works at the maximum power point;  ADC 1: ADC is incorporated into the traditional control strategy of the inverter.The PV plant is not configured with HESS and works at the maximum power point;  ADC 2: ADC is incorporated into the traditional control strategy of the inverter.The PV plant is not configured with HESS and works at the non-maximum power point;  ACDC: ADC is incorporated into the traditional control strategy of the inverter.The PV plant is configured with HESS which adopts DPCC and works at the maximum power point.
It can be seen from Figure 9 that the phase deviation between the output power of

ACDC Combining ADC with DPCC
This paper lists the following four damping control modes for the PV plant and compares their suppression effects on LFOs.

•
NDC: The inverter adopts a traditional control strategy.The PV plant is not configured with HESS and works at the maximum power point; • ADC 1: ADC is incorporated into the traditional control strategy of the inverter.The PV plant is not configured with HESS and works at the maximum power point; • ADC 2: ADC is incorporated the traditional control strategy of the inverter.The PV plant is not configured with HESS and works at the non-maximum power point; • ACDC: ADC is incorporated into the traditional control strategy of the inverter.The PV plant is configured with HESS which adopts DPCC and works at the maximum power point.
It can be seen from Figure 9 that the phase deviation between the output power of PV plant and the frequency cannot always be 180 • in mode ADC 1.Although the lowfrequency amplitude gradually decreases, there is no significant effect on shortening the oscillation period.However, in modes ADC 2 and ACDC, the output power is always phase opposite to the frequency, which makes the low-frequency amplitude decrease rapidly and the oscillation period shorten significantly.In particular, the proposed control not only suppresses the LFO well, but it also enables the PV plant to always maintain the maximum output power and avoid the waste of solar energy.As can be seen in Figure 10, if there is no power compensation source, the PV inverter with only ADC will cause dramatic and long-term fluctuations in the DC bus voltage.In mode ACDC, the DC bus voltage is within a small fluctuation range and can restore to stability quickly.

Conclusions
Due to the increased proportion of PV power generation, the LFOs are prone to occur during power system failures.To reduce the risk of LFOs to the power system, PV plants should suppress the LFOs through a damping control strategy.In this paper, an ACDC which combines ADC for the inverter and ADC-based DPCC for the HESS was proposed As can be seen in Figure 10, if there is no power compensation source, the PV inverter with only ADC will cause dramatic and long-term fluctuations in the DC bus voltage.In mode ACDC, the DC bus voltage is within a small fluctuation range and can restore to stability quickly.As can be seen in Figure 10, if there is no power compensation source, the PV inverter with only ADC will cause dramatic and long-term fluctuations in the DC bus voltage.In mode ACDC, the DC bus voltage is within a small fluctuation range and can restore to stability quickly.

Conclusions
Due to the increased proportion of PV power generation, the LFOs are prone to occur during power system failures.To reduce the risk of LFOs to the power system, PV plants should suppress the LFOs through a damping control strategy.In this paper, an ACDC

Conclusions
Due to the increased proportion of PV power generation, LFOs are prone to occur during power system failures.To reduce the risk of LFOs to the power PV plants should suppress the LFOs through a damping control strategy.In this paper, an ACDC which combines ADC for the inverter and ADC-based DPCC for the HESS was proposed to suppress the LFOs.The following conclusions are drawn from the whole analysis:

•
ADC is demonstrated to improve the damping performance of the system by the analysis of torque method and the small signal model;

•
The damping performance of ADC depends on the compensation power.The ACDC not only obviously enhances the damping performance of the PV plant during LFOs but also maintains the stability of the PV output and avoids the waste of solar energy.

Figure 2 .
Figure 2. Schematic of rotor speed during the LFOs.

Figure 2 .
Figure 2. Schematic of rotor speed during the LFOs.

Figure 3 .
Figure 3. Block diagram of additional damping controller.

Figure 3 .
Figure 3. Block diagram of additional damping controller.

Figure 5 .
Figure 5. Power distribution diagram of the PV plant.

Figure 5 .
Figure 5. Power distribution diagram of the PV plant.

Figure 6 .
Figure 6.The block diagram of ACDC.

Figure 7 .
Figure 7. Topology of three-machine nine-node system with a PV plant.

Figure 8 .
Figure 8.The power compensation effect of the HESS: (a) Active power output of a single PV array and inverter; (b) Dynamic power compensation for HESS; (c) Power sharing for the HESS.

Figure 8 .
Figure 8.The power compensation effect of the HESS: (a) Active power output of a single PV array and inverter; (b) Dynamic power compensation for HESS; (c) Power sharing for the HESS.

Figure 9 .
Figure 9.Comparison of the suppression effects of four control modes: (a) Tie-line frequency of the PV plant; (b) Active power injected into the system of the PV plant.

Figure 10 .
Figure 10.DC bus voltage of the PV plant.

Figure 9 .
Figure 9.Comparison of the suppression effects of four control modes: (a) Tie-line frequency of the PV plant; (b) Active power injected into the system of the PV plant.

Figure 9 .
Figure 9.Comparison of the suppression effects of four control modes: (a) Tie-line frequency of the PV plant; (b) Active power injected into the system of the PV plant.

Figure 10 .
Figure 10.DC bus voltage of the PV plant.

Figure 10 .
Figure 10.DC bus voltage of the PV plant.

Table 1 .
The expected relationships between ∆U v , ∆P v and ∆P e .

Table 2 .
Ratings of the main parameters of the system.