Modeling and Mechanism Investigation of Inertia and Damping Issues for Grid-Tied PV Generation Systems with Droop Control

: Inertia e ﬀ ect and damping capacity, which are the basic characteristics of traditional power systems, are critical to grid frequency stability. However, the inertia and damping characteristics of grid-tied photovoltaic generation systems (GPVGS), which may a ﬀ ect the frequency stability of the grid with high proportional GPVGS, are not yet clear. Therefore, this paper takes the GPVGS based on droop control as the research object. Focusing on the DC voltage control (DVC) timescale dynamics, the mathematical model of the GPVGS is ﬁrstly established. Secondly, the electrical torque analysis method is used to analyze the inﬂuence law of inertia, damping and synchronization characteristics from the physical mechanism perspective. The research ﬁnds that the equivalent inertia, damping and synchronization coe ﬃ cient of the system are determined by the control parameters, structural parameters and steady-state operating point parameters. Changing the control parameters is the simplest and most ﬂexible way to inﬂuence the inertia, damping and synchronization ability of the system. The system inertia is inﬂuenced by the DC voltage outer loop proportional coe ﬃ cient K p and enhanced with the increase of K p . The damping characteristic of the system is a ﬀ ected by the droop coe ﬃ cient D p and weakened with the increase of D p . The synchronization e ﬀ ect is only controlled by DC voltage outer loop integral coe ﬃ cient K i and enhanced with the increase of K i . In addition, the system dynamic is also a ﬀ ected by the structural parameters such as line impedance X , DC bus capacitance C , and steady-state operating point parameters such as the AC or DC bus voltage level of the system and steady-state operating power (power angle). Finally, the correctness of the above analysis are veriﬁed by the simulation and experimental results. terminal I of the PVA the voltage frequency droop control the problem of repeated control. U pv is multiplied by I pv to determine the output power P pv . To do this, you only need to select one of the variables between U pv and I pv for control. The frequency droop can be used to control I pv , to indirectly control P pv . In order to ensure the stability, speed and full power range of the GPVGS to respond to load balance, this paper takes the interval (0, I mp ) as an example for related research.


Introduction
In recent years, with the increasingly serious problems of energy crisis and environmental pollution, the need for development of green and clean energy sources has become the consensus of the world [1][2][3]. Among them, photovoltaic power generation, as one of the most promising power generation technologies, has been widely considered [4].
However, with the increasing penetration of photovoltaic (PV) in the public power grid, large-scale grid-tied PV inverters featuring low inertia and weak damping are being connected to the power relatively separated response times. Therefore, for DVC timescale dynamic analysis, AC or DC currents timescale dynamic can be considered to instantaneously track their reference values.

Electrical Torque Analysis Method
From the aspects of physical structure, characteristic parameters, physical mechanism and dynamic model of energy transfer process, there is a significant correspondence between the traditional RSG and the new energy grid-tied power generation system. There is a strong similarity among the structure, motion mechanism and mathematical model of system. Therefore, we can learn from classical electric torque analysis method to analyze the influencing factors and action laws affecting the stability of the GPVGS from the physical mechanism perspective [18].
Analogous to the small-signal stability method of the traditional RSG, the DVC timescale dynamic process of the GPVGS can be expressed by the incremental equation [14]: In order to analyze the inertia, damping and synchronization characteristics of the grid-tied inverter system, the static synchronous generator (SSG) model is proposed in literature [14]. The DVC timescale dynamic process of the grid-tied inverter is described by the following standard equation: where TJ, TD, and TS represent the equivalent inertia, damping, and synchronization coefficient of the SSG, respectively. The above three parameters are important physical concepts for characterizing the dynamic characteristics of SSG in classical stability theory. The electric torque analysis method based on the above concept can analyze the system stability from the physical mechanism perspective. And TJ, TD and TS respectively represent inertia level, damping and synchronization capability of the grid-tied inverter system [14].

System Description
The main circuit topology and control method of the GPVGS based on droop control is shown in Figure 2. This system consists of a photovoltaic array (PVA), boost converter, and inverter. The

Electrical Torque Analysis Method
From the aspects of physical structure, characteristic parameters, physical mechanism and dynamic model of energy transfer process, there is a significant correspondence between the traditional RSG and the new energy grid-tied power generation system. There is a strong similarity among the structure, motion mechanism and mathematical model of system. Therefore, we can learn from classical electric torque analysis method to analyze the influencing factors and action laws affecting the stability of the GPVGS from the physical mechanism perspective [18].
Analogous to the small-signal stability method of the traditional RSG, the DVC timescale dynamic process of the GPVGS can be expressed by the incremental equation [14]: where H = CU 2 dc 2S B is the inertia time constant of the system. In order to analyze the inertia, damping and synchronization characteristics of the grid-tied inverter system, the static synchronous generator (SSG) model is proposed in literature [14]. The DVC timescale dynamic process of the grid-tied inverter is described by the following standard equation: where T J , T D , and T S represent the equivalent inertia, damping, and synchronization coefficient of the SSG, respectively. The above three parameters are important physical concepts for characterizing the dynamic characteristics of SSG in classical stability theory. The electric torque analysis method based on the above concept can analyze the system stability from the physical mechanism perspective. And T J , T D and T S respectively represent inertia level, damping and synchronization capability of the grid-tied inverter system [14].

System Description
The main circuit topology and control method of the GPVGS based on droop control is shown in Figure 2. This system consists of a photovoltaic array (PVA), boost converter, and inverter. The boost converter adopts the frequency droop control to simulate the primary frequency modulation process of the prime mover. The inverter adopts the double closed-loop control of the conventional voltage and current to correspond to the rotational synchronous generator (RSG). This control strategy can simulate the traditional peak-regulation power plant when a large proportion of renewable energy is connected to the grid, so that the GPVGS is responsible for the load balancing. boost converter adopts the frequency droop control to simulate the primary frequency modulation process of the prime mover. The inverter adopts the double closed-loop control of the conventional voltage and current to correspond to the rotational synchronous generator (RSG). This control strategy can simulate the traditional peak-regulation power plant when a large proportion of renewable energy is connected to the grid, so that the GPVGS is responsible for the load balancing. In order to better make the GPVGS respond to the load balancing responsibility, when the power grid fluctuates, the system provides reasonable inertia and damping support, so that the system can reach the power balance as soon as possible. When the maximum output power of the PV is much larger than the system's load power or scheduling demand of power grid, the boost converter adopts the deloading maximum power point tracking (DMPPT) control method and works in the droop control mode to meet the supply and demand balance. When the PV output power is much smaller than the load power or scheduling requirements of power grid, the boost converter can only maintain system stability with the maximum power output.
The characteristic curve of PV-PU is shown in Figure 3. When the power frequency droop control is performed, it can be seen from the PV curve that one power command P1,2 at any time corresponds to the output voltages U1 and U2 of the two PV panels. However, each terminal voltage has a one-to-one correspondence with power. Therefore, the power frequency droop control can be improved to the frequency droop control. The frequency droop is used to control the PVA output voltage as the outer loop, and the PVA output current is used as the inner loop. Taking the maximum power point of the P-U curve as the boundary, the interval (0, Ump) and (Ump, Uoc) are opposite to the monotonicity of the power. In the interval (0, Umpp), the output voltage Upv of PVA is positively correlated with the output power Ppv, and is limited by the minimum voltage UDCmin of the DC-side inverter failure. Meanwhile, the adjustable power is limited and the In order to better make the GPVGS respond to the load balancing responsibility, when the power grid fluctuates, the system provides reasonable inertia and damping support, so that the system can reach the power balance as soon as possible. When the maximum output power of the PV is much larger than the system's load power or scheduling demand of power grid, the boost converter adopts the deloading maximum power point tracking (DMPPT) control method and works in the droop control mode to meet the supply and demand balance. When the PV output power is much smaller than the load power or scheduling requirements of power grid, the boost converter can only maintain system stability with the maximum power output.
The characteristic curve of PV-PU is shown in Figure 3. When the power frequency droop control is performed, it can be seen from the PV curve that one power command P 1 , 2 at any time corresponds to the output voltages U 1 and U 2 of the two PV panels. However, each terminal voltage has a one-to-one correspondence with power. Therefore, the power frequency droop control can be improved to the frequency droop control. The frequency droop is used to control the PVA output voltage as the outer loop, and the PVA output current is used as the inner loop. strategy can simulate the traditional peak-regulation power plant when a large proportion of renewable energy is connected to the grid, so that the GPVGS is responsible for the load balancing. In order to better make the GPVGS respond to the load balancing responsibility, when the power grid fluctuates, the system provides reasonable inertia and damping support, so that the system can reach the power balance as soon as possible. When the maximum output power of the PV is much larger than the system's load power or scheduling demand of power grid, the boost converter adopts the deloading maximum power point tracking (DMPPT) control method and works in the droop control mode to meet the supply and demand balance. When the PV output power is much smaller than the load power or scheduling requirements of power grid, the boost converter can only maintain system stability with the maximum power output.
The characteristic curve of PV-PU is shown in Figure 3. When the power frequency droop control is performed, it can be seen from the PV curve that one power command P1,2 at any time corresponds to the output voltages U1 and U2 of the two PV panels. However, each terminal voltage has a one-to-one correspondence with power. Therefore, the power frequency droop control can be improved to the frequency droop control. The frequency droop is used to control the PVA output voltage as the outer loop, and the PVA output current is used as the inner loop. Taking the maximum power point of the P-U curve as the boundary, the interval (0, Ump) and (Ump, Uoc) are opposite to the monotonicity of the power. In the interval (0, Umpp), the output voltage Upv of PVA is positively correlated with the output power Ppv, and is limited by the minimum voltage UDCmin of the DC-side inverter failure. Meanwhile, the adjustable power is limited and the Taking the maximum power point of the P-U curve as the boundary, the interval (0, U mp ) and (U mp , U oc ) are opposite to the monotonicity of the power. In the interval (0, U mpp ), the output voltage U pv of PVA is positively correlated with the output power P pv , and is limited by the minimum voltage U DCmin of the DC-side inverter failure. Meanwhile, the adjustable power is limited and the adjustment speed is slow. In the interval (U mp , U oc ), U pv is negatively correlated with P pv . P pv can be adjusted in a full range. The system sensitivity is good due to the large slope. In order to ensure the safe and stable operation of the GPVGS with operating at a faster adjustment speed in the full power range, (U mp , U oc ) is selected as the operating range of the PVA output voltage.
Energies 2019, 12, 1985 5 of 17 In order to simplify the modeling, according to the U-I curve shown in Figure 4, the output terminal voltage U pv and current I pv of the PVA under the voltage frequency droop control have the problem of repeated control. U pv is multiplied by I pv to determine the output power P pv . To do this, you only need to select one of the variables between U pv and I pv for control. The frequency droop can be used to control I pv , to indirectly control P pv . In order to ensure the stability, speed and full power range of the GPVGS to respond to load balance, this paper takes the interval (0, I mp ) as an example for related research.
adjusted in a full range. The system sensitivity is good due to the large slope. In order to ensure the safe and stable operation of the GPVGS with operating at a faster adjustment speed in the full power range, (Ump, Uoc) is selected as the operating range of the PVA output voltage.
In order to simplify the modeling, according to the U-I curve shown in Figure 4, the output terminal voltage Upv and current Ipv of the PVA under the voltage frequency droop control have the problem of repeated control. Upv is multiplied by Ipv to determine the output power Ppv. To do this, you only need to select one of the variables between Upv and Ipv for control. The frequency droop can be used to control Ipv, to indirectly control Ppv. In order to ensure the stability, speed and full power range of the GPVGS to respond to load balance, this paper takes the interval (0, Imp) as an example for related research. In this paper, a 10-string and 5-parallel Suntech Power STP200-18-UB-1 is used to form PVA, whose U-I characteristic curve is consistent with Figure 4 at a specific illumination and temperature. The electrical parameters of the PVA under standard conditions are shown in Table 1:  [19] has proved that the mathematical model of PVA can be linearized. So this approximation method is used in this paper. In the interval (0, Imp), the U-I curve shown in Figure 3 can be simplified by a straight line equation. The simplified expression is: where Kpv is the simplified slope of the U-I curve of Ipv ϵ (0, Imp). The voltage and current output of the PV are linearized as:

The Control Strategy of Boost Converter
Considering the above factors of the PVA, the control strategy of the PVA and the boost converter is shown in Figure 5. The control strategy is used the frequency droop as the outer ring, and the output current of the PVA as the inner ring. The frequency droop is used to control the output current of the PVA, and indirectly control the output power of the PVA. In this paper, a 10-string and 5-parallel Suntech Power STP200-18-UB-1 is used to form PVA, whose U-I characteristic curve is consistent with Figure 4 at a specific illumination and temperature. The electrical parameters of the PVA under standard conditions are shown in Table 1:  [19] has proved that the mathematical model of PVA can be linearized. So this approximation method is used in this paper. In the interval (0, I mp ), the U-I curve shown in Figure 3 can be simplified by a straight line equation. The simplified expression is: where K pv is the simplified slope of the U-I curve of I pv (0, I mp ). The voltage and current output of the PV are linearized as:

The Control Strategy of Boost Converter
Considering the above factors of the PVA, the control strategy of the PVA and the boost converter is shown in Figure 5. The control strategy is used the frequency droop as the outer ring, and the output current of the PVA as the inner ring. The frequency droop is used to control the output current of the PVA, and indirectly control the output power of the PVA. In the double closed-loop control strategy of frequency and current shown in Figure 5, the bandwidth of the general inner loop is much larger than the outer loop. That is to say, for the frequency control process of the outer loop, the current control timescale dynamic process of the inner loop can be ignored [20]. For the DVC timescale dynamic process, the current output of boost convert can be expressed as: where Dp is the droop coefficient, ω0 is the angular frequency set by the system, ωg is the angular frequency of the real-time detection of the grid, Ipv0 is the steady-state operating point of the system, and Ipv0 ϵ (0, Imp). Equation (6) is linearized and can be expressed as: For power node 1, capacitance C1 is similar to LCL filter, and its dynamic response speed is very fast [18]. It belongs to the current control timescale category, and its dynamic process can be ignored, namely: For the boost converter, ignoring its own loss, the power both before and after the converter is considered to be constant, i.e.: in pv pv dc dc For small-signal stability analysis, the incremental relationship among variables is generally considered. Therefore, after linearizing Equation (9), you can get: where Upv0 and Ipv0 are the steady-state operating point parameters of the PV. Substituting Equations (5) and (7) into (10), the output power of the boost converter can be linearized as:

The Control Strategy of Grid-Connected Inverter
As shown in Figure 6, the grid-tied inverter adopts double closed-loop control strategy of DC voltage outer loop and current inner loop. The DC voltage outer loop is based on the principle of In the double closed-loop control strategy of frequency and current shown in Figure 5, the bandwidth of the general inner loop is much larger than the outer loop. That is to say, for the frequency control process of the outer loop, the current control timescale dynamic process of the inner loop can be ignored [20]. For the DVC timescale dynamic process, the current output of boost convert can be expressed as: where D p is the droop coefficient, ω 0 is the angular frequency set by the system, ω g is the angular frequency of the real-time detection of the grid, I pv0 is the steady-state operating point of the system, and I pv0 (0, I mp ). Equation (6) is linearized and can be expressed as: For power node 1, capacitance C 1 is similar to LCL filter, and its dynamic response speed is very fast [18]. It belongs to the current control timescale category, and its dynamic process can be ignored, namely: For the boost converter, ignoring its own loss, the power both before and after the converter is considered to be constant, i.e.: For small-signal stability analysis, the incremental relationship among variables is generally considered. Therefore, after linearizing Equation (9), you can get: where U pv0 and I pv0 are the steady-state operating point parameters of the PV. Substituting Equations (5) and (7) into (10), the output power of the boost converter can be linearized as:

The Control Strategy of Grid-Connected Inverter
As shown in Figure 6, the grid-tied inverter adopts double closed-loop control strategy of DC voltage outer loop and current inner loop. The DC voltage outer loop is based on the principle of power balance to realize the voltage regulation control of the DC bus. The current loop mainly realizes Energies 2019, 12,1985 7 of 17 the tracking control of the grid side current to realize the sine wave current control of the unit power factor of the grid-connected inverter. At the same time, the grid-tied current is limited to ensure the safe operation of the grid-tied inverter. In the topology of the L-type grid-tied inverter, R s and L s respectively represent the equivalent series resistance and inductance of the L-type passive filter and the grid-tied inverter. And L g represents the equivalent reactance between the grid-tied inverter and the infinite grid. L g also represents the strength of the electrical connection between the grid-tied inverter and the infinite grid [21].
Energies 2019, 12, x FOR PEER REVIEW 7 of 17 unit power factor of the grid-connected inverter. At the same time, the grid-tied current is limited to ensure the safe operation of the grid-tied inverter. In the topology of the L-type grid-tied inverter, Rs and Ls respectively represent the equivalent series resistance and inductance of the L-type passive filter and the grid-tied inverter. And Lg represents the equivalent reactance between the grid-tied inverter and the infinite grid. Lg also represents the strength of the electrical connection between the grid-tied inverter and the infinite grid [21]. A simplified analysis of the main circuit of the grid-tied inverter is shown in Figure 7. Us is the excitation potential amplitude of the grid-tied inverter, corresponding to the fundamental component of the outlet voltage before the filter of the grid-tied inverter. δ is the phase angle difference between the grid-tied inverter and the grid terminal voltage. Ug is the amplitude of the grid-tied inverter, which corresponds to the terminal voltage of the grid. In the modeling and analysis of grid-tied inverter, a synchronous rotating coordinate system based on grid voltage vector orientation, is often used to make the grid voltage vector Ug coincide with the d-axis of the synchronous rotating coordinate system [22], as shown in Figure 8. The excitation potential amplitude Us of the grid-tied inverter rotates at a synchronous angular frequency ω0. The grid terminal voltage Ug is rotated according to the angular frequency ωg with reference to the d-axis. ϕ is the phase difference angle between the terminal voltage and output current of the grid-tied inverter. Φ is the phase angle difference between the excitation potential of the grid-tied inverter and the output current. According to Figure 8, the active power Pe of the grid-tied inverter is: where: the structural parameter X≈ω0L. A simplified analysis of the main circuit of the grid-tied inverter is shown in Figure 7. U s is the excitation potential amplitude of the grid-tied inverter, corresponding to the fundamental component of the outlet voltage before the filter of the grid-tied inverter. δ is the phase angle difference between the grid-tied inverter and the grid terminal voltage. U g is the amplitude of the grid-tied inverter, which corresponds to the terminal voltage of the grid. unit power factor of the grid-connected inverter. At the same time, the grid-tied current is limited to ensure the safe operation of the grid-tied inverter. In the topology of the L-type grid-tied inverter, Rs and Ls respectively represent the equivalent series resistance and inductance of the L-type passive filter and the grid-tied inverter. And Lg represents the equivalent reactance between the grid-tied inverter and the infinite grid. Lg also represents the strength of the electrical connection between the grid-tied inverter and the infinite grid [21]. A simplified analysis of the main circuit of the grid-tied inverter is shown in Figure 7. Us is the excitation potential amplitude of the grid-tied inverter, corresponding to the fundamental component of the outlet voltage before the filter of the grid-tied inverter. δ is the phase angle difference between the grid-tied inverter and the grid terminal voltage. Ug is the amplitude of the grid-tied inverter, which corresponds to the terminal voltage of the grid. In the modeling and analysis of grid-tied inverter, a synchronous rotating coordinate system based on grid voltage vector orientation, is often used to make the grid voltage vector Ug coincide with the d-axis of the synchronous rotating coordinate system [22], as shown in Figure 8. The excitation potential amplitude Us of the grid-tied inverter rotates at a synchronous angular frequency ω0. The grid terminal voltage Ug is rotated according to the angular frequency ωg with reference to the d-axis. ϕ is the phase difference angle between the terminal voltage and output current of the grid-tied inverter. Φ is the phase angle difference between the excitation potential of the grid-tied inverter and the output current. According to Figure 8, the active power Pe of the grid-tied inverter is: where: the structural parameter X≈ω0L. In the modeling and analysis of grid-tied inverter, a synchronous rotating coordinate system based on grid voltage vector orientation, is often used to make the grid voltage vector U g coincide with the d-axis of the synchronous rotating coordinate system [22], as shown in Figure 8. The excitation potential amplitude U s of the grid-tied inverter rotates at a synchronous angular frequency ω 0 . The grid terminal voltage U g is rotated according to the angular frequency ω g with reference to the d-axis. φ is the phase difference angle between the terminal voltage and output current of the grid-tied inverter. Φ is the phase angle difference between the excitation potential of the grid-tied inverter and the output current.
Energies 2019, 12, x FOR PEER REVIEW 7 of 17 unit power factor of the grid-connected inverter. At the same time, the grid-tied current is limited to ensure the safe operation of the grid-tied inverter. In the topology of the L-type grid-tied inverter, Rs and Ls respectively represent the equivalent series resistance and inductance of the L-type passive filter and the grid-tied inverter. And Lg represents the equivalent reactance between the grid-tied inverter and the infinite grid. Lg also represents the strength of the electrical connection between the grid-tied inverter and the infinite grid [21]. A simplified analysis of the main circuit of the grid-tied inverter is shown in Figure 7. Us is the excitation potential amplitude of the grid-tied inverter, corresponding to the fundamental component of the outlet voltage before the filter of the grid-tied inverter. δ is the phase angle difference between the grid-tied inverter and the grid terminal voltage. Ug is the amplitude of the grid-tied inverter, which corresponds to the terminal voltage of the grid. In the modeling and analysis of grid-tied inverter, a synchronous rotating coordinate system based on grid voltage vector orientation, is often used to make the grid voltage vector Ug coincide with the d-axis of the synchronous rotating coordinate system [22], as shown in Figure 8. The excitation potential amplitude Us of the grid-tied inverter rotates at a synchronous angular frequency ω0. The grid terminal voltage Ug is rotated according to the angular frequency ωg with reference to the d-axis. ϕ is the phase difference angle between the terminal voltage and output current of the grid-tied inverter. Φ is the phase angle difference between the excitation potential of the grid-tied inverter and the output current. According to Figure 8, the active power Pe of the grid-tied inverter is: where: the structural parameter X≈ω0L. According to Figure 8, the active power P e of the grid-tied inverter is: where: the structural parameter X≈ω 0 L. In the grid-tied inverter part, the conventional double closed loop control strategy is adopted. The DVC timescale modeling analysis method can also be adopted. The dynamic process of the current inner loop is ignored, and only the control process of the DC voltage outer loop is considered [23]. In this paper, only the active power part of the GPVGS is analyzed. Therefore, in the control block diagram of Figure 6, the reactive current reference I q * is set to 0, and the dynamic process of the active current I d can be expressed as: where K p and K i are the PI parameters of the DC voltage outer loop.

SSG Model of the GPVGS
In order to study the inertia, damping and synchronization characteristics of the GPVGS, the above research method are used as the theoretical basis to establish the SSG model of the GPVGS based on droop control.
Firstly, from the phasor diagram illustrated in Figure 8, it is easy to get: Combining Equations (13) and (14), we can get: For the small-signal stability analysis, linearizing Equation (15) to obtain: where K = U s X cos δ 0 , which is determined by the structural parameter and the steady-state operating point parameters of the system. Linearizing Equation (12), it can be expressed as: This paper not only analyzes the DVC timescale dynamic process of the grid-tied inverter, but also considers the dynamic effects of the PVA and the boost converter. Substituting Equations (11), (16) and (17) into (2), the SSG model of the GPVGS based on droop control is: Comparing Equation (18) with (3), the equivalent inertia coefficient T J , the equivalent damping coefficient T D and the equivalent synchronization coefficient T S of the GPVGS based on droop control are respectively expressed as:

The Physical law of the System Dynamic Characteristics
According to Equation (19), the inertia, damping and synchronization characteristics of the GPVGS based on droop control are not only affected by the control parameters of the system, but also influenced by the structural parameters and the steady-state operating point parameters of the system.

Influence of Control Parameters
From the perspective of system control parameters, T J is affected by the droop coefficient D p and the proportional coefficient K p of the DC voltage outer loop PI controller. With the decrease of D p , the stronger of the coupling between the output power of the boost converter and the system frequency. The greater the output power, the stronger the power support effect on the system, and the inertia effect of the system is enhanced. With the decrease of K p , the weaker of the inertia effect exhibited by the system.
T D is related to the PI parameter of the DC voltage outer loop and D p . The damping characteristic is positively correlated with the PI parameter of the DC voltage outer loop. That is to say, with the increase of PI parameter, the system of stability speed and quasi-degree are obviously accelerated to maintain the DC bus voltage. The damping effect of the system is enhanced. The damping characteristic is negatively correlated with D p . Namely, with the decrease of D p , the damping effect of the system is stronger.
T S is only affected by the integral coefficient K i of the DC voltage outer loop PI controller. The synchronization characteristic is positively correlated with K i . With the increase of K i , the synchronization effect of the system is stronger.

Influence of Structural Parameters
From the perspective of system structural parameters, T J , T D and T S are related to structural parameter X. With the decrease of X, the closer the electrical distance between the system and the infinite grid, the stronger the coupling degree of the large grid, the greater the inertia, damping and synchronization capability of the system. Therefore, the inertia, damping and synchronization characteristics of the system can be improved by reducing the line impedance X or reducing the installation distance from the large power grid.
The DC bus capacitor C is related to T J . With the increase of C, the more energy is stored or released, the stronger the ability to suppress interference, which means that the system inertia is stronger. Therefore, the system inertia can be improved by increasing C [24].

Influence of Steady-State Operating Point Parameters
From the perspective of the steady-state operating point parameters of the system, T J is related to U dc . With the increase of U dc , the system's inertia is enhanced. This is because the higher voltage, the more energy storage capacity, and the stronger the ability to suppress external interference. U g affects the damping and synchronization effects of the system. With the increase of U g , the damping and synchronization ability of the system is enhanced. The steady-state operating point parameters U s and δ 0 simultaneously affect the inertia, damping and synchronization characteristics of the system. Increasing U s can simultaneously improve the inertia, damping and synchronization capability of the system. δ 0 should be reasonably selected according to the stability margin of the system and the capacity utilization of the device. It can be seen that the higher the voltage-level of the grid connection, the better the electrical stability of the system. Therefore, for the PV system under the weak system, the grid voltage level should be improved as much as possible to improve the grid-tied stability of the GPVGS [25].

Simulation and Experimental Verification
In order to verify the validity of the above control law and the correctness of the analysis conclusion, the simulation model of the GPVGS based on droop control is built by MATLAB/Simulink, and the experimental platform is built by Simulink Real-Time. The simulation and experiment parameters of the system are shown in Table 2. When the system runs at 1 s, the power grid generates a power angle disturbance. The variation law of the DC bus voltage U dc and the electromagnetic power P e are analyzed under different control parameters and structural parameters, to indirectly express the strength of the system inertia, damping and synchronization characteristics.

System Inertia Feature Verification
The system inertia is affected by the control parameters D p and K p , and are more obvious with the influence of K p . Under the condition of keeping D p unchanged, the influence of K p on the system inertia characteristics is shown in Figure 9. With the increase of K p , the oscillation amplitude of U dc under disturbance is reduced, and the oscillation period of U dc is increased. It indicates that the system's anti-disturbance capability is enhanced, namely, the system inertia is enhanced. capability of the system. δ0 should be reasonably selected according to the stability margin of the system and the capacity utilization of the device. It can be seen that the higher the voltage-level of the grid connection, the better the electrical stability of the system. Therefore, for the PV system under the weak system, the grid voltage level should be improved as much as possible to improve the grid-tied stability of the GPVGS [25].

Simulation and Experimental Verification
In order to verify the validity of the above control law and the correctness of the analysis conclusion, the simulation model of the GPVGS based on droop control is built by MATLAB/Simulink, and the experimental platform is built by Simulink Real-Time. The simulation and experiment parameters of the system are shown in Table 2. When the system runs at 1 s, the power grid generates a power angle disturbance. The variation law of the DC bus voltage Udc and the electromagnetic power Pe are analyzed under different control parameters and structural parameters, to indirectly express the strength of the system inertia, damping and synchronization characteristics.

System Inertia Feature Verification
The system inertia is affected by the control parameters Dp and Kp, and are more obvious with the influence of Kp. Under the condition of keeping Dp unchanged, the influence of Kp on the system inertia characteristics is shown in Figure 9. With the increase of Kp, the oscillation amplitude of Udc under disturbance is reduced, and the oscillation period of Udc is increased. It indicates that the system's anti-disturbance capability is enhanced, namely, the system inertia is enhanced. The influence of Kp on Pe is shown in Figure 10. With the increase of Kp, the oscillation amplitude of Pe decreases, the speed of oscillation of Pe recovery balance increases, and the system inertia effect increases. The inertia corresponds to energy, the stronger inertia, the greater the change in Pe. Considering the stability margin limitation of the system, it is not possible to adjust Kp too large to pursue a large inertia, which affects the stable operation of the system. The influence of K p on P e is shown in Figure 10. With the increase of K p , the oscillation amplitude of P e decreases, the speed of oscillation of P e recovery balance increases, and the system inertia effect increases. The inertia corresponds to energy, the stronger inertia, the greater the change in P e . Considering the stability margin limitation of the system, it is not possible to adjust K p too large to pursue a large inertia, which affects the stable operation of the system. Experimental results in Figure 11 demonstrate the influence of control parameter K p on system transient stability. The system retains stability with small variations of K p value during operation (e.g., K p increases 0.05 to 0.1), as shown in Figure 11a,b. When K p increases, the oscillation amplitude of U dc and P e under disturbance is reduced, and the oscillation period of U dc and P e is increased. That is to say, the system inertia increases. The simulation results are consistent with the experimental results.
For structural parameters, the system inertia is positively correlated with the DC bus capacitance C. The influence of structural parameter C on the system inertia is shown in Figure 12. With the increase of C, the oscillation amplitude of U dc decreases, the oscillation period of U dc becomes longer, the time for restoring balance becomes longer, and the ability to suppress interference becomes stronger. That is to say, the system inertia is enhanced. Therefore, the inertia support capability of the system can be improved by increasing the capacitance of the DC bus capacitor C. Experimental results in Figure 11 demonstrate the influence of control parameter Kp on system transient stability. The system retains stability with small variations of Kp value during operation (e.g., Kp increases 0.05 to 0.1), as shown in Figures 11a,b. When Kp increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. That is to say, the system inertia increases. The simulation results are consistent with the experimental results. For structural parameters, the system inertia is positively correlated with the DC bus capacitance C. The influence of structural parameter C on the system inertia is shown in Figure 12. With the increase of C, the oscillation amplitude of Udc decreases, the oscillation period of Udc becomes longer, the time for restoring balance becomes longer, and the ability to suppress interference becomes stronger. That is to say, the system inertia is enhanced. Therefore, the inertia support capability of the system can be improved by increasing the capacitance of the DC bus capacitor C.   Experimental results in Figure 11 demonstrate the influence of control parameter Kp on system transient stability. The system retains stability with small variations of Kp value during operation (e.g., Kp increases 0.05 to 0.1), as shown in Figures 11a,b. When Kp increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. That is to say, the system inertia increases. The simulation results are consistent with the experimental results. For structural parameters, the system inertia is positively correlated with the DC bus capacitance C. The influence of structural parameter C on the system inertia is shown in Figure 12. With the increase of C, the oscillation amplitude of Udc decreases, the oscillation period of Udc becomes longer, the time for restoring balance becomes longer, and the ability to suppress interference becomes stronger. That is to say, the system inertia is enhanced. Therefore, the inertia support capability of the system can be improved by increasing the capacitance of the DC bus capacitor C. The influence of C on Pe is shown in Figure 13. With the increase of C, the oscillation amplitude of Pe decreases, the oscillation speed of Pe decreases, and the speed of the oscillation rises also slows  Experimental results in Figure 11 demonstrate the influence of control parameter Kp on system transient stability. The system retains stability with small variations of Kp value during operation (e.g., Kp increases 0.05 to 0.1), as shown in Figures 11a,b. When Kp increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. That is to say, the system inertia increases. The simulation results are consistent with the experimental results. For structural parameters, the system inertia is positively correlated with the DC bus capacitance C. The influence of structural parameter C on the system inertia is shown in Figure 12.
With the increase of C, the oscillation amplitude of Udc decreases, the oscillation period of Udc becomes longer, the time for restoring balance becomes longer, and the ability to suppress interference becomes stronger. That is to say, the system inertia is enhanced. Therefore, the inertia support capability of the system can be improved by increasing the capacitance of the DC bus capacitor C. The influence of C on Pe is shown in Figure 13. With the increase of C, the oscillation amplitude of Pe decreases, the oscillation speed of Pe decreases, and the speed of the oscillation rises also slows The influence of C on P e is shown in Figure 13. With the increase of C, the oscillation amplitude of P e decreases, the oscillation speed of P e decreases, and the speed of the oscillation rises also slows down. Namely, the system inertia is enhanced, and the ability to suppress external disturbances becomes stronger.
Experimental results in Figure 14 demonstrate the influence of structure parameter C on system transient stability. The system retains stability with small variations of the DC bus capacitance value during operation (e.g., C increases 4 mF to 6 mF), as shown in Figure 14a,b. When C increases, the oscillation amplitude of U dc and P e under disturbance is reduced, and the oscillation period of U dc and P e is increased. Namely, the system inertia increases. The simulation results are consistent with the experimental results. down. Namely, the system inertia is enhanced, and the ability to suppress external disturbances becomes stronger. Experimental results in Figure 14 demonstrate the influence of structure parameter C on system transient stability. The system retains stability with small variations of the DC bus capacitance value during operation (e.g., C increases 4 mF to 6 mF), as shown in Figures 14a,b. When C increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. Namely, the system inertia increases. The simulation results are consistent with the experimental results. Figure 14. Influence of C on system stability. The C increases from (a) 4 mF to (b) 6 mF.

System Damping Characteristics Verification
The damping characteristics of the GPVGS based on droop control are jointly affected by the control parameters Dp, Kp and Ki, but are more strongly affected by Dp. In the case of keeping Kp and Ki constant, the power angle disturbance is applied to the power grid. The damping characteristic of the system is affected by changing Dp. The simulation result is shown in Figure 15. With the decreases of Dp, the oscillation amplitude attenuation of Udc is significantly enhanced, but the oscillation period of Udc hardly changes. Namely, the damping capacity of the system is stronger.   Experimental results in Figure 14 demonstrate the influence of structure parameter C on system transient stability. The system retains stability with small variations of the DC bus capacitance value during operation (e.g., C increases 4 mF to 6 mF), as shown in Figures 14a,b. When C increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. Namely, the system inertia increases. The simulation results are consistent with the experimental results. Figure 14. Influence of C on system stability. The C increases from (a) 4 mF to (b) 6 mF.

System Damping Characteristics Verification
The damping characteristics of the GPVGS based on droop control are jointly affected by the control parameters Dp, Kp and Ki, but are more strongly affected by Dp. In the case of keeping Kp and Ki constant, the power angle disturbance is applied to the power grid. The damping characteristic of the system is affected by changing Dp. The simulation result is shown in Figure 15. With the decreases of Dp, the oscillation amplitude attenuation of Udc is significantly enhanced, but the oscillation period of Udc hardly changes. Namely, the damping capacity of the system is stronger. Figure 15. Influence of control parameter Dp on system damping. Figure 14. Influence of C on system stability. The C increases from (a) 4 mF to (b) 6 mF.

System Damping Characteristics Verification
The damping characteristics of the GPVGS based on droop control are jointly affected by the control parameters D p , K p and K i , but are more strongly affected by D p . In the case of keeping K p and K i constant, the power angle disturbance is applied to the power grid. The damping characteristic of the system is affected by changing D p . The simulation result is shown in Figure 15. With the decreases of D p , the oscillation amplitude attenuation of U dc is significantly enhanced, but the oscillation period of U dc hardly changes. Namely, the damping capacity of the system is stronger. Experimental results in Figure 14 demonstrate the influence of structure parameter C on system transient stability. The system retains stability with small variations of the DC bus capacitance value during operation (e.g., C increases 4 mF to 6 mF), as shown in Figures 14a,b. When C increases, the oscillation amplitude of Udc and Pe under disturbance is reduced, and the oscillation period of Udc and Pe is increased. Namely, the system inertia increases. The simulation results are consistent with the experimental results. Figure 14. Influence of C on system stability. The C increases from (a) 4 mF to (b) 6 mF.

System Damping Characteristics Verification
The damping characteristics of the GPVGS based on droop control are jointly affected by the control parameters Dp, Kp and Ki, but are more strongly affected by Dp. In the case of keeping Kp and Ki constant, the power angle disturbance is applied to the power grid. The damping characteristic of the system is affected by changing Dp. The simulation result is shown in Figure 15. With the decreases of Dp, the oscillation amplitude attenuation of Udc is significantly enhanced, but the oscillation period of Udc hardly changes. Namely, the damping capacity of the system is stronger. Figure 15. Influence of control parameter Dp on system damping. Figure 15. Influence of control parameter D p on system damping.
The influence of D p on P e is shown in Figure 16. With the decreases of D p , the period of system power oscillation is almost constant, and the attenuation rate of the oscillation amplitude is obviously accelerated. That is to say, the ability to suppress the oscillation is enhanced, and the damping ability is enhanced. From the variation of U dc and P e , the control parameter D p has the same effect on the system damping. The stronger the damping capacity, the more obvious the P e changes.
The influence of Dp on Pe is shown in Figure 16. With the decreases of Dp, the period of system power oscillation is almost constant, and the attenuation rate of the oscillation amplitude is obviously accelerated. That is to say, the ability to suppress the oscillation is enhanced, and the damping ability is enhanced. From the variation of Udc and Pe, the control parameter Dp has the same effect on the system damping. The stronger the damping capacity, the more obvious the Pe changes. Experimental results in Figure 17 demonstrate the influence of control parameter Dp on system transient stability. The system retains stability with small variations of Dp value during operation (e.g., Dp increases 4 to 5), as shown in Figures 17a,b. When Dp increases, the oscillation amplitude of Udc and Pe under disturbance is increased, but the oscillation period of Udc and Pe is hardly changed. Namely, the system damping capacity decreases. The simulation results are consistent with the experimental results. Under the condition that the control parameters and the steady-state operating point parameters are kept unchanged, the influence law of the structural parameter L on the damping characteristics of the system is shown in Figure 18. With the increase of L, the oscillation amplitude of Udc becomes larger and larger. However, the oscillation period of Udc is obviously unchanged. That is to say, the damping capacity is weaker. Experimental results in Figure 17 demonstrate the influence of control parameter D p on system transient stability. The system retains stability with small variations of D p value during operation (e.g., D p increases 4 to 5), as shown in Figure 17a,b. When D p increases, the oscillation amplitude of U dc and P e under disturbance is increased, but the oscillation period of U dc and P e is hardly changed. Namely, the system damping capacity decreases. The simulation results are consistent with the experimental results.
The influence of Dp on Pe is shown in Figure 16. With the decreases of Dp, the period of system power oscillation is almost constant, and the attenuation rate of the oscillation amplitude is obviously accelerated. That is to say, the ability to suppress the oscillation is enhanced, and the damping ability is enhanced. From the variation of Udc and Pe, the control parameter Dp has the same effect on the system damping. The stronger the damping capacity, the more obvious the Pe changes. Experimental results in Figure 17 demonstrate the influence of control parameter Dp on system transient stability. The system retains stability with small variations of Dp value during operation (e.g., Dp increases 4 to 5), as shown in Figures 17a,b. When Dp increases, the oscillation amplitude of Udc and Pe under disturbance is increased, but the oscillation period of Udc and Pe is hardly changed. Namely, the system damping capacity decreases. The simulation results are consistent with the experimental results. Under the condition that the control parameters and the steady-state operating point parameters are kept unchanged, the influence law of the structural parameter L on the damping characteristics of the system is shown in Figure 18. With the increase of L, the oscillation amplitude of Udc becomes larger and larger. However, the oscillation period of Udc is obviously unchanged. That is to say, the damping capacity is weaker. Under the condition that the control parameters and the steady-state operating point parameters are kept unchanged, the influence law of the structural parameter L on the damping characteristics of the system is shown in Figure 18. With the increase of L, the oscillation amplitude of U dc becomes larger and larger. However, the oscillation period of U dc is obviously unchanged. That is to say, the damping capacity is weaker.
The influence of Dp on Pe is shown in Figure 16. With the decreases of Dp, the period of system power oscillation is almost constant, and the attenuation rate of the oscillation amplitude is obviously accelerated. That is to say, the ability to suppress the oscillation is enhanced, and the damping ability is enhanced. From the variation of Udc and Pe, the control parameter Dp has the same effect on the system damping. The stronger the damping capacity, the more obvious the Pe changes. Experimental results in Figure 17 demonstrate the influence of control parameter Dp on system transient stability. The system retains stability with small variations of Dp value during operation (e.g., Dp increases 4 to 5), as shown in Figures 17a,b. When Dp increases, the oscillation amplitude of Udc and Pe under disturbance is increased, but the oscillation period of Udc and Pe is hardly changed. Namely, the system damping capacity decreases. The simulation results are consistent with the experimental results. Under the condition that the control parameters and the steady-state operating point parameters are kept unchanged, the influence law of the structural parameter L on the damping characteristics of the system is shown in Figure 18. With the increase of L, the oscillation amplitude of Udc becomes larger and larger. However, the oscillation period of Udc is obviously unchanged. That is to say, the damping capacity is weaker. The influence of structural parameter L on P e is shown in Figure 19. With the decreases of L, the oscillation amplitude of P e becomes smaller and smaller, but the oscillation period of P e changes insignificantly. It shows that the system damping capacity is stronger. Therefore, the system damping capacity can be improved by reducing inductance L. The influence of structural parameter L on Pe is shown in Figure 19. With the decreases of L, the oscillation amplitude of Pe becomes smaller and smaller, but the oscillation period of Pe changes insignificantly. It shows that the system damping capacity is stronger. Therefore, the system damping capacity can be improved by reducing inductance L. Experimental results in Figure 20 demonstrate the influence of structure parameter L on system transient stability. The system retains stability with small variations of equivalent inductance value during operation (e.g., L increases 4 mH to 8 mH), as shown in Figures 20a,b. When L decreases, the oscillation amplitude of Udc and Pe under disturbance is decreased, but the oscillation period of Udc and Pe is hardly changed. That is to say, the system damping capacity increases. The simulation results are consistent with the experimental results.

System Synchronization Feature Verification
The synchronization characteristic of the GPVGS based on the droop control is only determined by the control parameter Ki. Figure 21 shows the influence law of changing Ki on the synchronization characteristics of the system under the condition of keeping Dp and Kp unchanged. With the increase of Ki, the oscillation amplitude of Udc is not obvious, but the oscillation period of Udc is obviously shortened, indicating that the synchronization capability of the system is enhanced. Experimental results in Figure 20 demonstrate the influence of structure parameter L on system transient stability. The system retains stability with small variations of equivalent inductance value during operation (e.g., L increases 4 mH to 8 mH), as shown in Figure 20a,b. When L decreases, the oscillation amplitude of U dc and P e under disturbance is decreased, but the oscillation period of U dc and P e is hardly changed. That is to say, the system damping capacity increases. The simulation results are consistent with the experimental results.
The influence of structural parameter L on Pe is shown in Figure 19. With the decreases of L, the oscillation amplitude of Pe becomes smaller and smaller, but the oscillation period of Pe changes insignificantly. It shows that the system damping capacity is stronger. Therefore, the system damping capacity can be improved by reducing inductance L. Experimental results in Figure 20 demonstrate the influence of structure parameter L on system transient stability. The system retains stability with small variations of equivalent inductance value during operation (e.g., L increases 4 mH to 8 mH), as shown in Figures 20a,b. When L decreases, the oscillation amplitude of Udc and Pe under disturbance is decreased, but the oscillation period of Udc and Pe is hardly changed. That is to say, the system damping capacity increases. The simulation results are consistent with the experimental results.

System Synchronization Feature Verification
The synchronization characteristic of the GPVGS based on the droop control is only determined by the control parameter Ki. Figure 21 shows the influence law of changing Ki on the synchronization characteristics of the system under the condition of keeping Dp and Kp unchanged. With the increase of Ki, the oscillation amplitude of Udc is not obvious, but the oscillation period of Udc is obviously shortened, indicating that the synchronization capability of the system is enhanced.

System Synchronization Feature Verification
The synchronization characteristic of the GPVGS based on the droop control is only determined by the control parameter K i . Figure 21 shows the influence law of changing K i on the synchronization characteristics of the system under the condition of keeping D p and K p unchanged. With the increase of K i , the oscillation amplitude of U dc is not obvious, but the oscillation period of U dc is obviously shortened, indicating that the synchronization capability of the system is enhanced. The influence of Ki on Pe is shown in Figure 22. With the increase of Ki, the oscillation period of Pe changes significantly. While the oscillation amplitude and the attenuation speed of Pe change little, indicating that the system synchronization effect is enhanced. At the same time, it can be seen that with the enhancement of the system synchronization capability, Udc and Pe change more obviously. The greater the change amplitude of Udc, the greater the change corresponding to Pe.
Considering the system dynamic effect speed, Ki should be selected in an appropriate range. The influence of K i on P e is shown in Figure 22. With the increase of K i , the oscillation period of P e changes significantly. While the oscillation amplitude and the attenuation speed of P e change little, Energies 2019, 12,1985 15 of 17 indicating that the system synchronization effect is enhanced. At the same time, it can be seen that with the enhancement of the system synchronization capability, U dc and P e change more obviously. The greater the change amplitude of U dc , the greater the change corresponding to P e . Considering the system dynamic effect speed, K i should be selected in an appropriate range. The influence of Ki on Pe is shown in Figure 22. With the increase of Ki, the oscillation period of Pe changes significantly. While the oscillation amplitude and the attenuation speed of Pe change little, indicating that the system synchronization effect is enhanced. At the same time, it can be seen that with the enhancement of the system synchronization capability, Udc and Pe change more obviously. The greater the change amplitude of Udc, the greater the change corresponding to Pe. Considering the system dynamic effect speed, Ki should be selected in an appropriate range. Experimental results in Figure 23 demonstrate the influence of control parameter Ki on system transient stability. The system retains stability with small variations of Ki value during operation (e.g., Ki increases 4 to 6), as shown in Figures 23a,b. When Ki increases, the oscillation amplitude of Udc and Pe under disturbance is hardly changed, but the oscillation period of Udc and Pe is significant decrease. Namely, the system synchronization capability increases. The simulation results are consistent with the experimental results.

Conclusions and Future Work
In this paper, the GPVGS based on droop control is taken as the research object. The mathematical model of the GPVGS on the DVC timescale dynamics is firstly established. The Experimental results in Figure 23 demonstrate the influence of control parameter K i on system transient stability. The system retains stability with small variations of K i value during operation (e.g., K i increases 4 to 6), as shown in Figure 23a,b. When K i increases, the oscillation amplitude of U dc and P e under disturbance is hardly changed, but the oscillation period of U dc and P e is significant decrease. Namely, the system synchronization capability increases. The simulation results are consistent with the experimental results. The influence of Ki on Pe is shown in Figure 22. With the increase of Ki, the oscillation period of Pe changes significantly. While the oscillation amplitude and the attenuation speed of Pe change little, indicating that the system synchronization effect is enhanced. At the same time, it can be seen that with the enhancement of the system synchronization capability, Udc and Pe change more obviously. The greater the change amplitude of Udc, the greater the change corresponding to Pe. Considering the system dynamic effect speed, Ki should be selected in an appropriate range. Experimental results in Figure 23 demonstrate the influence of control parameter Ki on system transient stability. The system retains stability with small variations of Ki value during operation (e.g., Ki increases 4 to 6), as shown in Figures 23a,b. When Ki increases, the oscillation amplitude of Udc and Pe under disturbance is hardly changed, but the oscillation period of Udc and Pe is significant decrease. Namely, the system synchronization capability increases. The simulation results are consistent with the experimental results.

Conclusions and Future Work
In this paper, the GPVGS based on droop control is taken as the research object. The mathematical model of the GPVGS on the DVC timescale dynamics is firstly established. The Figure 23. Influence of K i on system stability. The K i increases from (a) 4 to (b) 6.

Conclusions and Future Work
In this paper, the GPVGS based on droop control is taken as the research object. The mathematical model of the GPVGS on the DVC timescale dynamics is firstly established. The electric torque method is used to analyze the inertia, damping and synchronization characteristics of the GPVGS from the physical mechanism perspective. The research results show that: (1) The GPVGS based on droop control also has a certain inertia, damping and synchronization effect.
At the same time, the equivalent inertia, damping and synchronization coefficient of the system are affected by the control parameters, structural parameters and steady-state operating points parameters, among which the adjustment control parameters are the simplest way to change the inertia, damping and synchronization characteristics of the system. (2) From the perspective of control parameters, the inertia characteristics of the system are influenced by the DC voltage outer loop proportional coefficient K p and positively correlated with K p . The damping characteristics of the system are affected by the droop coefficient D p and negatively correlated with D p . The synchronization effect is only affected by the DC voltage outer loop integral coefficient K i and positively correlated with K i .