System frequency-fan speed collaborative recovery and control method considering wind speed fluctuation

Abstract

The application discloses a system frequency-turbine speed coordination recovery and control method considering wind speed fluctuation, relates to the wind power wind speed control technical field, and realizes turbine speed recovery control by considering the influence of wind speed fluctuation on system frequency and turbine speed. The method comprises the following steps: S1, constructing a turbine multi-period exit recovery strategy; S2, constructing a frequency-speed coordination recovery model based on the multi-period exit; S3, constructing a system frequency response analysis model; S4, constructing a turbine speed analysis model; S5, constructing a turbine speed smooth recovery criterion; S6, constructing a frequency minimum point analysis model; and S7, performing adaptive setting of the multi-period exit parameters. The application effectively alleviates frequency secondary drop on the basis of guaranteeing smooth turbine speed recovery, and has great advantages compared with the current exit strategy.

Description

Technical Field

[0001] This invention relates to the field of wind power wind speed control technology, specifically a method for coordinated recovery and control of system frequency and wind turbine speed considering wind speed fluctuations. Background Technology

[0002] The process of wind turbines participating in frequency regulation can be divided into two stages: the frequency support stage and the exit stage. During the frequency support stage, the wind turbine can release internal rotor kinetic energy and adjust pitch angle through an additional power control circuit to provide active power support. The second frequency drop begins at the transition point between the frequency support and exit stages; the sudden decrease in output electromagnetic power caused by changes in control strategy is the root cause of this second frequency drop. Currently, wind turbines participate in frequency regulation on a timescale of minutes. The limit for active power change in a wind farm within one minute due to reduced wind speed or wind speed exceeding the cut-off wind speed is 10% of the rated power. Furthermore, based on actual wind farm data, active power changes caused by wind speed variations can reach 5% or even 15% of the rated power within one minute. Such large power fluctuations may lead to failure of turbine speed recovery. Current research on wind turbine frequency regulation rarely considers wind speed fluctuations and lacks analysis of the impact of wind speed fluctuations on system frequency and turbine speed. Summary of the Invention

[0003] The purpose of this invention is to provide a method for coordinated recovery and control of system frequency and fan speed considering wind speed fluctuations, thereby achieving fan speed recovery control by considering the impact of wind speed fluctuations on system frequency and fan speed.

[0004] The technical solution adopted by this invention to solve its technical problem is: a system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations, including the following steps:

[0005] S1. Construct a multi-period exit recovery strategy for wind turbines;

[0006] S2. Construct a frequency-speed collaborative recovery model based on multi-period exit;

[0007] S3. Construct an analytical model of the system frequency response;

[0008] S4. Construct an analytical model of the fan speed;

[0009] S5. Establish criteria for successful recovery of fan speed;

[0010] S6. Construct an analytical model for the lowest frequency point;

[0011] S7. Perform adaptive tuning of exit parameters for multiple time periods;

[0012] S7.1, Droop coefficient for multi-segment exit and segmented time tdi Perform the adjustment;

[0013] S7.2 Determine the number of sections where the fan will be deactivated.

[0014] Furthermore, in step S1, the multi-period exit recovery strategy divides the frequency regulation process of the wind turbine into four stages:

[0015] Phase 1: t∈[0,T] off The wind turbine participates in frequency regulation in a certain control mode, and the power increment during the frequency regulation period... Where Δf is the frequency deviation, k p k is the droop control coefficient. d T represents the virtual inertia control coefficient. off The frequency supports the end time;

[0016] Second stage: t∈(T) off ,T cov ], control the fan to gradually exit frequency regulation, T cov This is the initial moment when power becomes constant;

[0017] Third stage: t∈(T) cov ,T mpp The fan maintains T cov The electromagnetic power remains constant at time T, the rotational speed recovers, and T mpp This refers to the moment when the wind turbine enters the MPPT curve tracking phase.

[0018] Phase 4: t>T mpp The fan follows the MPPT curve.

[0019] Furthermore, the droop coefficient is expressed as in, This represents the droop coefficient for the first stage. This represents the droop coefficient in the i-th time period of the second stage, where i = (2, 3, ..., n); t di Let t represent the segmentation point between the i-th segment and the (i+1)-th segment, where i = (1, 2, ..., n). dn =T cov .

[0020] Furthermore, before the wind turbine operates according to the MPPT curve, the electromagnetic power output by the wind turbine through the additional power stage is: Where, ΔP eW,cov Indicates fan T cov The incremental increase in additional electromagnetic power output at any given time, Δf(T) cov ) represents T cov The system frequency at time k p (t) is the expression for the droop coefficient.

[0021] Furthermore, in step S2, a dynamic frequency regulation model considering the wind turbine speed is established by adding a power control loop to the traditional system frequency response (SFR) model, where ΔP L (t) represents the power disturbance, s is a complex variable, and F H For the power ratio of the high-pressure cylinder of the steam turbine, T R R is the reheater time constant, M is the synchronous machine droop coefficient, D is the synchronous machine inertial time constant, and ΔP is the synchronous machine damping coefficient. G Let ΔP be the change in mechanical power of the synchronous machine. eW X(s) represents the power change during frequency regulation of the wind turbine, X(s) is the relationship between the wind turbine's frequency regulation power and the frequency, and Δf is the difference between the actual frequency and the rated frequency f. n The difference, where α is the wind power penetration rate, ω0 is the initial rotational speed, and Δω is the rotational speed change;

[0022] In the fourth stage, the wind turbine recovers following the MPPT curve, and the output electromagnetic power of the wind turbine is: The increase in electromagnetic power input from the fan to the system after the disturbance occurs P ref The value is P opt .

[0023] Further, in step S3, a frequency time-domain analytical model is established, and the initial conditions of the segment points are solved by integration by parts to obtain the frequency response analytical model for each time period, and finally, the frequency response analytical model for t∈(0,T) is obtained. cov The frequency response expression is as follows: Where, Δf i (t) represents the frequency response in the i-th time period, i = (1, 2, ..., n); draw the corresponding simulation structure diagram of the system, write and simplify the state equations, and establish the variable-coefficient second-order non-homogeneous linear differential equation of the system frequency: in, a1, a2, a3, and a4 are coefficients. The first derivative of frequency, The second derivative of the frequency; The first derivative of the power disturbance is given. By solving the equation piecewise, equation (8) is simplified into multiple second-order non-homogeneous linear differential equations with constant coefficients. The general solution is then obtained by solving the initial conditions.

[0024] Furthermore, the frequency response analytical model calculation method for each stage is as follows:

[0025] (1) First-stage frequency response analytical model

[0026] First, solve for t∈(0,t) d1 (T off The frequency response of the wind turbine, which participates in frequency regulation in a comprehensive inertia control mode, is expressed as follows: in, The constant coefficient, For equation (7) in (0,t) d1 The characteristic roots of the homogeneous equation within the brackets are a5, where a5 is the coefficient and X is the characteristic root. 1 Let [variable] be the variable; integrate both sides of equation (9) in the interval [0-, 0+] respectively, and simplify to obtain:

[0027] And further simplification yields the initial conditions: in, For frequency deviation at 0 + The rate of change at time Δf 1 (0 + () represents the frequency deviation at 0 + The response value at time Δf 1 (0 + ) = 0;

[0028] Δf 1 (0 + )and Substituting into equation (10), we simplify to obtain the expressions for the two coefficients: a6 is the coefficient after combining the system parameters. Substituting it into equation (9), we obtain the frequency response expression for the first stage:

[0029] (2) Second-stage frequency response analytical model

[0030] The i-th time period (t) d(i-1) ,t di The analytical solution for the frequency response is: in, The constant coefficient, For equation (8) in (t) d(i-1) ,t di The characteristic roots of the homogeneous equation corresponding to X are shown in the image. i As a variable; according to equation (6), write t = t d1 The time-domain analytical model at time t, which is then applied to the interval [t] d1 -,t d1+ Integrating and simplifying, we get:

[0031]

[0032] Using integration by parts for k p (t) and Expanding the product, we get: Substituting equation (17) into equation (16) and simplifying, we obtain the initial condition equation:

[0033] Based on equation (6), write t = t di The time-domain analytical model at time [t], and its value in the interval [t] di -,t di+ Integrating and simplifying, we get: By simplifying using integration by parts, the initial conditions for the i-th time period are obtained:

[0034] i = 3, ..., n;

[0035] Substituting initial condition (18) and initial condition (20) into equation (15), we obtain constant coefficients. Among them, B1 i B2 i To simplify the coefficients, substitute equation (21) into equation (15) to obtain the frequency response expression for the i-th time period:

[0036] Furthermore, in step S4, the rotational speed function is piecewise linearized, in [T a-1 ,T a The linear change in rotational speed over the time period is expressed as follows: Where, ω a-1 Indicates t = T a-1 Rotational speed at time ω a Indicates t = T a The rotational speed at time T0 = 0, A is the total number of segments; in [T a-1 ,T a The energy equation for wind speed fluctuations within a given time period satisfies: The electromagnetic power integral term is expressed as: Substituting equations (2), (14), and (22) into (25), we can further simplify to obtain equation (25). [T a-1 ,t d(i+1) Interval k p Value [t d(i+1) ,Ta Interval k p Value Substituting into equation (26) respectively, where, Y1 is a coefficient; (28), A1, A2, A3, A4, and A5 are the simplified coefficients; thus, the integral term of mechanical power is obtained: in, Y2 is a transcendental function of ω, A6 is the simplified coefficient, and the exponential integral function is defined. Substituting equations (25) and (29) into equation (24), we simplify to: The corresponding rotational speed ω is calculated according to equation (32). a Equation (32) can be simplified to: H(ω) a )=B(33), where H(ω) a ) represents the rotational speed ω a A function of B, where B is related to the rotational speed ω. a Irrelevant functions.

[0037] Furthermore, in step S5, when the fan speed can be successfully restored, there exists a T... mpp At all times, ω = ω E ω E The rotational speed on the MPPT curve, i.e., within the time interval [T] cov ,T mpp Energy equation There is a real solution. According to equation (33), T can be obtained iteratively. cov Rotational speed ω at time Tcov According to the maximum power P on the MPPT curve MPPT formula: Find: Where, k opt ω is the MPPT control coefficient, and ω is related to the power value P. MPPT One-to-one correspondence, λ opt The optimal tip speed ratio of the wind turbine in the MPPT region is given by the wind power fluctuation function ΔP. b =b·t, where b represents the rate of change of wind power. Substituting equations (22) and (29) into equation (34), we get If equation (37) has real solutions, then it must satisfy the discriminant. Greater than or equal to zero.

[0038] Furthermore, in step S6, the lowest frequency points in the four stages of the frequency modulation process are represented as follows: in, This indicates the lowest frequency point in the first stage. Let represent the lowest point of the second frequency drop in the i-th time period of the second stage; according to the analytical expression of frequency response in equations (14) and (22), its derivative is obtained and equal to zero, and the time of the lowest frequency point is obtained as: in, This indicates the time of the lowest frequency point in the first phase. This represents the time of the lowest frequency point in the i-th time period, where i = 2, 3, ..., n; a7 is the simplified coefficient after combining the system parameters, Z i For coefficients;

[0039] Substituting equation (40) into equations (14) and (22), we obtain the expression for the lowest frequency point in the first stage: Substituting equation (41) into equations (14) and (22), we obtain the expression for the lowest frequency point in the i-th time period of the second stage:

[0040] Furthermore, in step S7.1, given the number of segments n, the lowest point of the second-order frequency drop in the multi-segment exit phase is represented as: in, Δf represents the maximum value of the minimum point of the second frequency drop when the number of segments is n. min n This represents the minimum point of the second frequency drop in the nth time period of the second stage, i.e., the segmented exit stage. A multi-segment exit parameter optimization model is established, with the objective function including the second frequency drop and the minimum rotational speed, expressed as: Where, ω m This represents the minimum speed during the frequency regulation process of the fan, where μ1 and μ2 are constants; the minimum speed constraint equation must be satisfied during the frequency regulation process: ω > ω min (46), where ω min This indicates the minimum operating speed of the fan. The total frequency regulation time of the fan is defined as the time until the speed recovers to the MPPT curve, denoted as T. mpp <80s(47), and at the same time, satisfying equation (38), when the frequency double drop is minimized, the minimum point constraint is satisfied: Add a minimum frequency constraint: ε1 is the target minimum value of the optimization objective; using the particle swarm optimization algorithm, with Equation (45) as the objective function and Equations (38), (46), (47), (48), and (49) as constraints, the droop coefficient with the minimum frequency second drop is finally obtained under the condition of releasing less rotor kinetic energy. and segmented time t di .

[0041] Further, in step S7.2, if the difference between the objective function value n_F with n segments and the objective function value n-1_F with n-1 segments is less than the threshold ε2, then the number of segments for the multi-segment exit strategy is selected as n-1.

[0042] The beneficial effects of this invention are as follows: Analysis of measured operational data reveals that during system frequency regulation, a continuous decrease in wind speed may prevent the fan speed from smoothly recovering to the MPPT curve, providing practical evidence for the impact mechanism of wind speed fluctuations on fan frequency regulation performance. A multi-period fan shutdown strategy is proposed to address the impact of wind speed fluctuations. A coupled mathematical model between system frequency, fan speed, and wind speed under fluctuating wind speed conditions is established. Based on this, a criterion for smooth fan speed recovery is constructed to ensure smooth recovery of fan speed after frequency regulation. Using the smooth fan speed recovery criterion as a constraint and suppressing secondary frequency drops as the objective, an adaptive parameter tuning method for the multi-period shutdown strategy is proposed. While ensuring smooth fan speed recovery, this effectively mitigates secondary frequency drops, demonstrating significant advantages compared to current shutdown strategies. Attached Figure Description

[0043] Figure 1 This is a power-rotor speed curve of the wind turbine based on the frequency of the rotor kinetic energy support system.

[0044] Figure 2 The graph shows the power and speed versus time curves for the first type of recovery strategy;

[0045] Figure 3 The graph shows the power and speed versus time curves for the second type of recovery strategy;

[0046] Figure 4 A graph showing the droop coefficients for a multi-period exit strategy;

[0047] Figure 5 A dynamic frequency regulation model diagram that takes into account the fan speed. Detailed Implementation

[0048] This invention first discusses the impact of wind speed fluctuations on the frequency regulation process of wind turbines, and then elaborates on the method for coordinated recovery and control of system frequency and wind turbine speed considering wind speed fluctuations.

[0049] I. The impact of wind speed fluctuations on the frequency regulation process of wind turbines

[0050] The fan captures mechanical power from the air. in, P mW The mechanical power converted is given by ρ, air density is given by R, the fan rotation radius is given by v, and ambient wind speed is given by C. p λ is the wind energy utilization coefficient, and λ is the tip speed ratio. kFor simplification, θ is the propeller pitch angle, and ω is the coefficient. t ω is the wind turbine speed, K is the generator rotor speed. G This refers to the gear ratio of the gearbox.

[0051] Wind turbines participate in frequency regulation by adding an incremental signal to the active power reference value. Since the wind turbine is connected to the grid via a converter, its electromagnetic power is controllable. Therefore, wind speed fluctuations affect wind turbine operation by influencing the mechanical power captured by the turbine. The wind turbine power-rotor speed curve based on the rotor kinetic energy support system frequency is shown below. Figure 1 As shown in the diagram. Point A is the initial operating point of the wind turbine. Curve AC represents the mechanical power variation with rotational speed, and curve D′A represents the maximum power point tracking the MPPT curve. The maximum power P on the MPPT curve is... MPPT for: Where, k opt ω is the MPPT control coefficient; and ω is related to the power value P. MPPT One-to-one correspondence, λ opt This represents the optimal tip speed ratio for the fan in the MPPT region.

[0052] When the frequency drops, the wind turbine participates in frequency regulation through an additional power control loop. Its electromagnetic power increases with curve ABC, providing power support for the system. At this point, the electromagnetic power is greater than the mechanical power, and the turbine speed decreases. After point C, the wind turbine exits the frequency support phase and enters the speed recovery phase. The electromagnetic power decreases to less than the mechanical power, the rotor speed begins to recover, and eventually returns to the initial operating state. Traditional wind turbine shutdown strategies directly reduce the electromagnetic power to the corresponding MPPT operating point at the shutdown moment, i.e., from point C directly to point D′. This process generates a significant power deficit, leading to a severe secondary frequency drop. The improved wind turbine shutdown strategy no longer directly reduces the operating point from point C to the MPPT operating curve. Instead, it mitigates the secondary drop by reducing the power deficit at the time of shutdown. The improved wind turbine shutdown strategy has two types: the first type directly reduces the power from point C to point D, and then operates to point E as the speed recovers; the second type slowly reduces the electromagnetic power from point C until it reaches point E. Both types ultimately recover to the initial operating state with the MPPT operating curve. Wind speed fluctuations can be categorized into three scenarios: constant wind speed, continuously decreasing wind speed, and continuously increasing wind speed. The impact of these three wind speed fluctuation scenarios on wind turbine speed is analyzed below.

[0053] By setting the same frequency support parameter electromagnetic power P eW The curves of power and rotational speed versus time for the two recovery strategies under three wind speed scenarios were obtained, as shown below. Figure 2 and Figure 3 As shown. The operation of the fan satisfies the rotor motion equation: Where ΔP bLet ΔP be the fluctuating power, and J be the wind turbine's inertial time constant. As wind speed increases, ΔP... b When the wind speed decreases, ΔP is positive. b Take the negative. The fan provides frequency support by releasing rotor kinetic energy, expressed as: ∫(P mW +ΔP b )-P eW dt=J∫ωdω(5). The first type of recovery strategy is analyzed below.

[0054] (1) Scenario where wind speed remains constant

[0055] like Figure 2 As shown in Figure a, when the wind speed remains constant, during the process of the wind turbine reaching point C, the electromagnetic power P... eW Greater than mechanical power The rotational speed decreased from ω0 to The area of ​​ABC represents the rotor kinetic energy released by the fan, expressed as: After this, the electromagnetic power decreases from point C to point D and remains at P. E The speed remains unchanged. At this point, the mechanical power is greater than the electromagnetic power, the rotational speed gradually recovers, and the mechanical power further increases until ω recovers to P. E The rotational speed ω on the corresponding MPPT curve E That is, it runs to point E. The area of ​​CDEE′ is equal to the rotor kinetic energy absorbed by the fan, expressed as: Subsequently, the fan gradually recovered to its rated operating state following the MPPT curve. During this process, the fan speed successfully recovered from point ABCDEA.

[0056] (2) Scenario where wind speed continues to decrease

[0057] If the wind speed continues to decrease, such as Figure 2 As shown in Figure b, the mechanical power considering only the effect of rotational speed is expressed as follows: The power fluctuation caused by wind speed is represented as ΔP. b The actual mechanical power is expressed as The fan speed decreases from ω0 to ω0 as it moves from ABC. Energy changes are represented as: After the fan descends to point D, initially the mechanical power is greater than the electromagnetic power, and the rotational speed is in the recovery phase. However, as the wind speed continues to decrease, the mechanical power continues to decrease, gradually decreasing until it equals the electromagnetic power. Figure 2 Point F in diagram b, then continues to decrease until it falls below the electromagnetic power. The area of ​​CDF represents the rotor kinetic energy absorbed by the fan, expressed as: Where ω F Let F be the rotational speed. During this process, the fan failed to recover its rotational speed from points ABCDF.

[0058] likeFigure 2 In Figure a, the area of ​​ABC minus the area of ​​CDEE′ equals the rotor's descent from ω0 to the set speed ω. E The released rotor kinetic energy is expressed as: exist Figure 2 In diagram b, the area of ​​ABC minus the area of ​​CDF is expressed as: Figure 2 In Figure b, ω F <ω E The engine released a significant amount of speed during the support phase, but failed to absorb enough energy during the speed recovery phase, resulting in the speed not returning to P. E The rotational speed ω on the corresponding MPPT curve E Mechanical power then drops below electromagnetic power, resulting in a decrease in power P. E The speed recovery failed because it did not intersect with the MPPT curve.

[0059] (3) Scenarios where wind speed continues to increase

[0060] As can be seen from the above analysis, as long as the rotational speed returns to P... E The corresponding rotational speed ω E The fan can then recover smoothly by following the MPPT curve. Figure 2 In Figure c, under the scenario of continuously increasing wind speed, the mechanical power... Continue to increase, in Afterwards, the mechanical power will not drop below the electromagnetic power, and the rotor will absorb sufficient energy to restore the rotational speed to ω. E Increased wind speed will not cause a failure to restore rotation speed.

[0061]

[0062] Similar to the first type of recovery strategy, the second type of recovery strategy occurs when the wind speed continues to decrease, and the turbine rotational speed has not yet recovered to P. E The rotational speed ω on the corresponding MPPT curve E Mechanical power has already dropped below electromagnetic power, power P E The rotational speed recovery failed because the curve did not intersect with the MPPT curve. However, there is no risk of rotational speed recovery failure in scenarios where wind speed continues to increase.

[0063] In summary, for the wind turbine speed recovery strategy that improves the frequency second drop by reducing power deficit, in scenarios where wind speed continuously decreases during wind turbine frequency regulation, the mechanical power captured by the wind turbine continuously decreases. If the wind turbine speed does not recover to the electromagnetic power P before the mechanical power drops below the electromagnetic power, the wind turbine speed will be affected. E The rotational speed ω on the corresponding MPPT curve E This leads to power P EIf the curve does not intersect with the MPPT curve, it will further lead to the failure of the fan speed recovery.

[0064] II. System Frequency-Fan Speed ​​Coordinated Recovery and Control Method Considering Wind Speed ​​Fluctuations

[0065] Figure 1 In the process of wind turbine operation, a significant drop in electromagnetic power in the CD segment can cause a substantial secondary frequency drop. However, if the drop in electromagnetic power in the CD segment is small, in scenarios where wind speed continues to decrease, the continuous reduction in mechanical power during the later stages of speed recovery may cause the electromagnetic power to not intersect with the MPPT curve, leading to speed recovery failure and the risk of turbine shutdown. Therefore, to mitigate the secondary drop and avoid the risk of speed recovery failure caused by wind speed fluctuations, this invention proposes a multi-stage exit strategy for wind turbine recovery. This strategy involves gradually reducing the turbine droop coefficient over multiple time periods to control the turbine to gradually exit frequency regulation.

[0066] S1. Construct a multi-period exit recovery strategy for wind turbines.

[0067] The frequency regulation process of the wind turbine is divided into the following four stages:

[0068] Phase 1: Frequency Support Phase, t∈[0,T] off The wind turbine participates in frequency regulation in a certain control mode, providing frequency support to the system. At the end of the frequency support at time T... off End. This analysis uses the most commonly used integrated inertia as an example to examine the power increment during frequency modulation. Where f is the frequency, Δf is the frequency deviation, and k p k is the droop control coefficient. d This represents the virtual inertia control coefficient.

[0069] Phase Two: Segmented Exit Phase, t∈(T) off ,T cov The fan exits virtual inertia control, and the droop coefficient gradually decreases in segments, gradually disengaging the fan from frequency regulation. cov This is the initial moment when the power becomes constant.

[0070] Third stage: Constant power stage, t∈(T) cov ,T mpp The fan maintains T. cov The electromagnetic power remains constant at time T, and the rotational speed recovers until T. mpp The time point intersects with the MPPT curve. T mpp This is the moment when the wind turbine enters the MPPT curve following the curve.

[0071] Phase 4: Recovery phase following the MPPT curve, t>T mpp The fan operates following the MPPT curve.

[0072] To more intuitively represent the change in droop coefficient during wind turbine frequency regulation, the droop coefficient is expressed as... Figure 4 The following are the formulas and expressions: in, This represents the droop coefficient for the first stage. This represents the droop coefficient in the i-th time period of the second stage, where i = (2, 3, ..., n); t di Let t represent the segmentation point between the i-th segment and the (i+1)-th segment, where i = (1, 2, ..., n). dn =T cov This shows that the droop coefficient of the wind turbine is divided into n time periods throughout the entire frequency regulation process, while in the segmented exit phase, the droop coefficient gradually decreases over n-1 time periods. Furthermore, the virtual inertia coefficient of the multi-time period exit strategy is only assigned a value during the frequency support phase.

[0073] Based on this, before the wind turbine operates according to the MPPT curve, the electromagnetic power output by the wind turbine through the additional power stage is expressed as: Where, ΔP eW,cov Indicates fan T cov The incremental increase in additional electromagnetic power output at any given time, Δf(T) cov ) represents T cov The system frequency at time k p (t) is the expression for the droop coefficient.

[0074] By employing a multi-stage exit recovery strategy for the wind turbine, a large drop in electromagnetic power at once is avoided, mitigating the secondary frequency drop. Simultaneously, as the droop coefficient gradually decreases in the later stages, the electromagnetic power also gradually decreases. By setting parameters appropriately, the problem of mechanical power falling below electromagnetic power due to a continuous decrease in wind speed, which further leads to the failure of speed recovery, is solved.

[0075] S2. Construct a frequency-speed collaborative recovery model based on multi-time period exit.

[0076] To rationally configure the parameters of the multi-segment exit strategy and mitigate the secondary drop while addressing wind speed fluctuations, it is necessary to establish the relationship between fluctuating power, turbine speed, system frequency, and multi-segment exit parameters. Therefore, a turbine speed-frequency collaborative recovery model considering wind speed fluctuations is established.

[0077] By adding a power control element of a wind turbine to the traditional system frequency response (SFR) model, a system can be established as follows: Figure 5 The dynamic frequency regulation model shown takes into account the fan speed. Where: ΔP L (t) represents the power disturbance; s is a complex variable; F H The power ratio of the high-pressure cylinder of the steam turbine; T RR is the reheater time constant; M is the synchronous machine droop coefficient; D is the synchronous machine inertial time constant; ΔP is the synchronous machine damping coefficient. G ΔP represents the change in mechanical power of the synchronous machine. eW X(s) represents the power change during frequency regulation of the wind turbine; X(s) is the relationship between the frequency-regulated power of the wind turbine and the frequency; Δf is the difference between the actual frequency and the rated frequency f. n The difference is α, where α is the wind power penetration rate, ω0 is the initial rotational speed, and Δω is the change in rotational speed.

[0078] During normal operation, the fan operates at the MPPT point, and the output electromagnetic power is P. opt After the disturbance occurs, the electromagnetic power output by the wind turbine in the first three stages is the power reference value P. ref Adding the increment ΔP eW In the fourth stage, the wind turbine recovers following the MPPT curve, and the output electromagnetic power of the wind turbine is: Compared to before the disturbance, the increase in electromagnetic power input from the wind turbine to the system after the disturbance occurs. Depend on Figure 5 It can be seen that by controlling the power control loop ΔP of the wind turbine, eW On the one hand, it affects ΔP add This, in turn, affects frequency variation; on the other hand, it affects the electromagnetic power P of the wind turbine. eW This, in turn, affects the change in rotational speed. Fluctuation power ΔP b By influencing mechanical power, P thus affects the fan speed. Similarly, P ref The value of P affects not only the frequency change but also the rotational speed change. ref The value of is generally P. MPPT P mW Or P opt From equations (1) and (2), we can see that P MPPT and P mW Both have a non-linear relationship with rotational speed. If P ref Value P MPPT or P mW This will lead to ΔP add The nonlinear coupling with the rotational speed further leads to nonlinear coupling between the frequency and the turbine rotational speed, making the frequency response unsolvable analytically. Therefore, to decouple the frequency from the turbine rotational speed while ensuring the analytical solvability of the SFR model, P ref The value is P opt Next, we will solve for ΔP. eW The relationship between frequency and ΔP eW ΔP b An analytical expression relating rotational speed and rotational speed.

[0079] S3. Construct an analytical model of the system frequency response.

[0080] First, based on equations (14), (15), and (17), we analyze the frequency response under multi-time period exit control. In the first and second stages, t∈(0,T) cov When ], due to the droop coefficient k p At the segmentation point t di The step jump decreases, resulting in ΔP add It will also decrease by a step at the segmentation point. ΔP add Multiple step decreases in frequency will result in multiple frequency minima. In the third stage, t∈(T) cov ,T mpp At that time, maintain the second stage T. cov The electromagnetic power remains constant at time t=T cov At that time, ΔP add There will be no abrupt change, and the third stage will not produce a frequency extremum. The transition from the third to the fourth stage is achieved by finding the intersection of the electromagnetic power and the MPPT curve, so at t=T cmpp At that time, ΔP add There will be no abrupt changes, and the frequency will not reach a minimum. Meanwhile, in the fourth stage, the wind turbine operates following the MPPT curve, and the electromagnetic power ΔP... add The frequency gradually increases, therefore no frequency minimum point will occur in the fourth stage. Thus, the frequency minimum point only exists during the first and second stages. A frequency time-domain analytical model is established, and the initial conditions of the segment points are solved using integration by parts to obtain the frequency response analytical model for each time period, ultimately yielding the result for t∈(0,T). cov The frequency response expression. According to equation (14), t∈(0,T) cov The frequency response is (18). Wherein, Δf i (t) represents the frequency response in the i-th time interval, where i = (1, 2, ..., n). According to... Figure 5 In the system part, draw the corresponding simulation structure diagram, then write and simplify the state equations, and establish the variable-coefficient second-order non-homogeneous linear differential equation of the system frequency: in, a1, a2, a3, and a4 are coefficients. The first derivative of frequency, The second derivative of the frequency; Let be the first derivative of the power disturbance. By solving piecewise equations, equation (20) is simplified into multiple second-order non-homogeneous linear differential equations with constant coefficients. The general solution is then obtained by solving the initial conditions. Let the system experience a disturbance ΔP. L (t)=u(t)ΔP L , where u(t) represents the unit step function.

[0081] (1) First-stage frequency response analytical model

[0082] First, solve for the frequency support phase t∈(0,t). d1 (T off The frequency response of the wind turbine, which participates in frequency regulation in a comprehensive inertia control mode, is expressed as follows: in, The constant coefficient, For equation (19) in (0,t) d1 The characteristic roots of the homogeneous equation within the brackets are a5, where a5 is the coefficient and X is the characteristic root. 1 For variables.

[0083] Since the system undergoes a step change at t=0, the coefficients in the general solution (21) are required to be... and Requires 0 + Two initial conditions Δf at time 1 1 (0 + )and Δf 1 (0 + () represents the frequency deviation at 0 + The response value at time t. For frequency deviation at 0 + The rate of change at time. Since the frequency is continuous, therefore Δf 1 (0 + )=Δf 1 (0-)=0. To solve... Integrating both sides of equation (21) over the interval [0-, 0+], and simplifying, we get:

[0084] And further simplification yields the initial conditions:

[0085] Substituting the two initial conditions into equation (22), we can simplify to obtain the expressions for the two coefficients: a6 is the coefficient after combining the system parameters. Substituting into equation (21), we obtain the frequency response expression for the first stage:

[0086] (2) Second-stage frequency response analytical model

[0087] Solve for the frequency response of the second stage, i.e., the general solution of the frequency response in the i-th time period. The i-th time period (t...) d(i-1) ,t di The analytical solution for the frequency response is: in, The constant coefficient, For equation (20) in (t) d(i-1) ,t di The characteristic roots of the homogeneous equation corresponding to X are shown in the image. i For variables. For solving. Δf needs to be obtained i (t d(i-1)+ )and in,

[0088] Since t = t d1 At time t, the virtual inertia coefficient becomes 0, and both the droop coefficient and the virtual inertia coefficient undergo a step change, while t = t di (i = 2, 3, ..., n-1) Only the droop coefficient changes. Therefore, it is necessary to solve for another initial condition for the frequency response in the second time period and the i-th (i = 3, ..., n) time period respectively.

[0089] Solve for the initial conditions of the second time period. For t=t d1 Analyze each moment separately, and write t = t according to equation (18). d1 The time-domain analytical model at time t, which is then applied to the interval [t] d1 -,t d1+ Integrating and simplifying, we get:

[0090]

[0091] Using integration by parts for k p (t) and Expanding the product, we get: Comparing equations (28) and (29), the integral term of the impulse function included in equation (28) can exactly cancel out the integral term obtained after expanding equation (29). Substituting equation (29) into equation (28) and simplifying, we obtain the initial condition equation:

[0092] Solve for the initial conditions of the i-th (i = 3, ..., n) time period. For t=t di The time intervals (i = 2, 3, ..., n-1) are analyzed separately, and t = t is written according to equation (18). di The time-domain analytical model at time [t], and its value in the interval [t] di -,t di+ Integrating and simplifying, we get: Similarly, by simplifying using integration by parts, we obtain the initial conditions for the i-th (i = 3, ..., n) time period:

[0093]

[0094] Substituting the initial condition equations (30) and (32) into equation (27), we obtain constant coefficients. B1 i B2 i To simplify the coefficients, substituting equation (33) into equation (27) yields the frequency response expression for the i-th time period:

[0095] S4. Constructing an analytical model of the wind turbine speed.

[0096] To solve for the analytical expression of the rotational speed, the rotational speed function is piecewise linearized, that is, in [T a-1 ,T a The linear change in rotational speed over the time period is expressed as follows: Where, ω a-1 Indicates t = T a-1 Rotational speed at time ω a Indicates t = T a The rotational speed at time T0 = 0, and A is the total number of segments. In [T... a-1 ,T a The energy equation for wind speed fluctuations within a given time period satisfies:

[0097] The analytical model for rotational speed is used to determine whether the rotational speed is below the minimum limit and whether it can recover smoothly. Therefore, it only needs to solve the interval (0, T). mpp The integral within the range is sufficient. According to equation (16), the electromagnetic power integral term is expressed as:

[0098] Substituting equations (14), (26), and (34) into equation (37) and further simplifying, we obtain equation (37). If [T] a-1 ,T a [Included in a time period of equation (14), for example t] di ≤T a-1 <t d(i+1) And T a ≤t d(i+1) Then the corresponding k p value Substituting into equation (38), the electromagnetic power in the interval [T] is obtained. a-1 ,T a The integral value of [T]; if [T] a-1 ,T a The two time periods shown in equation (14), for example t di ≤Ta-1 <t d(i+1) And t d(i+1) <T a Then the interval [T] a-1 ,T a [T] is divided into two parts: a-1 ,t d(i+1) ] and [t d(i+1) ,T a ]. [T a-1 ,t d(i+1) Interval k p Value [t d(i+1) ,T a Interval k p Value Substitute each into equation (38) to calculate. Among them, Y1 is a coefficient. Equation (1) is simplified to... A1, A2, A3, A4, and A5 are the coefficients after simplification using equation (1). Further, the integral term for mechanical power is obtained: in, Y2 is a transcendental function of ω, and A6 is the simplified coefficient. The Ei() function is an exponential integral function, defined as: Substituting equations (37) and (41) into equation (36), since Y2 is a transcendental function of ω, ω cannot be directly obtained. a The display function, therefore, simplifies to a function of ω. a Implicit functions: At the known starting point (T) a-1 ,ω a-1 ), and given a deadline T a Under the given conditions, the corresponding rotational speed ω is calculated according to equation (44). a Regarding ω a The implicit function (44) simplifies to: H(ω) a )=B(45). Where, H(ω a ) represents the rotational speed ω a A function of B, where B is related to the rotational speed ω. a Irrelevant functions.

[0099] To minimize the impact of secondary drops and ensure smooth speed recovery under fluctuating wind speeds, a criterion for smooth speed recovery is constructed based on the frequency response analytical model and the turbine speed analytical model. Furthermore, with the goal of minimizing the degree of secondary drops, a multi-segment exit strategy control parameter tuning procedure is proposed. S5. Constructing the criterion for smooth turbine speed recovery.

[0100] The continuous decrease in mechanical power prevents the fan speed from recovering to the speed indicated on the MPPT curve corresponding to the electromagnetic power, ultimately leading to the failure of fan speed recovery. The speed indicated on the MPPT curve corresponding to the electromagnetic power is represented by ω. E If the rotational speed recovery fails, it means that T does not exist. mpp At all times, ω = ω E Conversely, if the rotational speed can be restored smoothly, that is, if T exists... mpp At all times, ω = ω E That is, within the time interval [T] cov ,T mpp Energy equation There are real solutions. Based on equation (45), T is obtained iteratively. cov Rotational speed ω at time Tcov According to equation (3), we can obtain: The wind power fluctuation function is ΔP b = b·t, where b represents the rate of change of wind power. Substituting equations (34) and (41) into equation (46), we get Treat equation (48) as a function of T mpp For a quadratic equation in one variable, equation (48) must satisfy the discriminant if it has real solutions. Greater than or equal to zero.

[0101] In summary, the condition for the wind turbine to recover smoothly is: Δ≥0.

[0102] S6. Construct an analytical model for the lowest frequency point.

[0103] Under the criterion of successful speed recovery, to mitigate the secondary frequency drop as much as possible, it is necessary to first obtain the analytical expression for the lowest frequency point. Figure 5 It can be seen that the droop coefficient decreases abruptly at each segment, and the electromagnetic power output by the wind turbine also experiences a step drop. This results in a decrease in system frequency at each time interval, meaning there is a frequency minimum point at each time interval. Based on this, the frequency minimum points in the four stages of frequency regulation are represented as follows: in, This indicates the lowest frequency point in the first stage. This represents the lowest point of the second frequency drop in the i-th time period of the second phase.

[0104] Since all frequency responses have non-zero initial responses, there must be extreme points. Therefore, the minimum frequency point is obtained by differentiation. Based on the analytical expressions of the frequency response in equations (26) and (34), the derivative is obtained and equal to zero. The time of the minimum frequency point is then calculated as follows: in, This indicates the time of the lowest frequency point in the first phase. (i = 2, 3, ..., n) represents the time of the lowest frequency point in the i-th time period. a7 is the simplified coefficient after combining the system parameters, Z i is a coefficient.

[0105] Substituting equation (51) into equations (26) and (34), we obtain the expression for the lowest frequency point in the first stage: Substituting equation (52) into equations (26) and (34), we obtain the expression for the lowest frequency point in the i-th time period of the second stage: S7, Adaptive tuning of exit parameters for multiple time periods

[0106] Given the integrated inertia frequency regulation parameters, the goal of parameter tuning is to minimize the second frequency drop under the constraint of smooth speed recovery. The controllable parameters of the multi-stage exit strategy include: the exit time T during the frequency support phase. off (t d1 ), the number of segments in the exit phase n-1 (n≥2), and the droop coefficient for multi-segment exit. (i = 2, 3, ..., n) and the piecewise time t di (i = 2, 3, ..., n).

[0107] S7.1, Sag Coefficient for Multi-Segment Exit and segmented time t di Tuning

[0108] Given the number of segments n and the frequency modulation parameters, the lowest point of the second frequency drop during the multi-segment exit phase is represented as: in, This represents the maximum value of the minimum point of the second frequency drop when the number of segments is n. Δf min n This represents the lowest point of the second frequency drop during the nth time period of the second phase, i.e., the segmented exit phase.

[0109] A multi-segment exit parameter optimization model is established, with the objective function including the second frequency drop and the minimum speed, expressed as: Where, ω m This represents the minimum speed during the frequency regulation process of the fan, where μ1 and μ2 are constants.

[0110] To ensure the safe operation of the wind turbine, the minimum speed constraint must be met during frequency regulation: ω > ω min (57). Among them, ω minThis indicates the minimum operating speed of the fan. To avoid excessively long fan speed recovery time, a constraint is placed on the total frequency regulation time of the fan. The total frequency regulation time is defined as the time until the speed recovers to the MPPT curve, expressed as: T mpp <80s (58). Simultaneously, the constraint (49) for successful recovery of the fan speed is satisfied. Furthermore, in analysis (55), when the frequency dips to a minimum, the minimum point constraint is satisfied: Considering the large number of tuning parameters, a minimum frequency constraint is added to increase the convergence speed: ε1 is the target minimum value of the optimization objective.

[0111] The particle swarm optimization algorithm is used to solve the optimization model with equation (56) as the objective function and equations (49), (57), (58), (59), and (60) as constraints. Finally, the sag coefficient with the minimum frequency drop is obtained while releasing less rotor kinetic energy. and segmented time t di .

[0112] S7.2 Determine the number of sections where the fan will be deactivated.

[0113] The more segments a wind turbine exits, the less electromagnetic power drops with each exit, resulting in smaller frequency drops caused by segmentation and consequently smaller secondary frequency drops. However, too many segments increase control difficulty and require excessive control precision. Therefore, determining the appropriate number of segments is crucial. Balancing frequency regulation effectiveness and control convenience, if the difference between the objective function value n_F for n segments and the objective function value n-1_F for n-1 segments is less than the threshold ε2, then the multi-segment exit strategy should use n-1 segments. It's important to note that the parameters obtained from tuning are equivalent to those of a single turbine at the wind farm level. In practical applications, the wind farm uses these tuned parameters and, based on the operating conditions of each turbine within the wind farm, sends the parameters or power reference values ​​to the wind turbines to control their participation in frequency regulation.

[0114] This invention, through analysis of measured operational data, reveals that during wind turbine participation in system frequency regulation, a continuous decrease in wind speed may prevent the turbine speed from successfully recovering to the MPPT curve, providing practical evidence for the impact mechanism of wind speed fluctuations on wind turbine frequency regulation performance. A multi-period exit strategy for the wind turbine is proposed to address the impact of wind speed fluctuations. A coupled mathematical model of system frequency, turbine speed, and wind speed under fluctuating wind speed conditions is established. Based on this, a criterion for successful turbine speed recovery is constructed to ensure smooth speed recovery after frequency regulation. Using the successful turbine speed recovery criterion as a constraint and aiming to suppress secondary frequency drops, an adaptive parameter tuning method for the multi-period exit strategy is proposed. While ensuring smooth turbine speed recovery, this method effectively mitigates secondary frequency drops, demonstrating significant advantages compared to current exit strategies.

Claims

1. A method for coordinated recovery and control of system frequency and fan speed considering wind speed fluctuations, characterized in that, Includes the following steps: S1. Construct a multi-period exit recovery strategy for wind turbines; S2. Construct a frequency-speed collaborative recovery model based on multi-period exit; S3. Construct an analytical model of the system frequency response; S4. Construct an analytical model of the fan speed; S5. Establish criteria for successful recovery of fan speed; S6. Construct an analytical model for the lowest frequency point; S7. Perform adaptive tuning of exit parameters for multiple time periods; S7.1, Droop coefficient for multi-segment exit and segmented time t di Perform the adjustment; S7.2 Determine the number of sections where the fan will be deactivated; In step S1, the multi-period exit recovery strategy divides the frequency regulation process of the wind turbine into four stages: Phase 1: t∈[0,T] off The wind turbine participates in frequency regulation in a certain control mode, and the power increment during the frequency regulation period... Where Δf is the frequency deviation, k p k is the droop control coefficient. d T represents the virtual inertia control coefficient. off The frequency supports the end time; Second stage: t∈(T) off ,T cov ], control the fan to gradually exit frequency regulation, T cov This is the initial moment when power becomes constant; Third stage: t∈(T) cov ,T mpp The fan maintains T cov The electromagnetic power remains constant at time T, the rotational speed recovers, and T mpp This refers to the moment when the wind turbine enters the MPPT curve tracking phase. Phase 4: t>T mpp The fan operates following the MPPT curve; The droop coefficient is expressed as in, This represents the droop coefficient for the first stage. This represents the droop coefficient for the i-th time interval in the second stage, where i = (2, 3, ..., n); t di Let t represent the segmentation point between the i-th segment and the (i+1)-th segment, where i = (1, 2, ..., n). dn =T cov ; Before the fan follows the MPPT curve, the electromagnetic power output by the fan through the additional power stage is: Wherein, ΔP eW,cov Indicates fan T cov The incremental increase in additional electromagnetic power output at any given time, Δf(T) cov ) represents T cov The system frequency at time k p (t) is the expression for the droop coefficient.

2. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 1, characterized in that, In step S2, a dynamic frequency regulation model considering the wind turbine speed is established by adding a power control loop to the traditional system frequency response (SFR) model. Here, ΔP L (t) represents the power disturbance, s is a complex variable, and F H For the power ratio of the high-pressure cylinder of the steam turbine, T R R is the reheater time constant, M is the synchronous machine droop coefficient, D is the synchronous machine inertial time constant, and ΔP is the synchronous machine damping coefficient. G Let ΔP be the change in mechanical power of the synchronous machine. eW X(s) represents the power change during frequency regulation of the wind turbine, X(s) is the relationship between the wind turbine's frequency regulation power and the frequency, and Δf is the difference between the actual frequency and the rated frequency f. n The difference, where α is the wind power penetration rate, ω0 is the initial rotational speed, and Δω is the change in rotational speed; In the fourth stage, the wind turbine recovers following the MPPT curve, and the output electromagnetic power of the wind turbine is: The increase in electromagnetic power input from the fan to the system after the disturbance occurs P ref The value is P opt .

3. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 2, characterized in that, In step S3, a frequency time-domain analytical model is established, and the initial conditions of the segment points are solved using the integration by parts method to obtain the frequency response analytical model for each time period, and finally, the frequency response analytical model for t∈(0,T) is obtained. cov The frequency response expression is as follows: Where, Δf i (t) represents the frequency response in the i-th time period, i = (1, 2, ..., n); draw the corresponding simulation structure diagram of the system, write and simplify the state equations, and establish the variable-coefficient second-order non-homogeneous linear differential equation of the system frequency: in, a1, a2, a3, and a4 are coefficients. The first derivative of frequency, The second derivative of the frequency; The first derivative of the power disturbance is given. By solving the equation piecewise, equation (8) is simplified into multiple second-order non-homogeneous linear differential equations with constant coefficients. The general solution is then obtained by solving the initial conditions.

4. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 3, characterized in that, The frequency response analytical model calculation method for each stage is as follows: (1) First-stage frequency response analytical model First, solve for t∈(0,t) d1 (T off The frequency response of the wind turbine, which participates in frequency regulation in a comprehensive inertia control mode, is expressed as follows: in, The constant coefficient, For equation (7) in (0,t) d1 The characteristic roots of the homogeneous equation within the brackets are a5, where a5 is the coefficient and X is the characteristic root. 1 Let [variable] be the variable; integrate both sides of equation (9) in the interval [0-, 0+] respectively, and simplify to obtain: And further simplification yields the initial conditions: in, For frequency deviation at 0 + The rate of change at time Δf 1 (0 + () represents the frequency deviation at 0 + The response value at time Δf 1 (0 + ) = 0; Δf 1 (0 + )and Substituting into equation (10), we simplify to obtain the expressions for the two coefficients: a6 is the coefficient after combining the system parameters. Substituting it into equation (9), we obtain the frequency response expression for the first stage: (2) Second-stage frequency response analytical model The i-th time period (t) d(i-1) ,t di The analytical solution for the frequency response is: in, The constant coefficient, For equation (8) in (t) d(i-1) ,t di The characteristic roots of the homogeneous equation corresponding to X are shown in the image. i As a variable; according to equation (6), write t = t d1 The time-domain analytical model at time t is used to define the time domain model in the interval [t]. d1 -,t d1+ Integrating and simplifying, we get: Using integration by parts for k p (t) and Expanding the product, we get: Substituting equation (17) into equation (16) and simplifying, we obtain the initial condition equation: Based on equation (6), write t = t di The time-domain analytical model at time [t], and its value in the interval [t] di -,t di+ Integrating and simplifying, we get: By simplifying using integration by parts, the initial conditions for the i-th time period are obtained: i=3,…,n; Substituting initial condition (18) and initial condition (20) into equation (15), we obtain constant coefficients. Among them, B1 i B2 i To simplify the coefficients, substitute equation (21) into equation (15) to obtain the frequency response expression for the i-th time period:

5. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 4, characterized in that, In step S4, the rotational speed function is piecewise linearized, in [T a-1 ,T a The linear change in rotational speed over the time period is expressed as follows: Where, ω a-1 Indicates t = T a-1 Rotational speed at time ω a Indicates t = T a The rotational speed at time T0 = 0, A is the total number of segments; in [T a-1 ,T a The energy equation for wind speed fluctuations within a given time period satisfies: The electromagnetic power integral term is expressed as: Substituting equations (2), (14), and (22) into (25), we can further simplify to obtain equation (25). [T a-1 ,t d(i+1) Interval k p Value [t d(i+1) ,T a Interval k p Value Substituting into equation (26) respectively, where, Y1 is a coefficient; A1, A2, A3, A4, and A5 are the simplified coefficients; thus, the integral term of mechanical power is obtained: in, Y2 is a transcendental function of ω, A6 is the simplified coefficient, and the exponential integral function is defined. Substituting equations (25) and (29) into equation (24), we simplify to: The corresponding rotational speed ω is calculated according to equation (32). a Equation (32) can be simplified to: H(ω) a )=B(33), where H(ω) a ) represents the rotational speed ω a B is a function of rotational speed ω a Irrelevant functions.

6. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 5, characterized in that, In step S5, when the fan speed can be successfully restored, there is a T... mpp ω = ω at all times E ω E The rotational speed on the MPPT curve, i.e., within the time interval [T] cov ,T mpp Energy equation There is a real solution. According to equation (33), T can be obtained iteratively. cov Rotational speed ω at time Tcov According to the maximum power P on the MPPT curve MPPT formula: Find: Where, k opt ω is the MPPT control coefficient, and ω is related to the power value P. MPPT One-to-one correspondence, λ opt The optimal tip speed ratio of the wind turbine in the MPPT region is given by the wind power fluctuation function ΔP. b =b·t, where b represents the rate of change of wind power. Substituting equations (22) and (29) into equation (34), we get If equation (37) has real solutions, then it must satisfy the discriminant. Greater than or equal to zero.

7. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 6, characterized in that, In step S6, the lowest frequency points in the four stages of the frequency modulation process are represented as follows: in, This indicates the lowest frequency point in the first stage. Let represent the lowest point of the second frequency drop in the i-th time period of the second stage; according to the analytical expression of frequency response in equations (14) and (22), its derivative is obtained and equal to zero, and the time of the lowest frequency point is: in, This indicates the time of the lowest frequency point in the first phase. This represents the time of the lowest frequency point in the i-th time period, where i = 2, 3, ..., n; a7 is the simplified coefficient after combining the system parameters, Z i The coefficients are used; substituting equation (40) into equations (14) and (22) yields the expression for the lowest frequency point in the first stage: Substituting equation (41) into equations (14) and (22), we obtain the expression for the lowest frequency point in the i-th time period of the second stage:

8. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 7, characterized in that, In step S7.1, given the number of segments n, the lowest point of the frequency double drop in the multi-segment exit stage is represented as: Where, Δf″ min Δf represents the maximum value of the minimum point of the second frequency drop when the number of segments is n. min n This represents the minimum point of the second frequency drop in the nth time period of the second stage, i.e., the segmented exit stage. A multi-segment exit parameter optimization model is established, with the objective function including the second frequency drop and the minimum rotational speed, expressed as: (45), where ω m This represents the minimum speed during the frequency regulation process of the fan, where μ1 and μ2 are constants; the minimum speed constraint equation must be satisfied during the frequency regulation process: ω > ω min (46), where ω min This indicates the minimum operating speed of the fan; the total frequency regulation time of the fan is defined as the time until the speed recovers to the MPPT curve, denoted as T. mpp <80s(47), and at the same time, satisfying equation (38), when the frequency double drop is minimized, the minimum point constraint is satisfied: Add a minimum frequency constraint: ε1 is the target minimum value of the optimization objective; using the particle swarm optimization algorithm, with Equation (45) as the objective function and Equations (38), (46), (47), (48), and (49) as constraints, the droop coefficient with the minimum frequency second drop is finally obtained under the condition of releasing less rotor kinetic energy. and segmented time t di .

9. The system frequency-fan speed coordinated recovery and control method considering wind speed fluctuations according to claim 8, characterized in that, In step S7.2, if the difference between the objective function value n_F with n segments and the objective function value n-1_F with n-1 segments is less than the threshold ε2, then the number of segments for the multi-segment exit strategy is selected as n-1.

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