After the system with a high proportion of wind power encounters an active power disturbance, the system frequency support should be completed by the synchronous generator set and wind turbine. In order to improve the utilization rate of wind energy, wind farms usually do not use the deloading operation mode to reserve for primary frequency regulation. In this mode, the virtual inertial response will be the frequency active support function that wind power urgently needs. In the wind power grid-connected system, the synchronous generator and the wind turbine should jointly complete the inertial support, and the primary frequency modulation function is borne by the synchronous generator and the energy storage.

Taking a short-term frequency drop as an example, the dynamic response of wind turbines and synchronous generators participating in frequency adjustment is shown in Figure 1. In this figure, t ₀ is the frequency drop time, t _b is the primary frequency modulation action time, t _fm is the time when the frequency drops to the lowest value, and t _p is the end time of the primary frequency modulation.

At time t ₀, the load suddenly increases ΔP _d, and the system frequency drops sharply. The synchronous generator set and wind turbine need to respond quickly to the frequency change, and the system power demand is compensated by the fast active power support, that is, ΔP _e = ΔP _d.

At the t ₀∼t _fm stage, after the wind turbine starts the inertia support control, it will share the unbalanced power borne by the synchronous generator, thereby slowing down the system frequency drop speed. The common virtual inertia control of wind turbines adopts a differential link, and the power response is defined as Eq. (1): Δ P w = − K I × d f / d t , (1) where ΔP _w is the wind turbine inertial support power and K _I is the differential control coefficient.

As shown in Figure 1, during a frequency drop (df/dt <0), the power response of the virtual inertia controller is ΔP _w >0. At this stage, the synchronous generator and the wind turbine jointly maintain the inertia support power and satisfy the load demand ΔP _d. The wind turbine reduces the kinetic energy demand of the synchronous generator by releasing the kinetic energy.

At the t _fm ∼ t _p stage, during frequency recovery (df/dt >0), the power response of the virtual inertia controller is ΔP _w <0. At this stage, the wind turbine absorbs power from the system under virtual inertia control, and the wind turbine changes from releasing kinetic energy to absorbing kinetic energy, which increases the primary frequency regulation burden of the synchronous generator and slows down the frequency recovery speed.

Considering that the virtual inertia has the problem of grid-connected security, at present, GB/T19963.1–2021 “wind farm access power system technical regulations” have stipulated that the wind turbine is required to have the inertia support function after being connected to the system, but the additional controller must satisfy the following conditions: Δf×df/dt >0. The wind turbine should set the time t _fm as the end time of the virtual inertia control to satisfy the grid-connected requirements.

It is worth noting that it is necessary to detect the frequency signal at the grid-connected point of the wind turbine when determining the end t _fm of the inertial support. The differential signal has high-frequency noise in the field test. Combined with the actual test situation, it is difficult to determine whether Δf × df/dt is greater than zero. In addition, at the end of the moment of inertia support, the wind turbine has released kinetic energy, resulting in a decrease in speed. After restoring to the maximum power tracking control, the output power of the wind turbine will still be lower than the initial level before the frequency drop. This is because the wind turbine speed has dropped. Therefore, even if the inertial control can be terminated in time, the wind turbine will still absorb the power, accelerate the rotor, store kinetic energy, and complete the maximum power tracking target; however, this will not be conducive to frequency recovery during primary frequency modulation.

It can be seen from Figure 1 that during the active frequency support period, the virtual inertia control of the wind turbine cannot continuously provide effective active power support for the system. Combined with the inertia start-up conditions specified in the grid-connected standard, this paper defines the effective time of the inertia response as the frequency conversion extreme time t _fm; that is, after the system is disturbed, the frequency drops or increases from the initial value to the maximum frequency deviation.

Before adopting virtual inertia control, if the wind turbine can predict the extreme time of frequency conversion, it not only ensures the safe removal of the additional control and effectively avoids the misoperation caused by the large monitoring error of the frequency differential signal but also helps solve the problem of quantitative evaluation of virtual inertia, and then it provides a more reliable calculation method for the inertia demand under the system frequency safety.

The inertia of the wind power grid-connected system is composed of the inherent inertia of the synchronous generator and the virtual inertia of the wind turbine. The inertia time constant of the synchronous generator depends on the mechanical characteristics of the rotor, which can be expressed as Eq. (2) (Zhu et al., 2021) H g = E kg S g = J g ω e 2 2 p g 2 S g , (2) where J _g is the mechanical moment of inertia of the synchronous generator; ω _e is the synchronous speed; p _g is the number of rotor poles; E _kg is the rotor kinetic energy stored at the rated speed of the synchronous generator; and S _g is the rated capacity of the synchronous generator.

Referring to the definition of the inertia time constant of a synchronous generator, the virtual inertia time constant H _vir of a variable-speed wind turbine can be expressed as (Qi et al., 2022) H vir = J vir ω e 2 2 p w 2 S w = Δ ω r Δ ω e ω r 0 ω e H w , (3) where H _w is the inherent inertia time constant of the wind turbine; Δω _r is the change in the wind turbine speed; ω _r0 is the initial speed of the wind turbine before the inertial response; Δω _e is the synchronous speed variation; p _w is the number of wind turbine poles; S _w is the rated capacity of the wind turbine; and J _vir is the virtual moment of inertia of the wind turbine, which can be expressed as J vir = Δ ω r Δ ω e ω r 0 ω e J w , (4) where J _w is the inherent moment of inertia of the wind turbine.

According to the definition of the virtual inertia of the wind turbine in (3) and (4), it can be seen that if Δω _r/Δω _e >>1, the virtual inertia will be much larger than the inherent inertia of the wind turbine and even has better inertial support ability than the synchronous generator set. However, in practical control, H _vir is determined by ω _r0, H _w, and Δω _r/Δω _e, where ω _r0 depends on the real-time wind speed, which can be expressed as Eq. (5) ω r 0 = λ opt v R , v min < v < v max , ω max , v > v max (5) where λ_opt is the optimal tip speed ratio; v is the real-time wind speed; R is the radius of the wind wheel; ω _max is the maximum speed allowed for the stable operation of the wind turbine; v _min is the cut-in wind speed; and v _max is the maximum wind speed before the pitch control starts.

In the control process, it is necessary to comprehensively consider the dynamic changes in the inherent inertia H _w, wind speed, additional power, and system frequency of the wind turbine to obtain the effect of Δω _r>>Δω _e. Due to the coupling problem of multiple variables, the virtual inertia of the wind turbine can be much higher than the inherent inertia in theory, but the dynamic changes in the control process will make it difficult to predict its support performance and seriously weaken its application value.

In the current virtual inertia evaluation method, due to the real-time fluctuation of wind turbine speed and system angular frequency, Δω _r/Δω _e needs to be monitored in real-time. In the absence of time-scale constraints, the virtual inertia of the wind turbine will be an uncertain parameter. If reliable inertia reserves cannot be obtained, it will be impossible to predict the drop or increase in the amplitude of frequency after disturbance, which makes the key problem of frequency security early warning difficult to solve.

To solve this problem, a time scale must be introduced to constrain the virtual inertia. In this paper, the extreme time of frequency conversion is taken as the effective time of inertia response of the wind turbine. In the range of t ₀∼t _fm, if Δω _e is equal to the unit value of Δf _max, then H _vir can be expressed as H vir = Δ ω r H w Δ f max ω e × λ opt v R , v min < v < v max Δ ω r H w Δ f max ω e × ω max , v > v max . (6)

According to (6), Δω _r determines the size of H _vir when other parameters are known. At this time, the virtual inertia of the wind turbine can be quantitatively evaluated according to the speed variation in the frequency conversion extreme time. Therefore, the key to evaluating the virtual inertia of the wind turbine is to calculate the extreme value time of the system frequency conversion and obtain the speed change after the inertia response of the wind turbine.

Considering the limitation of the inherent inertia of the wind turbine on the speed, as well as the real-time changes in the wind turbine speed and system frequency, not only the potential of virtual inertia control remains unclear, but there are also still many problems in quantitative evaluation. In order to solve this problem, this paper will use the frequency conversion extreme time and the wind turbine operating state to constrain the virtual inertia for quantitative evaluation. Among them, the calculation process of the system frequency conversion extreme time as a key parameter is as follows.

In the system with high-proportion wind power, the aggregation model structure of the synchronous generator set and wind turbine is shown in Figure 2. The model includes the synchronous generator, wind turbine, and load frequency response module. The parameter design of each module is shown in Table 1.

According to Figure 2, the system frequency response equation can be expressed as 2 H d Δ f d t + D Δ f = − Δ P m − Δ P w − Δ P L + Δ P d , (7) where ΔP _m is the synchronous generator power response signal; ΔP _w is the wind turbine power response signal; ΔP _L is the load power response signal; and H is the system inertia time constant. Among them, ΔP _m depends on the synchronous generator adjustment coefficient and turbine parameters, which can be expressed as Δ P m = 1 − k σ × 1 + a T s 1 + T s Δ f , (8)

where ΔP _L depends on the load regulation coefficient, equal to K _L×Δf, and H depends on the system capacity and wind power penetration, which can be expressed as H = H g S g S B = H g 1 − k , (9) where k is the wind power penetration and S _B is the rated capacity of the system.

The system frequency variation can be calculated using (7) and expressed as Δ f s = 1 + T s 2 H T s 2 + 2 b ξ s + b 2 Δ P d s − Δ P w s . (10)

The inverse Laplace transform is applied to (10), and the system frequency response Δf(t) is Δ f t = Δ P d − Δ P w × G t = Δ P d − Δ P w × σ D + K L σ + 1 − k 1 + α e − b ξ t ⁡ sin w t + φ . (11)

In (11), each parameter is expressed as b = D + K L σ + 1 − k 2 H σ T , α = 1 − 2 b ξ T + b 2 T 2 1 − ξ 2 , ξ = D + K L σ T + 2 H σ + a T 2 D + K L σ + 1 − k / b , w = b 1 − ξ 2 , and  φ = ⁡ arctan w T 1 − b ξ T − ⁡ arctan 1 − ξ 2 − ξ . (12)

Without considering the power response of the wind turbine, ΔP _w = 0 is taken, and ΔP _d is regarded as a step disturbance. At this time, the derivative of (11) is obtained, and the extreme time of frequency conversion of the system can be expressed as t f m = 1 w arctan w T b ξ T − 1 . (13)

According to (11)–(13), the extreme time of frequency conversion is not only related to the inertia of conventional synchronous generators but also affected by wind power penetration and wind turbine power response. Among them, conventional synchronous generators can take typical parameter settings. The following section further discusses the influence of wind turbine-related parameters on the frequency conversion extreme time.

The virtual inertia of the wind turbine depends on its kinetic energy reserve and is closely related to its initial speed ω _r0. In addition, the initial active power P _we0 of the wind turbine determines the adjustment range of the power support ΔP _w, which in turn affects the kinetic energy release or absorption capacity of the wind turbine.

According to (6), the virtual inertia time constant of the wind turbine also depends on Δf _max. Since the lower limit of power system frequency security is 48 Hz, the frequency deviation extremum of the system should be limited within this range after the inertial response of the wind turbine. Since the wind turbine has a fast power response capability, it can be set within the frequency safety range to complete the predetermined virtual inertia support. Therefore, Δf _max = 2 Hz is used to conservatively estimate the virtual inertia of the wind turbine.

According to the evaluation results of Section 4.1 Δω _rmax, the range of the virtual inertia time constant of the wind turbine during the frequency conversion extreme time is as follows.

In the diagram, H _virmax1 and H _virmax2 are the maximum inertia time constants of the wind turbine under rotor kinetic energy constraint and power constraint, respectively. When the above two constraints are satisfied simultaneously, H _virmax can be expressed as Eq. (22) H vir max = ⁡ min H vir max 1 , H vir max 2 . (22)

It can be seen from Figure 5 that when ΔP _d > 0 and the speed of the rotor kinetic energy released by the wind turbine decreases, H _virmax depends on the rotor kinetic energy constraint at low speeds, and H _virmax depends on the wind turbine power constraint at high speeds. The H _virmax range is 0–18.61 s; when ΔP _d<0, when the wind turbine absorbs energy and the speed increases, H _virmax depends on the wind turbine power constraint at low speed, and H _virmax depends on the rotor kinetic energy constraint at high speed. The H _virmax range is 0–13.85 s.

However, Δf _max in the actual response process of the system is related to the disturbance power. When the disturbance power is small, Δf _max will be less than 2 Hz, and H _virmax of the wind turbine will be greater than the evaluation result, which can ensure that the wind turbine has a credible inertial support capability.

According to the above analysis, the wind turbine can show strong inertial support performance in a short time by changing the rotational speed through additional control. In theory, the wind turbine can cope with large power disturbances and has frequency support potential. In the actual control process, a large change in the speed in a short time will bring about problems such as power overshoot, increased mechanical load, and difficulty in speed recovery. Therefore, the wind turbine should perform an inertial response under the premise of considering the system’s inertia demand.

The inertia of the wind power high-proportion system is significantly reduced, and the virtual inertia of the wind turbine should be set according to the system frequency safety requirements. At present, foreign research has put forward relevant standards for microgrid island operation, requiring that the system frequency change rate (df/dt) is not higher than ±0.5 Hz/s (Wang et al., 2022). The maximum frequency change rate of the system occurs at the initial stage of the power disturbance. The primary frequency modulation has not yet acted, and the unbalanced power of the rotor side of the synchronous machine is the largest. At this time, the system frequency change rate can be expressed as Eq. (23) d f d t max = Δ P d 2 H . (23)

According to the above formula, when the frequency change rate constraint is determined, the system inertia requirement can be expressed as H ≥ H min = Δ P d / 2 d f d t max , (24)

where H _min is the minimum inertia requirement of the system.

When the wind turbine provides virtual inertia, the inertia time constant of the system with a high proportion of wind power can be further expressed using (9) as H = H g S g S B + H vir S w S B = H g 1 − k + H vir k . (25)

Combining (24) and (25), the inertia demand of the wind turbine is expressed as H vir = Δ P d / 2 k × d f d t | max − H g 1 − k k . (26)

Taking H _g = 5s and (df/dt)_max = ±0.5 Hz/s, the virtual inertia requirement of the wind turbine is calculated using the brought-in (26), as shown in Figure 6.

It can be seen from Figure 6 that the demand of system frequency security for the virtual inertia for the wind turbine mainly depends on disturbance power and wind power penetration. When the disturbance power is small and the wind power penetration rate is low, only the synchronous machine inertia H _g can meet the system inertia demand. When the permeability is lower than 20%, the inertia of the synchronous machine can cope with more than 8% of the disturbance. However, with the increase in wind power penetration, the ability of the system to cope with power disturbances is gradually weakened. When the wind power penetration reaches 50%, the system can cope with disturbances of less than 5%, which is not enough to cope with typical faults. At this time, the wind turbine should provide the necessary inertial support according to the system requirements. The inertia demand of the system increases with the increase in power disturbance. Under the same power disturbance, the virtual inertia demand of the wind turbine can be calculated according to the wind power penetration rate. When ΔP _d = 0.15 pu, the system inertia requirement is 7.5 s. When k = 20%, the wind turbine needs to provide 17.5 s of virtual inertia to make the total inertia of the system reach 7.5 s. When k = 50%, the wind turbine needs to provide 10 s of virtual inertia to make the total inertia of the system reach 7.5 s.

Combined with the system frequency safety requirements, the wind turbine can use its speed tracking performance to complete the virtual inertial support within the frequency conversion extreme time. The structure of the wind turbine virtual inertia controller proposed in this paper is shown in Figure 7, which consists of two modules: virtual inertia control and virtual inertia evaluation. Among them, the virtual inertia evaluation module has two evaluation functions: the maximum inertia of the wind turbine and the system inertia demand.

In the wind turbine virtual inertia evaluation module, the maximum speed variation and maximum inertia are evaluated according to the operating state and frequency conversion extreme time constraint, which are used as the limiting conditions of the wind turbine inertia demand and speed variation demand evaluation results. For the evaluation of the wind turbine’s virtual inertia demand, according to (26), disturbance power and wind power permeability can be introduced to calculate the wind turbine’s inertia demand. According to the evaluation results of the wind turbine’s inertia demand, the wind turbine’s speed demand can be calculated. The specific analysis is as follows:

The real-time equivalent inertia time constant H _vir in the process of wind turbine inertia response can be expressed as H vir = Δ P w t 2 d f / d t . (27)

In the extreme time of frequency conversion, both sides of (27) are integrated at the same time to obtain ∫ 0 t f m Δ P w t d t = 2 H vir Δ f max , (28) where Δf _max is the frequency deviation value corresponding to t _fm, which can be calculated according to (11) under the assumption that the system inertia meets the demand. According to the calculation results, the simultaneous formulas (19) and (28) are solved, and the rotational speed variation that meets the inertia demand of the wind turbine can be expressed as Δ ω r = ω r 0 − 2 H vir Δ f max H w + ω r 0 2   Δ P d > 0 − ω r 0 + 2 H vir Δ f max H w + ω r 0 2   Δ P d < 0 . (29)

According to the above formula, the required speed variation Δω _r of the wind turbine at different initial speeds can be obtained by introducing the operating state parameters and inertia requirements of the wind turbine. Then, within t _fm time, wind turbine corresponding speed can be calculated as ω _r1 = Δω _r+ω _r0.

The wind turbine virtual inertia control module generates additional power signals through speed tracking control to make the wind turbine track the reference speed in real-time, and the reference speed ω _{r_ref} is set according to ω _r1. First, in order to ensure that the wind turbine speed can change from ω _r0 to ω _r1 within t _fm, the speed-tracking control principle based on the wind turbine rotor motion equation is designed as follows: ∫ 0 t K p ω r _ ref − ω r d t = ∫ ω r 0 ω r 1 2 H w ω r d ω r , (30)

where K _p is the speed-tracking controller parameter.

According to (30), the value of K _p in t _fm can be calculated as K p = 2 H w t f m ω r _ ref × ⁡ ln ω r 0 − ω r _ ref ω r 1 − ω r _ ref + Δ ω r   Δ P d > 0 2 H w t f m ω r _ ref × ⁡ ln ω r _ ref − ω r 0 ω r _ ref − ω r 1 − Δ ω r   Δ P d < 0 , (31) where ω _{r_ref} = ω _r1±Δω _r1 and Δω _r1 is the speed change margin.

According to (31), the value of K _p can be calculated to realize the change in the wind turbine speed from ω _r0 to ω _r1 in t _fm to realize the quantitative control of the wind turbine speed.

Second, in order to ensure the smooth exit of the inertial support power of the wind turbine after the t _fm moment, the first-order inertial link is introduced, as shown in Figure 7. When the wind turbine speed changes to ω _r1 at t ₀+t _fm, the switches S₁ and S₂ switch from 0 to 1, and the speed tracking control exits through the first-order inertia link. Under the above control, the wind turbine inertial support power signal can be expressed as Δ P w = K p × ω r _ ref − ω r , t 0 < t < t 0 + t f m K p × ω r _ ref − ω r 1 × e − 1 T t , t > t 0 + t f m , (32) where T is the first-order inertial link time parameter, taking 5 s.

Under the control of (32), the inertial support power of the wind turbine is the largest at the initial moment of disturbance, which can effectively suppress the frequency change rate. After the frequency reaches the extreme point, the rotational speed changes to the demand evaluation value ωr1, and the smooth exit of the inertial support power is realized under the action of the first-order inertial link.

In order to verify the effectiveness of the virtual inertia evaluation and control method of the wind turbine proposed in this paper, the IEEE-9 bus system (None, 2015) with high-proportion wind power shown in Figure 8 is built using DIgSILENT/PowerFactory simulation software. The test system includes three thermal power plants (G1, G2, and G3) and a wind farm (DFIG), which can change the wind power penetration by adjusting the capacity of thermal power units and wind turbines. Assuming that the wind speed remains unchanged at 8 m/s, the main parameters of the system are shown in Table 3. The load mutation occurs when t ₀ = 2.0 s.

In order to verify the correctness of the frequency conversion extreme time theory calculation, the test system adopts the following parameter settings to analyze the frequency response characteristics after disturbance.

As shown in Table 4, in example 1, the wind power penetration rate in the test system is k = 20%. At the period of 2.0 s, the power disturbance is encountered, and the variation is ΔP _d = 0.06 pu. According to Figure 6, the inherent inertia of the synchronous machine can meet the system frequency safety requirements, and the wind turbine is not required to provide virtual inertia. When the wind turbine is not controlled by virtual inertia, the dynamic response of system frequency and synchronous machine power is shown in Figure 9.

As shown in Figure 9, the synchronous machine responds to frequency changes by increasing/decreasing power when the load changes suddenly. The simulation results of Figure 9 are compared with the theoretical calculation results, as shown in Table 5.

In order to verify the frequency modulation effect of the virtual inertia control strategy proposed in this paper, the power disturbance is increased and compared with the commonly used differential control. The system parameters in example 2 are set as Table 6:

In example 2, the load disturbance variation increases to 180 MW. The test system uses formula (26) to analyze the frequency safety, and the demand for the virtual inertia of the wind turbine is 10 s. In order to meet the needs of inertial support, the wind turbine adopts the following two control strategies for comparison: 1) when differential control is adopted, K _I is 20 to meet the inertia demand; 2) when the proposed control is adopted, speed tracking is used. According to the formula (27), when ΔP _d > 0 and ΔP _d < 0, the required speed changes in the wind turbine are 0.03 pu and 0.029 pu, respectively, and the K _p values obtained using formula (30) are 3.2 and 3.3, respectively. Under the two control strategies, the dynamic response of the system is shown in Figures 10, 11.

As shown in Figure 10, without additional control, the wind turbine hardly responds to frequency changes. The maximum frequency drop amplitude of the system Δf _max is −0.61 Hz, and the maximum frequency change rate (df/dt)_max is −0.67 Hz/s, which has exceeded the allowable value of frequency safety.

When the differential control is adopted, the speed change in the wind turbine is 0.025 pu within the frequency conversion extreme time t _fm, and the maximum frequency change rate (df/dt)_max and the drop amplitude Δf _max of the system are reduced to −0.54 Hz/s and −0.58 Hz, respectively, but still do not meet the maximum frequency change rate constraint. The H _vir value of the wind turbine in t _fm is 8.79 s, which does not meet the inertia demand of the wind turbine under this example. In addition, since the differential control cannot exit at t _fm, the overshoot occurs during the frequency recovery process, which is not conducive to frequency security and stability.

When the control strategy proposed in this paper is adopted, the wind turbine speed variation is 0.028 pu, the system frequency change rate (df/dt)_max and the drop amplitude Δf _max are reduced to −0.49 Hz/s and −0.52 Hz, respectively, and H _vir of the wind turbine within t _fm is 10.98 s, which meets the system‘s demand for virtual inertia. According to Figure 10(b1)∼(b3), the smooth exit of the inertial support power of the wind turbine can be realized in the speed tracking control, which reduces the overshoot in the system frequency recovery process. In addition, under the action of the first-order inertial link, the inertial support power of the wind turbine is reduced to 0 after experiencing delay, and the speed begins to recover later, which avoids the wind turbine absorbing power in the frequency recovery stage and is conducive to system frequency recovery. The frequency modulation effect is better than the traditional differential control.

Similarly, when ΔPd <0, the wind turbine speed variation under differential control is 0.026 pu, the system frequency change rate (df/dt)_max and the drop amplitude Δf _max are reduced to 0.54 Hz/s and 0.58 Hz, respectively. The H _vir value of the wind turbine within t _fm is 9.14 s, which does not meet the inertia demand of the wind turbine under this example; under the control strategy proposed in this paper, the wind turbine speed variation is 0.029 pu, and the system frequency change rate (df/dt)_max and the drop amplitude Δf _max are reduced to 0.48 Hz/s and 0.52 Hz, respectively. The H _vir value of the wind turbine within t _fm is 11.37 s, which meets the system’s demand for virtual inertia.

In summary, in both cases of ΔP _d > 0 and ΔP _d < 0, the proposed control can make the wind turbine show a virtual inertia that meets the system requirements within t _fm by tracking the speed and can achieve a smooth exit of the inertial support power after t _fm, avoiding frequency overshoot. The test results show that compared with the current differential control, the inertial support proposed in this paper aims to meet the inertia requirements of the system and combines the virtual inertia constraint of the wind turbine to complete the design of control parameters, which is more conducive to the reliability of the wind turbine to improve frequency support.

In order to further test the maximum inertia performance of the wind turbine under the operating state constraints, we will further increase the power disturbance and improve the wind power penetration rate; the system parameters in example 3 are set as Table 7:

In example 3, the wind power penetration rate is increased to 30%, and the disturbance variation reaches 450 MW. In order to ensure that the system frequency change rate meets the constraints, the test system’s inertia requirement is set to 15 s, and the virtual inertia requirement of the wind turbine is set to 50 s. In this case, the inertia demand of the system is far greater than the maximum virtual inertia that the wind turbine can provide, so the wind turbine should provide the maximum inertia support according to the initial operating state during the frequency conversion extreme time. By changing the wind speed, the initial speed of the wind turbine is set to 0.8 pu and 1.1 pu, and the dynamic response of the system frequency, wind turbine speed, and power output is obtained when ΔP _d > 0 and ΔP _d < 0, as shown in Figures 12–15.

When the initial speed of the wind turbine is 1.1 pu, the theoretical analysis of Figures 4, 5 shows that the maximum speed change in the wind turbine in t _fm is 0.062 pu and the maximum inertia is 7.44 s. As shown in Figure 13, when ΔP _d > 0, although the kinetic energy of the rotor that the wind turbine can release is large, due to the power constraint, the speed change in the wind turbine during the frequency conversion extreme time is only 0.06 pu, which can increase the maximum frequency deviation by 0.3 Hz. The maximum inertia H _vir = 7.56 s, allows for the smooth exit of wind turbine inertial support after the frequency conversion extreme moment, under the action of the first-order inertial link.

When the initial speed of the wind turbine is ω _r0 = 0.8 pu, the maximum speed change in the wind turbine in t _fm is 0.1 pu and the maximum inertia is 8 s. As shown in Figure 13, due to the constraint of the rotor kinetic energy reserve, the inertia response of the wind turbine immediately exits after the speed of the wind turbine drops to the minimum value of 0.7 pu at the extreme time of frequency conversion, which will cause a secondary drop in frequency. However, due to the large inertial support power available at this speed, the maximum frequency deviation can be increased by 0.4 Hz, and the maximum inertia of the wind turbine during the extreme time of frequency conversion is H _vir = 10 s.

Similarly, when ΔP _d <0, it can be seen from Figures 4, 5 that the theoretical values of the maximum speed change in the wind turbine within t _fm are 0.1 pu and 0.034 pu at the initial speeds of 1.1 pu and 0.8 pu, respectively. The maximum inertia is 12 s and 2.75 s, respectively.

According to the test results in Figures 14, 15, when ω _r0 = 1.1 pu, due to the constraint of the rotor kinetic energy reserve, the inertia response of the wind turbine increases to 1.2 pu and the frequency continues to increase. However, due to the large inertial support power provided by the wind turbine, the maximum frequency deviation can be reduced by 0.4 Hz, and the maximum inertia H _vir = 13.75 s. When ω _r0 = 0.8 pu, due to the small inertial support power provided by the wind turbine, the speed change in the wind turbine is 0.035 pu in the extreme time of frequency conversion, which can reduce the maximum frequency deviation by 0.2 Hz, and the maximum inertia H _vir = 3.5 s.

In summary, when the wind turbine needs to provide the maximum inertia support in the face of large disturbances, for the two cases of ΔP _d > 0 and ΔP _d< 0, the maximum speed variation of the wind turbine within t _fm under the constraint of the operating state is basically consistent with the theoretical analysis results in this paper. Since Δf _max is lower than 2 Hz under this disturbance, the maximum inertia of the wind turbine is slightly larger than the conservative evaluation result at Δf _max = 2 Hz, as shown in Figure 5. The simulation test results verify the accuracy of the maximum inertia evaluation analysis method of the wind turbine proposed in this paper.