Abstract
In this paper, the dynamic coupling between the wind turbine rotor speed recovery (WTRSR) and inertial response of the conventional virtual synchronous generator (VSG) controlled wind farms (WFs) is analyzed. Three distinguishing features are revealed. Firstly, the inertial response characteristics of VSG controlled WFs (VSG-WFs) are impaired by the dynamic coupling. Secondly, when the influence of WTRSR is dominant, the inertial response characteristics of VSG-WFs are even worse than the condition under which WFs do not participate in the response of grid frequency. Thirdly, this phenomenon cannot be eliminated by only enlarging the inertia parameter of VSG-WFs, because the influence of WTRSR would also increase with the enhancement of inertial response. A decoupling scheme to eliminate the negative influence is then proposed in this paper. By starting the WTRSR process after inertial response period, the dynamic coupling is eliminated and the inertial response characteristics of WFs are improved. Finally, the effectiveness of the analysis and the proposed scheme are verified by simulation results.
WITH the increase of wind power penetration in the power grid, the mechanical inertia of the entire system reduces, which results in an increasing rate of change of frequency (RoCoF) and a decrease of frequency nadir during the frequency events [
The specific grid code requirements for inertial response from wind power vary according to different PSOs. In the case of a significant frequency deviation, wind turbines (WTs) are required to provide an active power response equivalent to that of a synchronous generator (SG) with an inertial constant of 3.5 s for a period of 10 s in Hydro Quebec [
To obtain inertial response from wind power, both the energy source and the control scheme should be considered [
For the control scheme, there are mainly two categories of methods in the literature. One aims to release a certain amount of energy to the power grid during frequency response [
The previous studies have pointed out the phenomenon that the inertial response characteristics of WT are impaired by the dynamic of maximum power point tracking (MPPT) controller [
According to the analysis in this paper, the dynamic coupling has three distinctive characteristics. Firstly, due to this dynamic coupling, the inertial response characteristics for VSG controlled WFs (VSG-WFs) are always impaired. Secondly, when the influence of WTRSR is dominant, VSG-WFs are harmful to the grid frequency response. Thirdly, this phenomenon cannot be eliminated by only enlarging the inertia parameter of VSG-WFs with the enhancement of inertial response, and the influence of WTRSR also increases. A decoupling scheme to eliminate the negative influence is then proposed in this paper. The dynamic coupling is eliminated by starting the WTRSR process after inertial response and the inertial response characteristics for WFs would also be improved.
In this paper, the analysis and verification are based on the permanent magnet SG (PMSG) based WFs for its increasing popularity [
The typical frequency response processes of the conventional SG-based power grid with frequency drop includes the following two stages as demonstrated in

Fig. 1 Typical processes of frequency response.
1) Inertial response: when power disturbance occurs, SG would firstly respond automatically by changing its rotor speed, which is called inertial response with typical lasting time up to 2-9 s [
2) Primary frequency regulation (PFR): PFR is implemented by the governor of SG with typical response time of several seconds. PFR can last from more than 10 s to several minutes based on the amount of reserved steam/water to provide additional continuous power.

Fig. 2 Equivalent model of power grid with WFs.
The WFs are simply represented by a PMSG-based wind energy conversion system (WECS) for the study of frequency response. SG is used to emulate the power grid with reduced mechanical inertia. SG participates in both inertial response and PFR processes while WFs only participate in the inertial response. The load characteristics are simulated by two local loads L1 and L2. The VSG scheme is achieved by the grid-side converter (GSC). The DC bus voltage Vdc is controlled by the machine-side converter (MSC). Generally, the DC bus voltage control and the MPPT control are achieved by two different converters [
Because of the widely practical application, the power speed feedback (PSF) MPPT algorithm is studied in this paper [

Fig. 3 Rotation speed characteristics of WT.
The active power control scheme of PMSG-based VSG-WFs can be expressed as follows.
(1) |
(2) |
(3) |
where Kmppt is the coefficient related to WT characteristics; is the WT rotor speed; Pref, Pe, and are the input power, output power and virtual rotor frequency of VSG, respectively; is the frequency at PCC; and Hvsg and Dvsg are the virtual inertia constant and damping coefficient of VSG, respectively.
The reactive power control scheme of PMSG-based VSG-WFs is given as follows [
(4) |
(5) |
(6) |
where Vs is the reference voltage value; Dq is the voltage droop constant; Qe is the practical value of reactive power; KQ is the integrator gain; Qref is the reference value of reactive power; and Vvsg is the terminal voltage of VSG. Because this paper is focused on frequency response, Qref is assumed to be 0.
According to the power conservation of WT, we can obtain:
(7) |
where is the captured wind power of WT, and according to
(8) |
Taking the wind speed equals V1 as an example. The stable operation point is point O in
(9) |
By substituting (8) and (9) into (7), the power released from KE of WT rotor PWTKE can be expressed as:
(10) |
According to (10), the inertial response of VSG-WFs is always impaired by WTRSR because PWTKE is negatively correlated with PWTRSR.
Specifically, PWTRSR increases with the release of KE of WT rotor. Therefore, at the beginning of the frequency drop event, the release of KE of WT rotor is small and the influence of PWTRSR is not prominent. With the continuation of the frequency response process, the release of KE of WT rotor increases gradually and the influence of PWTRSR becomes greater. When PIR is smaller than PWTRSR, WT absorbs energy from the power grid. Under this condition, the influence of WTRSR is dominant, and the inertial response characteristics of VSG-WFs are even worse than the condition where WFs do not participate in frequency response.
Particularly, this phenomenon cannot be eliminated by only enlarging the inertia parameter of VSG-WFs. With the enhancement of inertial response, more KE of WT rotor is released and in turn, the influence of WTRSR increases.
When the grid frequency increases, similar coupling and phenomenon can be observed.
The model shown in

Fig. 4 Operation curves under different conditions. (a) Frequency response curves. (b) Output active power. (c) RoCoF curves. (d) Grid frequency comparison of different Hvsg.
1) WFs are controlled by the original vector control (WFs-VC). In this application, the VSG controller in
2) WFs are replaced by an SG with the same capacity. This SG is different from the one which simulates the power grid with reduced mechanical inertia (noted as SGgrid) and participates in inertial response only.
In
According to these simulation results, the original VSG-WFs can improve RoCoF, but worsen the frequency nadir. Besides, as the results shown in

Fig. 5 Virtual rotor frequency of VSG under different conditions.
Therefore, the weakening of inertial response by WTRSR can not be offset by enhancing the effect of inertial response and a scheme to decouple WTRSR, and the inertial response in VSG-WFs should be proposed.
Ⅲ Decoupling Scheme for VSG-WFs to Participate in Inertial Response

Fig. 6 Proposed scheme for VSG applied in WFs.

Fig. 7 APRC of proposed scheme when grid frequency decreases.
In order to ensure the normal operation of WT, a minimum acceptable WT rotor speed curve is defined (F→B curve in
(11) |
The flowchart of the proposed scheme is shown in

Fig. 8 Flowchart of proposed scheme.
In this stage, the original VSG scheme is employed to control the WT. The wind speed is assumed to be V1. Point O is the corresponding optimal operation point and the steady-state operation point of VSG-WFs. The corresponding optimal power is P0 and the WT rotor speed is .
When the grid frequency drop event occurs, VSG-WFs start the inertial response automatically. If the power imbalance is small, the influence of WTRSR is not significant and the WFs can still operate with the original VSG scheme. If the disturbance is large enough, the influence of WTRSR on inertial response cannot be ignored any more, and then the dynamic of WTRSR should be decoupled with that of inertial response. Therefore, the flag to leave this stage can be chosen as (Flag 1).
When Flag 1 is obtained, the decoupling scheme is activated. It will disable the MPPT operation during inertial response stage and Pref is maintained at P0.
After inertial response period, WTRSR should be realized. Based on whether the WT rotor speed is reduced to the minimum value during inertia response stage, the operation can be divided into two specific conditions:
1) Stage 2(a) represents the minimum rotor speed during the operation, F→G curve: according to (11), when the WT rotor speed is decreased to be smaller than the minimum acceptable WT rotor speed , is obtained. Thereafter, the grid frequency is supported by SGs in the power grid and the operation goal of WT is to maintain the stable operation without large power disturbance to the power grid. In the proposed scheme, this goal is achieved by setting the reference of the VSG controller according to the minimum rotor speed F→B curve. And Pref is obtained according to (11). Because the reference of the proposed scheme is the output power, the small-signal stability caused by the mismatch between the expected output power and the practical output power [
2) Stage 2(b) represents the maximum available power operation, A→D curve: if the KE of WT rotor is enough, the WT rotor speed will not reach the minimum value when the inertial response finishes. After PFR of the grid is built, the power imbalance is mainly undertaken by the grid. WFs gradually operate into its steady state. Therefore, the flag of this stage can be chosen as (Flag 2(b)). To make sure that the judgment of operation stage is correct, the duration of Flag 2(b) should last at least Tdz2.
Assume that the operation point is point A in
(12) |
where A is the rotor speed of point A; and is the WT cut in rotor speed (point B' in

Fig. 9 APRC of proposed scheme when grid frequency increases.

Fig. 10 Operation stage signals of proposed scheme. (a) During frequency response. (b) During MPPT operation.
The operation after Stage 2 for the two conditions is similar and Stage 2(b) is taken as an example to illustrate the basic principles.
When the grid frequency is stable, WFs operate stably and the input and output power of VSG are nearly the same. Then (Flag 3) is obtained. To make sure that the judgment of operation stage is correct, the duration of Flag 3 is required to be at least Tdz3. Then the WT rotor speed can start to recover.
In order to achieve WTRSR smoothly, Pref is controlled to equal P which is a little bit smaller than PD, e.g., 99%×PD. Then the WT rotor speed and the corresponding MPPT value increase. When (Flag 0) is obtained, WFs can switch to VSG-WFs operation automatically.
For practical operation, the grid frequency increase should be considered. The corresponding decoupling scheme is similar to the above situation of grid frequency decrease. The operation curves are shown in
The operation stages corresponding to this condition are described as follows. WFs originally operate in VSG-WFs operation stage (Stage 0, O→B curve). When Flag 1 is satisfied, WFs operate in inertial response stage, and the MPPT operation is disabled (Stage 1, O→A1 curve). The WT rotor speed increases until the value reaches to the maximum WT rotor speed, then WFs operate in approximately optimal power operation stage (Stage 2, A1→D1 curve). When Flag 3 is satisfied, WFs operate in WTRSR stage (Stage 3, curve D1K1→K1O). The WT rotor speed decreases until the value reaches to the optimal rotor speed. Then the WFs operate in VSG-WF operation stage again (Stage 0, O→B curve). The operation path is O→A1→D1→K1→O.
is the parameter to define the minimum or maximum WT rotor speed curve. Because the design of the two conditions is similar, we take the condition for the curve of the minimum WT rotor speed as an example. In fact, is determined by the requirements for the stored energy for inertial response and the captured wind power.
The stored energy for inertial response is the KE of WT rotor between the MPPT point and the minimum rotor speed point ΔEKE. The expression is given as:
(13) |
where Jwt is the inertia of the wind turbine; and are the nominal WT rotor speed and the minimum WT rotor speed, respectively.
The stored KE of WT rotor is released to the power grid by inertial response of VSG, and the maximum energy released by the VSG ΔEIR is expressed as:
(14) |
where Jwt is the virtual inertia of the VSG; is the nominal grid angular frequency; and is the minimum grid angular frequency defined by grid code.
The energy released by the VSG should be smaller than the stored energy. Then according to (13) and (14), the following expression is obtained:
(15) |
Because the rated power of WT and VSG is the same, the expression for inertia constant is also obtained:
(16) |
The relationship between the WT captured wind power and the WT rotor speed is given as follows [
(17) |
(18) |
(19) |
where Cp is the power coefficient; is the tip-speed ratio; and and are the coefficients related to the characteristics of WT. For practical operation, the deviation of the WT captured wind power from the optimal power is required to be as small as possible.
The inertia constant of WT is 4.32 s [
To estimate the influence of WTRSR to inertial response, the equivalent inertia constant and damping coefficient are deduced.
As mentioned above, the coupling is introduced by the operation of MPPT controller. Therefore, the equivalent parameters are obtained by comparing with the condition where MPPT controller is disabled in the inertial response stage. Under this condition, the input power of VSG equals to the optimal power P0 according to
(20) |
By comparing (13) with (2), the equivalent parameters Heq and Deq can be obtained as:
(21) |
where is the coefficient between the equivalent parameters and their corresponding setting parameters.
The smallest acceptable equivalent inertia is marked as . When , the influence of WTRSR on inertial response can be ignored. Otherwise, the decoupling scheme proposed in this paper should be activated. According to (1), (3) and (21), the minimum Heq is obtained when the WT rotor speed reaches the minimum acceptable value μωwt0. Therefore, the decoupling scheme would be activated when and the corresponding relationship is:
(22) |
Considering , Pdz1 is obtained as:
(23) |
When = 0.9 and , the value of Pdz1 is .
5) Design of , , ,
Pdz2 and Tdz2 are parameters used to estimate the start of PFR of SG in the power grid. In this stage, the disturbance of the power grid is mainly undertaken by SG, and PIR of WT is small. Therefore, the value of Pdz2 should be small, e.g., . Tdz2 is the period of Flag 2(b). To make sure the judgment of the operation stage is correct, the larger Tdz2 is the better. Considering the regulation time of PFR, Tdz2 is recommended to be no more than 1 s. Pdz3 and Tdz3 are parameters used to estimate that the grid frequency is stable. The power difference between Pref and Pe in this stage is nearly equal to 0. Therefore, the Pdz3 value should be very small, e.g., . Tdz3 is the period of Flag 3. To make sure the judgment of the operation stage is correct, the larger Tdz3 is better. Because the next stage is the WTRSR stage, a shorter Tdz3 means that WT can operate in MPPT mode more quickly. Then, more power production can be obtained. In this paper, Tdz3 is also recommended to be no more than 1 s.
The theoretical analysis and the proposed scheme are verified based on MATLAB 2014a/Simulink platform. The model study has already shown in
PL1 and PL2 are set to be 1.63 p.u. and 0.2 p.u., respectively. The wind speed is 9 m/s. The load L2 is switched on when t = 5 s. The effectiveness of the judgment of the stage signals is verified in

Fig. 11 Results for factors considered in frequency response. (a) Grid frequency response. (b) RoCoF curves.

Fig. 12 WT operation curves under different conditions. (a) Output active power. (b) WT rotor speed curves.
The frequency nadir improvement of the proposed scheme is given as:
(24) |
(25) |
where and are the maximum grid frequeny drop of the original VSG scheme and the proposed scheme, respectively. The maximum grid frequeny drop is calculated according to (25). and are defined according to

Fig.13 Frequency nadir improvement of proposed scheme under different wind speeds.
PL1 and PL2 are set as 1.63 p.u. and 0.13 p.u., respectively. The initial wind speed is 9 m/s. L2 is switched on when . To emulate the condition when KE of WT rotor is insufficient and the WT rotor speed is reduced to the minimum value in inertial response stage, the wind speed is decreased to 8 m/s when t = 5 s and back to 9 m/s when t = 6 s.

Fig. 14 WT operation curves in this case. (a) Output active power. (b) Grid frequency response. (c) WT rotor speed.
The benchmark IEEE 4-machine 2-area system for power system study is carried out to verify the effectiveness of the proposed scheme. The simulation model is shown in

Fig. 15 Simulation model of IEEE 4-machine 2-area system.
The parameters of the IEEE 4-machine 2-area system can be found in [

Fig. 16 Simulation results in IEEE 4-machine 2-area system. (a) Frequency drop event occurs. (b) Frequency increase event occurs.
According to the results shown in
In this paper, a decoupling scheme is proposed to eliminate the coupling between WTRSR and inertial response in conventional VSG-WFs. By adopting the proposed scheme, the negative influence of WTRSR on the inertial response characteristic of VSG-WFs is eliminated. The inertial response characteristics of WFs are improved. The analysis on the coupling and the proposed scheme is verified by the simulation results. In future study, the proposed scheme can be applied to doubly-fed induction generator (DFIG) based WFs and inertial emulation schemes of type. More work should be done for the application under the conditions of unbalanced grid voltage.
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