The DFIG captures mechanical energy through the wind turbine, which spins the rotor and then converts the mechanical energy into electrical energy. The captured mechanical power P_m can be expressed as: (1)Pm=12ρAvw3Cp(λ,β)=12ρπR2vw3Cp(λ,β)where, ρ is the air density; v_w is the wind velocity; A, R, λ, β are the unit swept area, impeller radius, blade tip speed ratio, and pitch angle, respectively; C_p(λ,β) is the wind energy utilisation coefficient, which is a non-linear function consisting of λ and β.

Fig. 1 shows the relation characteristic curve of the C_p-λ-β and its expression can be described as [21]:

(2){Cp(λ,β)=0.645{116λi−0.4β−6e21λi+0.00912λ}λ=ωrRvwλi=1λ+0.08(β+2.5)−0.0351+(β+2.5)3where, λ_i is the intermediate variable; ω_r is the rotor speed of the DFIG.

Under different wind speeds, since R is a constant, the maximum wind energy capture of WTGs can be achieved only if ω_r and v_w are always maintained at the best ratio, that is, the optimal tip speed ratio.

The MPPT curve of DFIG can be represented by Eq. (3): (3)PMPPT=12ρπR2(ωrRλopt)3CP,max=koptωr3where, λ_opt is the optimal tip speed ratio of the wind turbine; k_opt is the characteristic coefficient of the MPPT curve; C_P,max is the maximum wind energy utilisation coefficient of the wind turbine, at this time β = 0°, λ = λ_opt.

The DFIG is grid-connected using a doubly-fed converter to achieve a flexible connection to the grid. Although DFIGs can deliver power to the grid, they cannot provide inertial support to the system through rotating equipment, as with conventional thermal turbines. To enhance the inertia of the power system, the flexibility of the DFIG’s control is utilised to release the rotor kinetic energy using the FFRC strategy to give it FM capability. FFRC strategy consists of virtual inertia control with a frequency rate of change as input and droop control with frequency deviation as input. The power system containing DFIG with FFRC strategy is shown in Fig. 2.

In Fig. 2, ΔE_DFIG, J_DFIG-vir, P_m-D, P_e, P_DFIG and ΔP_DFIG-vir are rotor kinetic energy variation, virtual moment of inertia, captured mechanical power, electromagnetic power, output power, and FFRC strategy additional active power of the DFIG during the inertial response, respectively. P_m-G, P_G, ω_m, and J_G are the mechanical power, electromagnetic power, mechanical angular velocity and moment of inertia of the SG, respectively.

The frequency dynamic response equation of DFIG is shown in Eq. (4): (4)ΔPDFIG−vir=−(2HDFIG−virdfdt+DDFIG−virΔf)where, H_DFIG-vir and D_DFIG-vir are the virtual inertia time constant and virtual damping coefficient of the DFIG, respectively.

The simplified model of the power system with DFIG is shown in Fig. 3. The system’s generation part mainly consists of thermal units and DFIGs with FFRC strategy; the power consumption part is the load.

Where, K_m is the mechanical power gain coefficient; F_H is the fraction of the total power of the high-pressure turbine; T_R is the turbine reheating time constant; K is the static modulation factor of the SG; H_G-D and D_G-D are the inertia time constant and damping constant of the system; ΔP_L is the load power variation of the system; ΔP_G is the output power variation of thermal power units.

The dynamic response equation of the system frequency can be expressed as: (5)2HG−Ddfdt=ΔPG+ΔPDFIG−vir−ΔPL−DG−DΔf

Eq. (6) can be obtained from Eqs. (4) and (5): (6)2(HG−D+HDFIG−vir)dfdt=ΔPG−ΔPL−(DG−D+DDFIG−vir)Δf

The mathematical expressions for the maximum frequency rate of change (RoCoF_max) and the maximum frequency deviation (Δf_max1) of the grid-connected WTGs system with FFRC strategy after disturbance are shown below, and the specific derivation process is detailed in the literature [22,23]. (7)RoCoFmax=dfdt|t=0=−ΔPL2(HG−D+HDFIG−vir) (8)Δfmax1=KΔPL[1+1−ζ2αe−ζωntnadir{1}](DG−D+DDFIG−vir)(K+1)where, ζ is the damping ratio; α is the coefficient resulting from the model derivation process; ω_n is the natural oscillation frequency; and t_nadir1 is the time at which the frequency minimum occurs.

The RoCoF_max and Δf_max1 of the power system after disturbance are essential indicators of the frequency dynamic response. From Eqs. (7) and (8), it can be seen that the RoCoF_max and Δf_max1 of the system are positively correlated with the load disturbance presentation degree. The equivalent inertia time constant and damping coefficient of the system play a vital role in the frequency dynamic response of the system under a certain load disturbance. Fig. 4 shows the curve of the system frequency at different H_DFIG-vir and D_DFIG-vir after the step disturbance. K_d and K_p are the virtual inertia and droop coefficients of FFRC, which are described in the next chapter. In summary, wind power participation in the system FM can be equated to increasing the system’s equivalent inertia and damping.

The frequency support stage is divided into 2 main processes, corresponding to the point A and the curve A-B-C in Fig. 5.

A: The system is steady, and the DFIG operates at point A of the MPPT curve. At this point, the DFIG wind energy utilisation is maximum, and the output power is P₀. (9)P0=PMPPT(ωr)|ωr=ω0=koptω03

A→B→C: FFRC strategy action when the system frequency is reduced by a disturbance or load increase. The DFIG with FFRC can simulate the SG’s inertia support and primary FM characteristics in this process, and its output electromagnetic power moves along the curve A-B-C.

As the DFIG releases rotor kinetic energy, the rotor speed decreases and the turbine captured power is shifted away from the maximum power output point A. At the same time, the outer loop power reference value P_ref of the rotor-side inverter is changed.

The reference power input to the rotor side inverter is expressed as: (10)Pref=PMPPT+ΔPDFIG−vir (11)ΔPDFIG−vir=ΔPd+ΔPp=−KpΔf−Kddfdtwhere, K_d and K_p are the virtual inertia and droop coefficients of FFRC, respectively.

When the electromagnetic power of the DFIG in Fig. 5 runs along the curve A-B-C to point B, meaning that the rotor speed decreases from ω(t₀) to ω(t_B), the captured power of the WTG moves from point A along the mechanical power curve to point A^* at constant wind speed. The corresponding capture power variation ΔP_cap is expressed as: (12)ΔPcap=PA−PA∗=12ρAvw3[CP(λA,β)−CP(λA∗,β)]where, λ_A and λ_A^* are the tip speed ratios corresponding to points A and A^* under the wind speed v_w, respectively; C_P(λ_A,β) and C_P(λ_A*,β) are the corresponding wind energy utilisation coefficients of A and A^* points, respectively.

The DFIG’s governor impedes the active FM of the WTG, and the rotor speed controller output reference power deviates from the original maximum power tracking point, which is a drop from point A in Fig. 5 along the MPPT curve to point B^*. The difference ΔP_sup between the captured power P_A^* and the reference power P_B^* of the DFIG can be expressed as: (13)ΔPsup=P0−PB∗−ΔPcap=kopt[ω(t0)3−ω(tB)3]−ΔPcap

At a steady wind speed with a small range of rotor speed variation, the captured power at points A^* and B^* is approximately equal, i.e., ΔP_cap ≈ 0. Eq. (13) can be simplified as: (14)ΔPsup≈kopt[ω(t0)3−ω(tB)3]=koptΔωt3

At this point, the reference power of the control power outer loop of the rotor side inverter can be expressed as: (15)Pref,B=P0+ΔPDFIG−vir−ΔPsup

From Eqs. (14) and (15), the DFIG responds to the frequency change by releasing rotor kinetic energy and simultaneously inputs additional power to the system. The reference output power of the DFIG governor gradually deviates from the set value with a cubic exponential function. It reduces the rotor-side inverter power reference value and inhibits the FM capability of the DFIG. Because ΔP_sup acts as a suppressor of P_ref, ΔP_sup is called OPSA.

When the frequency support stage is over, if the rotor speed is not restored and the rotor kinetic energy is not lifted in time, it will not only cause the DFIG to deviate from the optimal power point, thus reducing the efficiency of wind energy utilisation, but may even lead to the rotor stalling, resulting in the DFIG going off-grid and severe system frequency fluctuations.

This paper’s judgement condition for entering the speed recovery stage is set as dω_r/dt > 0 or ω_r ≤ 0.67 p.u.

The rotor kinetic energy recovery stage is mainly divided into 2 processes, corresponding to the curves C-D-E and E-A in Fig. 5:

C→D→E: The DFIG exits FM when the electromagnetic output power from the DFIG is running to point C. The rotor speed recovery is accelerated by reducing the electromagnetic power to point D and maintaining constant power operation to point E.

E→A: When the rotor speed is accelerated to point E at constant output power, it recovers to point A along the MPPT curve.

After the DFIG exits the FM, only the SG participates in the primary FM, and at this time, the wind turbine has to absorb energy from the grid, which exacerbates the system power imbalance. The unbalanced power ΔP_U(t_C) in the system is: (16)ΔPU(tC)=(PL0+ΔPL)−PG(tC)−[PDFIG(tC)−ΔPde]where, P_L0 is the initial value of load.

At this time, the rotor equation of motion for a synchronous unit can be expressed as: (17)fdfdt=12HG−D[ΔPG(tC)−ΔPU(tC)] (18)TRdΔPG(tC)dt+ΔPG(tC)=−1KΔf

By substituting Eq. (18) into Eq. (17), the frequency variation of the rotor speed recovery stage can be obtained as: (19)2HG−DTRf′′+2HG−Df′+1Kf=1Kf(tC)−ΔPU(tC)where, f ′ and f ″ are the first and second derivatives of the system frequency, respectively; f(t_C) is the system frequency at t_C. (20){f|t=tC=f(tC)f′|t=tC=−ΔPU(tC)2HG−D

By substituting Eq. (20) into Eq. (19), the time-domain expression of system frequency during speed recovery is: (21)Δf(t)=ΔPU(tC)2ω2HG−Deα(t−tC)cos⁡[ω2(t−tC)+θ]+[f(tC)−KΔPUtC]where, the intermediate variables θ, γ and ω₂ are expressed as [24]: (22){θ=arccos⁡(Kω2HG−D)γ=arctan⁡(−2TRω2HG−D)ω2=1KTRHG−D−14TR2

By further derivation of Eq. (22), the maximum deviation of the frequency second drop Δf_max2 is expressed as: (23)Δfmax2=f(tC)−ΔPU(tC)2ω2HG−Dcos⁡(π/2−γ)eα(π/2−θ−γ)ω2−[f(tC)−KΔPU(tC)]

As shown in Eq. (23), the severity of SFD is affected by t_C and ΔP_U(t_C). ΔP_U(t_C) is closely related to ΔP_de. Therefore, the starting rotor speed recovery strategy should be reasonably selected at the starting moment and the size of the derating power.

Currently, many scholars have improved the FFRC strategy of DFIG. They improved the frequency response characteristics of the WTG when it is involved in FM, but none of them analysed and solved the OPSA generated when DFIG applies the FFRC strategy. In addition, few studies have combined the improvement of the SFD phenomenon in the rotor kinetic energy recovery process with the enhancement of rotor speed recovery performance. In this paper, we first propose using FLC to weaken the OPSA in the frequency support stage. Then, an ES output power control strategy coupled with the rotor speed is proposed to further compensate for the power deficit generated during the speed recovery stage of the DFIG, thus eliminating the SFD phenomenon. Finally, the control strategy flow of the combined wind and storage FM is proposed based on the timing logic of the DFIG and the ES system cooperating at different stages in the frequency response process.

The analysis in Chapter 3 shows that the FFRC strategy of the DFIG provides inertia to the system and performs primary FM through rotor kinetic energy release, whereas the OPSA generated during the rotor speed reduction weakens the effect of the control to a certain extent. In this section, a variable coefficient FFRC based on fuzzy logic optimisation is proposed by improving on the conventional FFRC. The structural block diagram of the control strategy proposed in this paper is shown in Fig. 7.

In Fig. 7, ω_MPPT and P_MPPT are the rotor speed and output power of DFIG in MPPT mode, respectively; K_d,FLC, K_p,FLC and ΔP_d, ΔP_p are the control parameters and the incremental electromagnetic power of the response frequency rate of change, frequency deviation when the DFIG is involved in FM, respectively; P₁, P₂ and P₃ correspond to the reference power of the DFIG in the curves A-B-C, D-E and E-A of Fig. 5, respectively; f, f_N and Δf are the actual frequency, rated frequency, and frequency deviation of the system, respectively; P_max and P_min are the maximum and minimum limits of DFIG output power, respectively; P_ref is the active reference value output to the control side of the DFIG converter.

In this paper, we perform fuzzy inference on the virtual inertia coefficient (K_d) and droop coefficient (K_p) of the FFRC. The FLC constructed in this paper takes the system frequency change rate (df/dt) and the system frequency deviation (Δf) as inputs, and adjusts the coefficients of the FFRC in real-time according to the detected frequency changes. The input quantities of df/dt take values in the range of −0.1~0.1 Hz/s, and Δf takes values in the range of −0.3~0 Hz. The range of values of df/dt is divided into seven fuzzy intervals {NH, NC, NT, NP, PT, PC, PH} (Letters indicate fuzzy intervals, which will not be discussed in this paper), and the range of values of Δf is divided into seven fuzzy intervals {ET, CT, T, C, H, CH, EH}. The divided intervals of df/dt and Δf together determine the frequency state of the system. The value of K_d in the output ranges is 0~0.8, and the value of K_p ranges is −0.8~0.8. The range of K_d is divided into seven fuzzy intervals {ET, CT, T, C, H, CH, EH}, and the range of K_p is divided into seven fuzzy intervals {NH, NC, NT, NP, PT, PC, PH}. Real-time variation of FFRC coefficients achieved by interval division of K_d and K_P. FLC is calculated using the trimf affiliation function with Mamdani fuzzy system inference.

The fuzzy rule designed according to the frequency response process when the system load increases is: At the beginning of the system frequency drop, df/dt is significant, and Δf changes from small to large. In this case, a larger K_d should be output to reduce the df/dt, and a smaller K_p should be output to avoid excessive release of rotor kinetic energy at the beginning of the frequency drop, which would cause the rotor speed to drop too quickly and produce a large OPSA. As the frequency drop gradually approaches its nadir, df/dt is small, and Δf is large. At this point, the FLC should output smaller K_d and larger K_p to raise the frequency nadir. When the frequency recovers, df/dt becomes positive and Δf gradually decreases. At this time, the WTG can appropriately reduce the active power output to promote the rotor speed recovery. The table of fuzzy logic rules and the figure of the FLC affiliation function are shown in Tables 1, 2 and Fig. 8.

The output K_d,FLC and K_p,FLC results after editing according to the rules of Tables 1 and 2 are shown in Fig. 9.

When the system load increases, the system frequency fluctuates, and the FFRC strategy of DFIG proposed in this paper starts to respond, the reference value of the outer-loop power of the rotor-side inverter at point B shown in Fig. 5 becomes: (24)Pref=P0+ΔPDFIG−vir−ΔPsup=P0+(−Kp,FLCΔf−Kd,FLCdfdt)−koptΔωt3

Fig. 9 shows that K_d,FLC tends to decrease gradually and K_p,FLC tends to increase and then decrease. Combined with Eq. (24), it can be seen that the rotor speed decreases less, and ΔP_sup is small in the pre-inertial support. At this time, the larger K_d,FLC can effectively solve the problem of the large df/dt. In the middle and late periods of inertia support, the rotor speed changes greatly, and the output power is strongly inhibited. In this case, a large K_p,FLC multiplied by a large Δf to increase the additional power can eliminate the suppression effect and thus raise the frequency nadir. During speed recovery, K_d,FLC gradually decreases to zero, and K_p,FLC gradually decreases to a negative value. At this time, the rotor absorbs energy from the grid, speeding up the rotor speed recovery.

Chapter 3 analyses that when the DFIG with conventional FFRC strategy enters the rotor kinetic energy recovery stage, it no longer provides power to the system and absorbs energy from the grid. This causes an active power imbalance in the system, which leads to the SFD phenomenon. ES has a fast and flexible power control capability, which can eliminate the SFD phenomenon through storage-assisted FM and enable the rotor speed to be quickly recovered to the initial state. An ES output power control strategy coupled with the rotor speed, as shown in Fig. 10, is proposed to enable the ES to make instantaneous power adjustments.

The active power output from the ES system is zero when the system is in a steady state. When the system is perturbed and the speed of the DFIG decreases and is greater than the minimum speed, the DFIG can respond to the frequency change by releasing rotor kinetic energy. At this time, the active power output of the ES system remains at zero value. At the end of the measured DFIG frequency support stage, the rotor speed begins to recover (dω_r/dt > 0). or when the rotor speed is lower than the minimum speed (ω_r ≤ 0.67 p.u.), the DFIG starts deriving power to recover the rotor kinetic energy. At this point, the ES switches to the power output mode to compensate for the unbalanced power due to the power deficit of the DFIG and to reduce the amplitude of the SFD. Its output power P_E1 is:

(25)PE1=PC−PD=ΔPdewhere, P_C and P_D are the electromagnetic power at points C and D in Fig. 5, respectively.

If the active power from storage is less than the actual active power deficit of the system, it is ineffective in improving the SFD; on the contrary, if the active power from storage is too large, it may lead to frequency overshooting. To let the ES reasonably output FM power, when the measured DFIG speed reaches point E in Fig. 5 and is recovered along the MPPT curve, the power output from the ES decreases smoothly with the increase of the rotor speed. The variable power P_Eva of the ES output power in this process is:

(26)PEva=[1−ωr−ω(tE)ω(t0)−ω(tE)]PE1=KEPE1where, ω_r, ω(t_E), ω(t₀) are the actual rotor speed of the DFIG and the rotor speeds at points E and A in Fig. 5, respectively; K_E is the ES power modulation factor.

The difference between the actual power P_Emeas of the ES feedback and the output power reference P_Eref in Fig. 10 is outputted by the PI controller. The PI control loop is used as an auxiliary control, and the output result ΔP_E superimposed on the P_Eva can slow down the magnitude of the stored power reduction. This allows the ES system to exit FM slowly, reducing power fluctuations to ensure smooth frequency recovery.

In summary, during the whole DFIG rotor speed recovery stage, the reference value of ES output power P_Eref is:

(27)PEref={PE1=PC−PDω(tC)<ωr≤ω(tE)PE2=PEva+ΔPEω(tE)<ωr≤ω(t0)where, ΔP_E is the output power of the PI control loop; ω(t_C) is the rotor speed of DFIG at point C in Fig. 5.

When the DFIG rotor speed returns to the initial value, ω_r = ω(t₀), the ES smoothes out the FM, and slower responding synchronous units take over from storage for subsequent power support.

The coordination between DFIG and ES can not only fully use the rotor kinetic energy to improve the frequency response process of the primary FM but also effectively solve the SFD problem and accelerate the rotor speed back to the value before the disturbance. The flow of the control strategy containing the wind-storage system is shown in Fig. 11.

The system operates steadily, and the DFIG operates at the maximum power output point. When the load changes and the system frequency fluctuation is detected beyond the dead zone and the DFIG rotor speed is not lower than the minimum speed of 0.67 p.u., the FLC outputs the appropriate coefficients of FFRC to increment the output power of DFIG and releases the rotor kinetic energy according to df/dt and Δf of the system frequency. The DFIG derates active power when it detects that the speed is beginning to recover or when the rotor speed is below 0.67 p.u. At the same time, it is determined whether the storage state of charge (SOC) is above the minimum limit. If the SOC exceeds the minimum value, the storage assists FM and provides power support to the system according to Eq. (25).

When the DFIG rotor speed rises to ω(t_E) in Fig. 5, it starts to recover to the initial value along the MPPT curve. The DFIG’s output power constantly rises at this stage according to the MPPT curve’s tendency. According to Eq. (26), the ES reduces the output power until it exits the FM to minimise the system’s overshooting phenomenon.

To verify the effectiveness of the wind-storage combined FM control strategy proposed in this paper, this chapter takes the IEEE 39-bus test system as an example and conducts real-time digital simulation verification based on the RTLAB OP5707 simulation platform. The RTLAB OP5707 simulation platform is shown in Fig. 12.

The system consists of 10 SGs (G01–G10), 2 aggregated wind farms (W01, W02) and 2 ES systems (E01, E02). The nominal parameters of each power generation equipment are shown in Table 3. The specific parameters of the DFIG and SG are shown in Table 4.

Initial conditions are balanced between load and generation. The system frequency is 50 Hz, the WTGs are running at maximum power tracking, the wind speed is set to a constant 8 m/s, and there is no wind abandonment. The penetration rate of WTGs is 10%, and the proportion of wind power is 9.13%. After 35 s of stable operation, the load of bus 16 step increases by 300 MW.

The changes in system frequency, the reference power, the actual power and the rotor speed of DFIG are analysed under DFIG without participating in FM (Case1), with additional conventional FFRC strategy (Case2), and with additional FFRC strategy combined with fuzzy prediction (Case3) proposed in this paper. To visualise the effect of ΔP_sup, no active power derating of the DFIG is performed when the rotor speed is recovered, and the rotor speed is only slowly recovered through the wind turbine’s intrinsic governor.

From Fig. 13a combined with Table 5 (Table 5 is at the end of this chapter), it can be seen that the use of FFRC strategy combined with fuzzy prediction proposed in this paper can enhance the system’s perturbation resistance and improve the frequency response characteristics of the DFIG. This can be illustrated by Fig. 13b: the governor reference power decreases with time when the FFRC strategy is used, and the OPSA becomes larger. In the 36th s, the additional reference power starts to decrease continuously, which causes the DFIG output power to drop too fast, greatly weakening the FM ability of the DFIG. The use of fuzzy logic control can enhance the DFIG additional reference power as the governor reference power of the WTG decreases towards its minimum value. This reduces the weakening effect of OPSA on the FM capability of DFIG and improves the DFIG primary FM effect. In Fig. 13c, the DFIG of Case3 eliminates the impact of OPSA and outputs the most energy to the grid in participating in FM, further proving the effectiveness of the improved FFRC proposed in this paper.

According to Fig. 13d and Table 5, it can be seen that the rotor speed recovery time (Δt_ω) of Case3 is longer, because the rotor speed of Case3 drops more. But the rate of recovery is the fastest. This is because, during the frequency recovery stage, the FLC output K_d,FLC gradually decreases to 0 and K_p,FLC gradually decreases to a negative value, which promotes the recovery of the rotation speed. It is worth noting that because no active power derating is performed on DFIG, Δt_ω of Case2 and Case3 is too long and cannot return to the initial value, which is not conducive to the system’s dealing with secondary disturbances.

When the rotor speed is recovered, the changes in system frequency, output power, and DFIG rotor speed are analysed under different ΔP_de for DFIG with the FFRC strategy. In turn, the effect curves of |Δf_max1| and Δt_ω under different ΔP_de are plotted. It is worth noting that in Fig. 14a–c, the dark blue line is the simulation result curve of DFIG not participating in FM. Therefore, ΔP_de = 0.

From Fig. 14 and Table 5, it can be seen that with the increase of ΔP_de, the degree of SFD increases, the speed of rotor recovery is accelerated, and the time for the frequency to reach a steady state (Δt_ss) is prolonged. A smaller ΔP_de results in a longer Δt_ω, which is not favourable for the DFIG to participate in the next FM in time. When ΔP_de takes a larger value of 0.12 p.u., the system takes 22.69 s to return to a steady state, and the second drop in the system frequency is already lower than the lowest value of the primary drop. Therefore, considering the rotor recovery speed, second frequency deviation, and other factors, the active power derating is set to 0.08 p.u. for the simulation conditions in this paper.

The changes in system frequency, the output power and the rotor speed of the DFIG, and the output power of ES are analysed under DFIG without participating in FM (Case*1), with additional FFRC strategy (Case*2), and with the adoption of the combined wind-storage FM control strategy (Case*3) proposed in this paper. It should be noted that ΔP_de is set to 0.08 p.u. for Case*2 in this section. To induce faster speed recovery, the ΔP_de of Case*3 is set to 0.12 p.u., increasing the difference between the mechanical and electromagnetic power of the DFIG. In Fig. 15d, the green dotted line is the SOC curve of ES.

Fig. 15, combined with Table 5, shows that using the wind-storage combined FM control strategy proposed in this paper improves the frequency nadir of the system after disturbance by 0.05 Hz compared to the conventional FFRC strategy of DFIG. This is because it eliminates the output power suppression problem of conventional FFRC and enhances the FM capability of DFIG. At the same time, it also weakens the SFD under the premise of ensuring rapid rotor speed recovery. It avoids the overshooting phenomenon by adjusting the output power of ES, so that the system frequency returns to the steady state 5.98 s earlier.

To further verify the superiority of the control strategy proposed in this paper, the FM performance of the proposed control method is tested in complex wind conditions with a simulation time of 100 s.

Under complex wind conditions, the output power of the wind farm has strong volatility. The system frequency fluctuation range is within ±0.1 Hz, which meets the requirement of safe and stable operation of system frequency. When t = 35 s, the load fluctuation causes the frequency drop event. When the DFIG does not participate in FM, the system frequency deteriorates rapidly, which poses a threat to the safe and stable operation of the system. It can be seen from Fig. 16 that although the lowest frequency of the system is improved under FFRC, the effect is not obvious. When the method proposed in this paper is used for FM, it has the best FM effect under complex wind conditions, effectively reduces the degree of frequency drop, and verifies that the method has strong robustness.