Enhanced Power Decoupling Strategy for Virtual Synchronous Generator

Power coupling caused by high impedance ratio and nonzero power angle is a crucial issue for virtual synchronous generator (VSG), which may result in output power error, slower power response and even invalid operation. To solve this issue, a novel enhanced power decoupling method by using virtual steady-state synchronous impedance (VSSI) and current dynamic decoupling compensation (CDDC) is proposed. VSSI with the unique characteristic that the value of virtual reactance maintains constant in all frequencies, can solve the power coupling caused by impedance ratio. CDDC can solve the power coupling caused by nonzero power angle in the fastest way by the designed compensation in inner current loop. The reshaped output impedance characteristics are also analyzed in detail. Then, by state-space modelling and analysis, it is proved that, compared to the traditional methods, the proposed method can improve the dynamic performance and enhance the system stability further. Finally, the results of comparative experiments demonstrate that the proposed method can solve the power coupling problem more effectively and improve the dynamic and steady-state responses of active power and reactive power.


I. INTRODUCTION
The development of renewable energy sources (RESs), such as photovoltaics and wind power generation, plays an important role in responding to the energy crisis and environmental problems [1]. However, the RESs mostly interface with the power grid by grid-connected converters, which lack inertia and damping and have weak support capability of frequency and voltage [2]- [4]. As a consequence, a huge challenge has been posed, that is how to maintain the stable operation of the power system with high penetration of grid-connected converters [5]. To cope with this challenge, the concept of virtual synchronous generator (VSG) control [6]- [11], also called virtual synchronous machine (VISMA) [12], [13], or synchronverter [14], has been proposed. VSG firstly emulates the function of primary frequency and voltage regulation of synchronous generator (SG) The associate editor coordinating the review of this manuscript and approving it for publication was Mohsin Jamil . by using droop control. Furthermore, VSG mimics the swing equation of SG to increase the inertia of grid-connected converter and improve the transient response characteristics. VSG has become a promising approach for interfacing RES with power systems due to its excellent features.
The foundation of normal operation of VSG is the decoupling characteristics of power flow through transmission line, that is, for the circumstances of a small power angle and pure inductive impedance between two voltage sources, the active power depends predominantly on voltage frequency, whereas reactive power depends predominantly on voltage amplitude [15]. However, the two fundamental preconditions, i.e. small power angle and pure inductive impedance, are not always satisfied. As a result, the dynamic performance and stability of VSGs are deteriorated.
VSG is often linked to low-voltage lines/networks, where the impedance ratio R/X is high. Consequently, the aforesaid power decoupling precondition cannot be satisfied. To solve this problem, four groups of power decoupling VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ methods, mainly including virtual impedance method [15]- [18], virtual power method [19]- [21], virtual frequency and voltage method [22] and power feedforward compensation method [23]- [26], are proposed. The idea of virtual impedance method is to reshape the output impedance of VSG to become mainly inductive by implementing a virtual impedance loop. The virtual power method and virtual frequency and voltage method, are to rotate the vectors of active power and reactive power by an impedance angle, or to rotate the vectors of frequency and voltage amplitude, so as to obtain the mutually independent relationship. The power feedforward compensation method is to add a pair of cross channels between active power and reactive power control path to counteract the effect of power coupling channel. The above methods provide effective solutions to address the high impedance ratio issue, but the effect of error due to small power angle assumption is often ignored. However, several phenomena caused by power coupling, e.g. power oscillation, reactive power steady-state error, have been still observed even though the output impedance of VSG is purely inductive [7], [27], [28]. Due to the existence of virtual inertia in VSG, a potential oscillation characteristic will transfer between the active power loop and reactive power loop. Therefore, it causes a dynamic and steady-state performance deterioration in the meanwhile and thereby affects the primary control and power sharing. Besides, the coupling oscillation also damages the VSGs due to their poor overcurrent capacity, and even becomes diverging and makes the system unstable. Hence, the power coupling issue of VSG is much more serious than droop control. To ensure good control performance of VSG, a more accurate decoupling method is necessary to relax the small power angle assumption which may cause the performance degradation and instability problem.
Considering the effect of line impedance ratio and power angle on active power and reactive power control simultaneously, an oscillation suppression method from the perspective of designing optimal damping coefficient is presented in [7]. Dynamic coupling phenomenon is analysed by small-signal modelling and a power oscillation suppression method by adding virtual resistance is proposed in [29]. However, these methods cannot eliminate the coupling between active power and reactive power, and the corresponding issues caused by power coupling, e.g. control error and stability degradation, are not solved. Furthermore, the oscillation suppression capacity of damping coefficient is limited by the tradeoff within primary frequency regulation requirement, power oscillation suppression performance and dynamic response time. The virtual resistance can eliminate the oscillation and enhance the stability, but it deteriorates the coupling. The accurate tracking of the voltage in PCC by modifying the excitation voltage regulator is realised to satisfy the requirements of power decoupling in [30], but this method depends on the highly accurate identification of line impedance.
Motivated by this issue, this paper studies an enhanced power decoupling method to improve the performance and stability of VSG. This method can also be used in other droopbased grid-connected converters. The rest of this paper is organized as follows. In Section II, the basic principle of VSG control is briefly reviewed and the power coupling issue of VSG is analyzed quantitatively by using relative gain array method. In Section III, an accurate power decoupling method is proposed. In Section IV, the dynamic response performance and stability of VSG with the proposed enhanced decoupling strategy are analyzed. The experiment results are shown in Section V. Finally, conclusions are draw in Section VI.

II. POWER COUPLING ISSUE OF VSG A. BASIC PRINCIPLE OF VSG CONTROL
The basic structure of VSG system is depicted in Fig. 1. The control strategy is built in d-q reference frame. The power control loop generates the magnitude and frequency of the output voltage reference. The virtual impedance is used to emulate the electric characteristic of the stator in SG. The current control loop adopts PI regulators to realize the accurate tracking property and overcurrent protection function.
Active power loop emulates the function of primary frequency control and rotating inertia of SG, which is expressed mathematically (ignoring the low pass filter) as: where P and P ref are the output active power and its reference respectively, ω and ω ref are radian frequency of virtual inner voltage of VSG and the nominal radian frequency, J is the virtual inertia, k P is the active power droop coefficient, D is the damping coefficient. The structure of reactive power loop obtains the RMS reference of virtual inner voltage E by Q-E droop control. The reactive power loop ignoring the low pass filter can be expressed as: where Q and Q ref are the output reactive power and its reference respectively, E ref and E are the nominal voltage amplitude and the RMS value of virtual inner voltage of VSG, k Q is the reactive power droop coefficient. VSG regulates the phase to control the output active power according to (1), and regulates the magnitude of voltage to control the output reactive power according to (2) independently.

B. ANALYSIS OF POWER COUPLING ISSUE
According to the principle of VSG control explained by (1) and (2), in order to ensure the normal operation of VSG, it is necessary that there should exist same decoupling characteristics when power flows through the transmission line. For an AC system with a given transmission line impedance, illustrated in Fig. 2, the active and reactive power flowing  between two voltage sources can be expressed as where R and X are equivalent resistance and reactance between VSG and AC bus respectively, δ is the power angle, E and U are the RMS values of virtual inner voltage and voltage at PCC.
It can be seen that both active power and reactive power are functions of two variables, power angle and voltage magnitude. Linearizing (3) at a steady-state point yields where γ c = δ + arctan(R/X ), indicates the perturbation of the corresponding variable, the subscript 0 represents the steady-state value. Expression (4) indicates that when γ c =0, the active power and reactive power are coupled with each other rather than mutually independent. Consequently, the active power and reactive power control will be affected by each other and thus the performance and stability will deteriorate.
To quantitatively analyse the coupling degree, relative gain array (RGA) analysis method [31] is used in this paper.
Assuming y i is the i th controlled variable of a multiple-inputmultiple-output (MIMO) system and u j is the j th manipulated variable, the relative gain of the u j -y i channel is defined as the ratio of the u j -y i channel gain with other channels open, indicated by p ij , and the u j -y i channel gain with other channels closed and other controlled variables constant, indicated by q ij . The mathematical expression can be written as where ''const'' represent constant value. Arranging λ ij in the order marked in subscript can construct the RGA , which describes the coupling relationship and degree of a MIMO system. For the VSG system studied in this paper, the corresponding RGA can be derived as To quantify the coupling level, define relative coupling coefficient K c as According to the theory of RGA, a larger K c indicates a higher coupling level. Only when K c ∈[0,0.5), the pairing relationship of δ-P and E-Q is satisfied and thereby the effectiveness of the VSG power control loops can be guaranteed. The closer to 0 K c is, the weaker the coupling is. When K c > 0.3, the coupling becomes quite severe. Fig. 3(a) shows the curve of K c vs. δ and R/X. Fig. 3(b) shows the vertical profile of the three-dimensional graph in Fig. 3(a) at different δ. The stability regions of the cases are in the left of the points of K c = 1 which are marked in Fig. 3(b). It can be seen that the stability region gets narrower with the increase of the power angle δ. Taking the curve of δ = 0.26 rad for example, the stability region is located in R/X < 3.73. Actually, K c = 0.3 when R/X = 0.33, which means that there already exists severe coupling. With the rise of R/X , the level of coupling gets higher. When R/X > 0.58, K c > 0.5 and the coupling channel is predominant in controlling the output power. Fig. 3(c) gives the relationship between K c and δ for different R/X . Similarly, the stability region gets narrower with the increase of R/X . Taking the curve of R/X = 0.25 for example, the stability region is in δ < 1.33 rad. With the rise of δ, the coupling becomes more serious. When δ increases to 0.33 rad, K c = 0.3 and the coupling has become serious. When δ > 0.54 rad, K c > 0.5 and it indicates the coupling channel has a greater influence on the output power than the control channel.
It can be seen from (7) and Fig. 3(c), the coupling level is related not only to the transmission impedance ratio R/X but also to the power angle δ. Only when the transmission is purely inductive and power angle is zero, the active power and reactive power are decoupled, which meets the prerequisite of VSG control strategy.

III. ENHANCED POWER DECOUPLING METHOD
In order to address the power coupling issue, an enhanced power decoupling method is proposed in this section, which can simultaneously eliminate the power coupling caused by the high impedance ratio and small power angle condition. The droop control can be regarded as a special type of VSG with zero virtual inertia. Therefore, the proposed method can also be used in droop control.
The control strategy mainly contains two parts: virtual steady-state synchronous impedance (VSSI) and current dynamic decoupling compensation (CDDC), where VSSI can eliminate the power coupling caused by the high impedance ratio and CDDC can eliminate the power coupling caused by nonzero power angle δ.
The whole proposed decoupling control block diagram is shown in Fig. 4. The control block of VSSI part is depicted in the green box and control block of CDDC part is depicted in the yellow box and serves as the initial current reference. The d-q reference frame is oriented according to the VSG virtual inner voltage, so that e d = E, e q = 0. Then two pairs of current feedforward references, which are used to eliminate the power coupling caused by the power angle, are added to the initial current reference and then the modified current reference is obtained. After that, the reference goes through PI controller to generate the control signal of converter, where a voltage feedforward is introduced. This method obtains the current reference algebraically with no need of regulator; thus, it has faster regulation performance than cascaded voltage and current controllers.
The principle and implementation of each part are interpreted as follows.

A. VSSI PART
In VSSI, the synchronous admittance matrix is expressed as where R v is the virtual resistance, and X v is the virtual steadystate synchronous reactance that is the product of nominal frequency ω ref and virtual inductance L v as shown in (9).
It should be emphasized that as long as L v is certain, the value of X v maintains constant rather than changes with frequency like traditional virtual reactance. The proposed novel design of X v makes the voltage on it be 90 degrees ahead of the current flowing through it, while its gain amplitude to the current remains constant at all frequencies. That makes VSG with VSSI more stable than VSG with Traditional Virtual Impedance (TVI), which will be demonstrated by root locus in Section IV. In order to verify the effectiveness of reshaping output impedance in both the resistance and inductance dimensions, the VSG system is modelled by a dq-frame Norton equivalent circuit and the output currents are calculated as where G i (s) is the current gain matrix, i * d_mod and i * q_mod are the d-and q-axis current references respectively, u d and u q are the d-and q-axis components of voltage at PCC, s is the Laplace operator. Z odq (s) is the output impedance that satisfies In practice, the voltage feedforward plays an important role in reshaping the output impedance, which is discussed here. The output impedances with voltage feedforward (VSSI-1), denoted as Z dd_1 and Z qd_1 , and without voltage feedforward (VSSI-2), denoted as Z dd_2 and Z qd_2 , are shown as follows. where k cp and k ci are the proportional and integral coefficients of PI controller of current loop, L l and R l are the connection inductance and resistance. Obviously, Z dd_2 and Z qd_2 have more complex forms than Z dd_1 and Z qd_1 . Z dd_1 and Z qd_1 are equal to the given impedance values multiplied by a transient transfer function VOLUME 8, 2020 G h (s), and G h (s)| s=0 = 1, which means that the DC output impedance in d-q reference frame (namely, the output impedance at nominal frequency (50Hz) in stationary abc reference frame) is totally determined by the given virtual impedance and independent of the controller and output filter parameters.
The bode diagrams of equivalent output impedances of VSSI-1 and VSSI-2 can be drawn in Fig. 5 according to (12)- (15). Likewise, for the purpose of comparative analysis, the bode diagrams of equivalent real physical impedance model, traditional virtual impedance method with voltage feedforward (TVI-1) and traditional virtual impedance method without voltage feedforward (TVI-2) are also drawn in Fig. 5. The setting value of resistance and reactance are all 1 and 2 .
It can be seen from the bode plots, in the low-frequency range, all the curves coincide with each other, which indicates that the VSSI can guarantee the pre-designed output impedance characteristics at the nominal frequency and its vicinity, and void the influence of filter and controller parameters. Therefore, for the purpose of optimal decoupling performance, the purely inductive output impedance can be realized directly by setting R v = 0 in VSSI.
In the high frequency region, Z dd of TVI-1 are larger than equivalent real inductance in magnitude and lead 90 • in phase. Z dd of TVI-2 are almost the same with the equivalent real inductance in magnitude and phase. Differently, Z dd of VSSI-1 and VSSI-2 are both smaller than the equivalent real inductance in magnitude and have the same phase with the equivalent real inductance. It implies that the VSSI strategy lowers the high-frequency output impedance, reduces the harmonic voltage drop in output impedance caused by a disturbance of nonlinear loads, and thus improves the antidisturbance capability.

B. CDDC PART
The VSSI strategy presented in Section III.A ensures the inductive output impedance to eliminate the power coupling caused by the existence of line impedance ratio R/X . After that, (3) can be simplified as Linearizing (16) and (17) at the steady-state operating point (E 0 , δ 0 ) yields

1) Q-DECOUPLING
Letting Q = 0 in (18), yields where E represents the error of virtual inner voltage caused by the power angle disturbance. Thus if E can be compensated as (19), the coupling effect on reactive power can be eliminated. Based on this idea, a novel current dynamic decoupling compensation (CDDC) method for the purpose of relaxing small power angle condition is presented, which is derived as following process. The phasor diagram of the equivalent circuit of gridconnected VSG is shown in Fig. 6.
According to the phasor diagram, the d-and q-components of grid voltage are represented respectively as The d-and q-components of output current are given by Linearizing (21) and (22) at (E 0 , δ 0 ), yields The expressions of output active power and reactive power can be written as The small signal models in terms of current variable are given by Expression (27) and (28) can be derived from (23) and (24) respectively, Substituting (19), (20), (25) and (27) into (28) gives Equation (29) shows that the error Q caused by the undesired coupling can be eliminated if the output current is changed from (i d0 , i q0 ) to (i d0 +i q0 · δ, i q0 −i d0 · δ). Therefore, the current compensation references for Q-δ decoupling are designed as 2) P-DECOUPLING According to (18), at the initial operating point (E 0 , δ 0 ), the active power error caused by voltage disturbance is written as Assuming that the corresponding d-and q-components of output current error caused by the disturbance of voltage E are i d and i q , combining (26) with (31) yields where i d0 and i q0 are the steady-state value of output current. Therefore, the current feedforward reference for P-E decoupling  To make it easier to obtain the P-E decoupling compensation current reference, the voltage steady-state value can be replaced with voltage reference. Then, combining (30) and (33), the modified current reference is designed as It can be seen from (34) and (35), the calculation of feedforward compensation only needs to measure the real-time operating state, i.e. current, power angle, but does not depend on the parameters which can hardly measure accurately, e.g. line impedance, etc. Therefore, the proposed strategy can realize the accurate decoupling theoretically and are well robust to the variation of parameters.

IV. DYNAMIC PERFORMANCE AND STABILITY ANALYSIS FOR ENHANCED VSG STRATEGY
In order to study the effectiveness and characteristics of the proposed decoupling strategy, a small signal model in state space for the whole VSG system shown in Fig. 1 is also built. Linearized small signal model can be expressed as where A, B, C, D are shown in Appendix and the state vector, input vector and output vector are given by where γ d is the small signal of integral of current difference between i * d_ mod and i d , and γ d is that between i * q_ mod and i q .
Then, the transfer function matrix can be derived as where G(s) is a 2 × 5 matrix. G 11 (s) and G 23  The characteristic root locus diagrams of A in constant impedance magnitude but different impedance ratio are shown in Fig. 7, where only the locus of dominant poles is drawn.
It can be seen from Fig. 7 (a), when no decoupling method is adopted, there are two poles located at right half plane at small impedance ratio, which means the system is unstable under very small impedance ratio without any decoupling strategy. Along with the increase of impedance ratio, these two poles move to left half plane gradually and the system becomes stable. However, these two poles are still conjugate poles and are underdamped over a wide range of impedance ratios. Meanwhile, there are four poles that are close to imaginary axis but always stay at left half plane. When the TVI is adopted with R v = 0 , there are two poles always moving at right half plane. That means the system cannot be stable if TVI is adopted with R v = 0 . Nevertheless, when the TVI is adopted with R v = R/3, these two poles are located at right half plane at very small impedance ratio but move to left half plane along with the increase of R/X . That means the system stability increases and the damping of these two poles increases along with the increase of R/X when TVI is adopted with R v larger than 0. By the contrast between root locus without decoupling and the root locus with TVI, it can be found that R v smaller than R brings weaker damping to those two poles under TVI. However, to weaken the power coupling, R v should be set as a value smaller than R. Therefore, oscillation may occur during dynamic process due to those two poles in TVI.
When VSSI is adopted, thanks to the unique characteristic of VSSI that the value of virtual reactance does not increase with frequency, A under the VSSI strategy is two orders less than that under the TVI strategy. As a result, as shown in Fig. 7 (b), those two unstable roots do not exist under VSSI, so all the poles under VSSI only move at left half plane and the system is stable with any impedance ratio. It is demonstrated that the VSSI can improve the system stability more effectively than the strategy without decoupling and TVI. In addition, without the limitation of the two poles at right half plane, R v in VSSI can be set to 0, which is helpful to give VSSI better decoupling effect than TVI. In Fig. 7 (b), when the VSSI and CDDC are adopted at the same time, as shown in the diagram of conjugate roots locus that is zoomed in, the damping of the two conjugate roots are further increased, which demonstrates that the proposed VSSI+CDDC strategy can not only improve the system stability but also benefit the dynamic response of the system.

V. EXPERIMENTAL RESULTS
The experiments are conducted in the hardware-in-the-loop platform as shown in Fig. 8 to verify the effectiveness and superiority of the proposed enhanced decoupling strategy. The main circuit is simulated by real time simulation in the slave computer while the control algorithm runs in the core controller of TMS320F28335 DSP. The data transition between them is implemented by a multifunction I/O card MF624 that is embedded in the slave computer. The topology is the same with that in Fig. 2. but the DGs are replaced by a constant voltage DC source with 700V. Four control strategies, i.e. VSG strategy without decoupling strategy, TVI based decoupling strategy, only the proposed VSSI based decoupling strategy and the proposed VSSI with CDDC strategy, are adopted respectively in the system with the same main parameters listed in Table 1.

A. COMPARATIVE EXPERIMENTS OF Q-DECOUPLING PERFORMANCE
When t < t 0 , VSG operates steadily with P = 0 and Q = 300Var. the response to active power reference step at t 0 with the value of R/X as 0.25 is shown in Fig. 9. The data is calculated by DSP according to the control algorithm and the measured voltage and current from the main circuit, and converted to analog signal by MF624 then displayed on the oscilloscope.
In Fig. 9 (b), when no decoupling methods are adopted, the reactive power output exhibits an unwanted descent to -3.4kVar and reaches a new steady-state value of -3.1kVar. That means -3.4pu steady-state deviation of reactive power is generated by the active power step because of the coupling impact from active power loop. Such large deviation of reactive power brings great overcurrent risk, which is very necessary to avoid.
When the TVI method is added, the power coupling weakens markedly. However, as analysed in Section IV, zero virtual resistance in TVI will destabilize the system. The virtual resistance in TVI thus can be set as a smaller value than real line resistance but not zero. Then the power coupling caused by nonzero impedance ratio still exists but is weakened than that with no decoupling method. Thus, the impact of active VOLUME 8, 2020 When only the proposed VSSI is added, the virtual resistance can be set to 0, which gives the VSSI better effect on weakening the power coupling caused by line impedance. Then the deviation of reactive power is decreased to −0.9kVar. But the power coupling caused by the nonzero power angle is not complemented yet, which leads the reactive power to deviate from initial value −1.2kVar.
As shown in Fig. 9 (b), when the proposed VSSI and CDDC operate simultaneously, the deviation of reactive power during the whole process almost disappears. The main reason for such excellent performance is that the feedforward decoupling currents, i * d_dδ and i * q_dδ are adjusted according to the change of power angle along with the active power change as shown in Fig. 10.
As a result, the phase and amplitude of the inverter are adjusted at the same time to maintain reactive power unchanged while active power follows the reference accurately. Q-coupling problem is addressed better. It proves that the proposed method in this paper can eliminate the steadystate error of reactive power and enable VSG to output reactive power in strict accordance with the requirement of the reactive power control loop regardless of the influence of the active power control loop.  When the impedance ratio R/X is larger, the power coupling will be more serious. As shown in Fig. 11, with the impedance ratio as 1, the power angle diverges due to serious power coupling when the active power reference steps, and the system even destabilized without decoupling strategy.
Fortunately, when the proposed VSSI+CDDC decoupling strategy is adopted under the same circumstances, the system can response to the active power reference step stably as shown in Fig. 12. And the reactive power almost maintains unchanged during the active power step response. It demonstrates the proposed strategy can achieve power decoupling effectively and benefit the system stability.

B. COMPARATIVE EXPERIMENTS OF P-DECOUPLING PERFORMANCE
The reactive power reference is set properly to make output reactive power of VSG produce a step ascent of 4kVar at t 0 and the responses under circumstances of the four different control strategies are shown in Fig. 13 and zoomed in as shown in Fig. 14.
In Fig. 13. (a) and Fig. 14. (a), under circumstance of basic VSG strategy without any decoupling method, obvious shock and oscillatory are shown in active power, which does not agree with the pre-designed dynamic characteristics. The reason is that the change of reactive power reference transmits to the active power through power coupling channels. Then the adjustment of active power loop in turn affect the adjustment of reactive power, which leads to slower response of reactive power as shown in Fig. 13. (b) and Fig. 14. (b).
Under circumstance of TVI, smaller virtual resistance is set to weaken the power coupling caused by large line impedance ratio. The fluctuation of frequency is smaller than that without any decoupling methods as shown in Fig. 13. (c) and Fig. 14. (c). It indicates that the low frequency component of the active power fluctuation caused by the reactive step decreases, which means TVI indeed weakens the power coupling lightly. However, smaller resistance leads to weaker damping effect at the same time, which makes the high frequency oscillation more serious as shown in Fig. 13. That is in accordance with the analysis in Section IV.
When only the proposed VSSI is adopted, the virtual resistance can be set as 0, which weakens the coupling caused by large impedance ratio effectively. Thanks to the unique characteristic of VSSI, damping of the system is still enough with zero virtual resistance, so oscillation is restrained effectively. So the shock and oscillation in active power is restrained obviously as shown in Fig. 13. (a) and Fig. 14. (a), and the reactive power reaches steady-state value rapidly without oscillation Fig. 13. (b) and Fig. 14. (b). However, due to the coupling caused by power angle that is not complemented, 0.9kW shock is still generated in active power (see Fig. 14. (a)) and frequency fluctuation is caused as a result (see Fig. 14. (c)). Nevertheless, no oscillation or shock should be observed in the ideal response of active power during the whole process.
When the proposed VSSI + CDDC strategy is added, the ideal response is realized. As shown in Fig. 15, the feedforward decoupling currents are adjusted rapidly at the moment that reactive power is adjusted, so the phase and amplitude of output voltage are changed at the same time to maintain unchanged active power and realize the expected reactive power. As shown in Fig. 13, active power has been shielded from the effects of reactive power, and reactive power reaches the steady-state value rapidly, which indicates that the proposed VSSI+CDDC weakens the coupling caused by both large impedance ratio and power angle effectively.

VI. CONCLUSION
Power coupling issue of VSG can produce output power error, amplify power oscillation and influence the system stability. In this paper, the power coupling characteristics of VSG have been analysed, and an enhanced power decoupling method by using virtual steady-state synchronous impedance and current dynamic decoupling compensation has been proposed. This method can eliminate the coupling effect caused by the high line impedance ratio and nonzero power angle at the same time. In the meanwhile, the output impedance and its characteristics analysis of improved VSG strategy are presented. Then, the state space models of traditional VSG and improved VSG strategy are built. Through comparative analysis, it is proved that the proposed enhanced decoupling method can mitigate the power coupling more effectively. In addition, the stability of VSG system is enhanced. Finally, the experimental results demonstrate that the proposed method can eliminate the steady-state error of output power, alleviate the power oscillation, and improve the dynamic and steady-state responses of active power and reactive power. This method can also be transplanted to the other droop-based control strategies.

APPENDIX
See appendix equation as shown at the bottom of previous page.