Startup time estimation method and startup time estimation program

Abstract

To easily estimate the startup time of a wind turbine. [Solution] In the startup time estimation method performed by the processor of the startup time estimation device, the processor numerically integrates the equation of motion for the rotation of the wind turbine over time and calculates the rotational speed ω corresponding to a specific cut-in wind speed. start The point at which this value is exceeded is estimated as the wind turbine's startup time.

Description

[Technical Field]

[0001] This invention relates to a startup time estimation method and a startup time estimation program for estimating the startup time of a wind turbine. [Background technology]

[0002] Conventionally, horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs) are known as wind turbines used in wind power generation systems (see, for example, Patent Documents 1 and 2). Vertical-axis wind turbines, compared to horizontal-axis wind turbines, do not require a yaw control mechanism because they can generate electricity regardless of wind direction, and they have lower operating noise, a lower center of gravity, and lower costs, but it has been pointed out that their power generation performance is inferior. On the other hand, it has been experimentally confirmed that as they are made larger, their power generation efficiency can reach the same level as horizontal-axis wind turbines, and in line with the recent trend of larger wind turbines, vertical-axis wind turbines are also expected to be one of the options for wind power generation in the future. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2000-69797 [Patent Document 2] Japanese Patent Application Publication No. 56-42752 [Overview of the project] [Problems that the invention aims to solve]

[0004] By the way, when a wind power generation operator tries to match the specifications of a wind turbine with the installation location, the power generation performance is mainly evaluated based on wind condition data and a power curve. By estimating the power generation output considering the case where it is ideally controlled based on the wind condition data, the expected values of the operating rate and the equipment utilization rate can be predicted. However, in the case of an actual wind turbine, in order to suppress the wear of the rotating shaft under conditions lower than the cut-in wind speed, the wind turbine is actively stopped, and when the cut-in wind speed is exceeded, the wind turbine is started to begin power generation. Therefore, since the estimated operating rate and equipment utilization rate do not consider the loss time due to startup, it is necessary to consider the contribution of startup for more accurate estimation. In addition, as a recent global trend, the development of a movement for increasing the size of wind turbines is underway, but there is a situation where it is becoming difficult for large wind turbines to start completely spontaneously. These achieve startup by using a motor to assist the initial rotational speed, but the importance of considering the startup performance when calculating the operating rate and equipment utilization rate is considered to be increasing more and more. Therefore, there is a demand for a technology that can easily estimate the startup time of a wind turbine.

[0005] The present invention has been made in view of the above, and an object thereof is to provide a startup time estimation method and a startup time estimation program that can easily estimate the startup time of a wind turbine.

Means for Solving the Problems

[0006]

[0007] In order to solve the above-described problems and achieve the object, a startup time estimation method according to the present invention is a startup time estimation method executed by a processor of a startup time estimation device. The processor numerically integrates a motion equation related to the rotation of a wind turbine over time, and estimates the time when the rotational speed exceeding the rotational speed corresponding to a specific cut-in wind speed is the startup time of the wind turbine.

[0007] Furthermore, in the startup time estimation method according to the present invention, the processor numerically integrates the equation of motion over time using wind condition data relating to wind speed at the wind turbine installation site observed over a specific period in the past and wind condition data that is artificially created, and obtains statistics on the startup time.

[0008] Furthermore, in the startup time estimation method according to the present invention, the processor numerically integrates the equation of motion over time using the initial rotational speed of the wind turbine, which is set in advance.

[0009] Furthermore, in the startup time estimation method according to the present invention, the processor numerically integrates the equation of motion in the following equation (1) over time, where I is the moment of inertia of the wind turbine, ω is the rotational speed of the wind turbine, t is the time, and T is the rotational torque of the wind turbine.

[0010]

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[0011] Furthermore, in the startup time estimation method according to the present invention, the wind turbine in the above invention is a floating-axis wind turbine in which a floating body floating on the ocean and a vertical-axis wind turbine are rigidly coupled and rotate relative to a support bearing, and the processor calculates the rotational torque T based on the driving torque of the vertical-axis wind turbine, the frictional loss torque of the floating body with respect to seawater, and the mechanical loss torque generated in the support bearing that maintains the attitude of the generator connected to a transmission system that transmits rotational force from the floating body and the vertical-axis wind turbine to the generator and a mooring line when the floating body and the vertical-axis wind turbine rotate relative to the support bearing.

[0012] Furthermore, the startup time estimation program according to the present invention is a startup time estimation program to be executed by a computer, and the startup time estimation program instructs the computer to perform the following: numerically integrate the equation of motion relating to the rotation of the wind turbine over time, and estimate the time when the rotational speed corresponding to a specific cut-in wind speed is reached as the startup time of the wind turbine. [Effects of the Invention]

[0013] According to the startup time estimation method and startup time estimation program of the present invention, the startup time of a wind turbine can be easily estimated. [Brief explanation of the drawing]

[0014] [Figure 1] Figure 1 shows the configuration of a floating-axis wind turbine, which is the target of startup time estimation in the startup time estimation method according to the embodiment. [Figure 2] Figure 2 is a block diagram showing the configuration of a startup time estimation device that performs the startup time estimation method according to the embodiment. [Figure 3] Figure 3 shows an example of the relationship between the output and rotational speed of a floating-axis wind turbine. [Figure 4] Figure 4 shows an example of wind condition data. [Figure 5] Figure 5 shows an example of a torque coefficient. [Figure 6] Figure 6 is a flowchart showing the startup time estimation method according to the embodiment. [Figure 7] Figure 7 shows an example of the calculation results obtained using the startup time estimation method. [Figure 8] Figure 8 is a flowchart showing a modified example of the embodiment. [Modes for carrying out the invention]

[0015] The embodiments for carrying out the present invention (hereinafter referred to as "embodiments") will be described below with reference to the drawings. However, the present invention is not limited to the embodiments described below. Furthermore, in the drawings, the same parts are denoted by the same reference numerals.

[0016] [Outline configuration of a floating-axis wind turbine] First, before explaining the startup time estimation method according to this embodiment, we will describe the configuration of the floating-axis wind turbine 100, which is the target of the startup time estimation method. Figure 1 shows the configuration of the floating-axis wind turbine 100, which is the target of the startup time estimation method according to the embodiment. The floating-axis wind turbine 100 is a floating offshore wind turbine used in wind power generation systems. As shown in Figure 1, this floating-axis wind turbine 100 comprises a floating body 200, a vertical-axis wind turbine 300, and a support bearing 400.

[0017] The floating body 200 is a component for floating on the ocean. In this embodiment, as shown in Figure 1, a spar-type (cylindrical) floating body is used as the floating body 200. That is, because a spar-type floating body 200 is used, the portion that penetrates the water surface is small, and it has the characteristic of being less affected by waves. Note that the floating body 200 is not limited to the spar type; other types of floating bodies may also be used.

[0018] As shown in Figure 1, the vertical-axis wind turbine 300 comprises a rotating shaft 301, multiple blades 302 (three in this embodiment), and multiple support arms 303. The rotating shaft 301 has a cylindrical shape and is rigidly coupled to the floating body 200 so as to be coaxial with the floating body 200. The multiple blades 302 are the parts that receive the wind and are attached to the rotation axis 301 by multiple support arms 303 so as to be parallel to the central axis of the rotation axis 301.

[0019] The support bearing 400 has a cylindrical shape that allows the rotating shaft 301 and the floating body 200 to pass through it, and supports the rotating shaft 301 and the floating body 200 so that they can rotate around the central axis of the rotating shaft 301 (hereinafter referred to as rotating around the rotating shaft 301). The floating body 200 and the vertical-axis wind turbine 300 rotate around the rotating shaft 301 relative to the support bearing 400 (rotating in the yaw direction) as the multiple blades 302 and multiple support arms 303 receive wind.

[0020] [Outline configuration of the startup time estimation device] Next, the configuration of the startup time estimation device 1 that executes the startup time estimation method according to this embodiment will be described. Figure 2 is a block diagram showing the configuration of the startup time estimation device 1 that performs the startup time estimation method according to the embodiment. The startup time estimation device 1 estimates the startup time of the floating shaft type wind turbine 100. As shown in Figure 2, the startup time estimation device 1 comprises an input unit 2, a storage unit 3, and a processor 4.

[0021] The input unit 2 is configured using operating devices such as a mouse, keyboard, and touch panel, and accepts user input. The input unit 2 then outputs an operation signal corresponding to the user input to the processor 4.

[0022] The storage unit 3 stores various programs executed by the processor 4 (including the startup estimation program according to this embodiment), and data necessary when the processor 4 performs processing.

[0023] Processor 4 is implemented by a controller such as a CPU (Central Processing Unit) or MPU (Micro Processing Unit) executing various programs stored in the memory unit 3, and controls the operation of the entire startup time estimation device 1. Note that processor 4 is not limited to a CPU or MPU, but may also be composed of integrated circuits such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field-Programmable Gate Array). The functions of processor 4 will be explained later in the section titled "Method for Estimating Startup Time".

[0024] [Regarding the method for estimating startup time] Next, we will describe the startup time estimation method performed by the startup time estimation device 1 described above. The following sections will explain the startup time estimation method in order: "Overview of the startup time estimation method," "Wind condition data," "Torque coefficient," "Friction coefficient," "Mechanical loss torque," "Processor execution flow," and "Calculation results."

[0025] [Overview of the startup time estimation method] First, I will explain the overview of the startup time estimation method. The processor 4 estimates the startup time of the floating-axis wind turbine 100 by numerically integrating the following equation of motion (2) over time, which relates to the yaw rotation of the floating-axis wind turbine 100 (rotation around the rotation axis 301).

[0026]

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[0027] In equation (2), I is the moment of inertia of the floating-axis wind turbine 100 around the rotation axis 301. ω is the rotational speed of the floating-axis wind turbine 100. total This is the rotational torque around the rotation axis 301 of the floating-axis wind turbine 100.

[0028] Here, the rotational torque T total is set by the following equation (3).

[0029] [Number]

[0030] In equation (3), T q is the driving torque around the rotation axis 301 in the vertical-axis windmill 300 (FIG. 1). T Fric is the frictional loss torque with respect to seawater in the floating body 200. T Mech is the mechanical loss torque generated in the support bearing 400 that holds the posture of the generator connected to the transmission system and the mooring measures that transmit the rotational force from the floating body 200 and the vertical-axis windmill 300 to the generator when the floating body 200 and the vertical-axis windmill 300 rotate with respect to the support bearing 400. That is, in the present embodiment, the processor 4 calculates the rotational torque T q based on the driving torque T Fric the frictional loss torque T Mech and the mechanical loss torque T total .

[0031] Also, the driving torque T q is set by the following equation (4).

[0032] [Number]

[0033] In equation (4), C q is the torque coefficient. ρ a is the air density. U is the wind speed set from the wind speed data described later. α is the inclination angle of the rotation axis 301 with respect to the vertical direction (FIG. 1). S rotorR is the projected area of ​​the vertical-axis wind turbine 300, which is the value obtained by multiplying the diameter of the vertical-axis wind turbine 300 (diameter centered on the rotation axis 301) by the height of the blades 302. R is the radius of the vertical-axis wind turbine 300 (radius centered on the rotation axis 301).

[0034] Furthermore, friction loss torque T Fric This is set by the following equation (5).

[0035]

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[0036] In equation (5), C F ρ is the coefficient of friction. W is the density of water. S is the surface area of ​​the floating body 200. R Float This is the radius of the floating body 200.

[0037] Figure 3 shows an example of the relationship between the output and rotational speed of a floating-axis wind turbine 100. In Figure 3, a 20kW class floating-axis wind turbine 100 is used. Specifically, in Figure 3, the horizontal axis shows the rotational speed ω, and the vertical axis shows the output. As shown in Figure 3, the floating-axis wind turbine 100 has a rotational speed at which its output is maximized, depending on the wind speed. Since there is a one-to-one relationship between the maximum output and the rotational speed at each wind speed, it can be expected that the control mechanism will be designed to achieve the rotational speed in accordance with the wind speed. In this embodiment, the processor 4 numerically integrates the equation of motion in equation (2) over time and obtains a rotational speed of 2.4 rad / s (hereinafter, speed threshold ω) at which the maximum output is obtained at a cut-in wind speed of 3 m / s for a 20 kW class floating-axis wind turbine. start The time exceeding the specified threshold is estimated as the startup time.

[0038] [Regarding wind condition data] Next, I will explain the wind condition data. Figure 4 shows an example of wind condition data. Figure 4 represents one year's worth of continuous wind condition data measured at an arbitrary location. Specifically, the horizontal axis of Figure 4 shows the date and time, and the vertical axis shows the wind speed. In this embodiment, the wind speed U in equation (4) is set using the wind condition data for one year shown in Figure 4. This wind condition data is stored in the storage unit 3. The wind condition data used to set the wind speed U in equation (4) is not limited to the wind condition data shown in Figure 4; artificially created wind condition data may also be used, and a combination of the wind condition data shown in Figure 4 and the artificially created wind condition data may be used.

[0039] [Regarding the torque coefficient] Next, the torque coefficient C q I will explain this. Figure 5 shows the torque coefficient C q This figure shows an example. Specifically, Figure 5 shows the tip speed ratio (TSR) on the horizontal axis and the torque coefficient C on the vertical axis. q This indicates that. In this embodiment, a double-multiple streamtube model (DMS) based on the general blade momentum theory is used as a method for predicting the characteristics of a wind turbine, and the torque coefficient C in equation (4) is used. q Set it.

[0040] Specifically, focusing only on the blades 302 of the floating-axis wind turbine 100, the torque coefficient C was measured using DMS under conditions of TSR of -1 to 7 and wind speed of 0.1 to 30 m / s. q This was estimated (Figure 5). Note that TSR is the value obtained by multiplying the radius R of the vertical-axis wind turbine 300 by the rotational speed ω and dividing the result by the wind speed U. The two-dimensional data obtained from the TSR and wind speed using the DMS is stored in the storage unit 3.

[0041] Furthermore, when numerically integrating the equation of motion (2) over time, an arbitrary TSR and a torque coefficient C corresponding to the wind speed obtained at each step of the numerical integration are used. qTo calculate this, the two-dimensional data obtained from the TSR and wind speed using the DMS described above is interpolated using linear interpolation.

[0042] [Regarding the coefficient of friction] Next, the coefficient of friction C F I will explain this. In this embodiment, the coefficient of friction C in equation (5) is calculated based on the following reference A, which measures the fluid friction resistance acting on a rotating cylindrical body in still water. F Set it. (Reference A) "T. Theodorsen et al.: Experiments on drag of revolving disks, cylinders and streamline rods at high speeds, NACA, Report no. 793, 1946."

[0043] Specifically, the turbulent region (log 10 For Re>2), use equation (6) below. Note that Re is the Reynolds number, and the radius R of the floating body 200 is relative to the rotational speed ω. Float This is the value obtained by dividing the kinematic viscosity by the value obtained by multiplying the square of the given value.

[0044]

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[0045] Note that in the laminar flow region (log 10 For Re≦2, (log 10 Re,C F We use a linear approximation with ) = (0.6,0) and (3,-1.8). Then, in the turbulent and laminar flow regions, the friction coefficient C F The information needed to calculate this is stored in memory unit 3.

[0046] [Regarding mechanical torque loss] Next, mechanical loss torque T Mech I will explain this. Mechanical Torque Loss T Mech This is set by the following equation (7).

[0047]

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[0048] In equation (7), T Mech0 This is the static mechanical torque loss. Mech,ω This is the dynamic mechanical torque loss, which depends on the rotational speed ω.

[0049] [Regarding the flow executed by the processor] Next, we will explain the flow (startup time estimation method) that processor 4 executes. Figure 6 is a flowchart showing the startup time estimation method according to the embodiment. Based on the information described in "Overview of Startup Time Estimation Method," "Wind Condition Data," "Torque Coefficient," "Friction Coefficient," and "Mechanical Loss Torque" above, the processor 4 estimates the startup time of the floating-axis wind turbine 100 as shown in Figure 6.

[0050] First, processor 4 sets m to 1 (step S1) and n to 1 (step S2).

[0051] After step S2, the processor 4 calculates the static mechanical loss torque T at the initial time t0. Mech0,m , and the initial rotational speed ω0 is set (step S3). In this embodiment, the initial time t0 is set to 0, 6, 12, and 18 o'clock each day in the wind condition data shown in Figure 4. Also, assuming a 20kW class floating shaft wind turbine, the static mechanical loss torque T Mech0 Set the values ​​to 0, 20, 40, 60, 80, and 100 Nm respectively. For example, when m=1, the static mechanical loss torque T Mech0 Set to "0" and when m=2, the static mechanical loss torque T Mech0Set this to "20". Furthermore, set the initial rotational speed ω0 for idling the floating shaft wind turbine 100 with the motor to 0, 0.1, 0.2, 0.3, 0.4, and 0.5 rad / s respectively. For example, if n=1, set the initial rotational speed ω0 to "0", and if n=2, set the initial rotational speed ω0 to "0.1".

[0052] After step S3, the processor 4 sets the wind speed U according to the time based on the wind condition data stored in the memory unit 3, and also sets the rotation speed ω according to the time based on the initial rotation speed ω0 (step S4).

[0053] After step S4, the processor 4 calculates the torque coefficient C based on the wind speed U and rotational speed ω set in step S4. q and friction coefficient C F Calculate (Step S5).

[0054] After step S5, the processor 4 determines that the absolute value of the initial rotational speed ω0 is greater than 0, and the rotational torque T total From mechanical loss torque T Mech The absolute value obtained by adding these two values ​​is the mechanical loss torque T. Mech Determine whether it is greater than or equal to (Step S6).

[0055] If "Yes" is determined in step S6, the processor 4 calculates the rotational torque T in the equation of motion shown in equation (8) below. total Toshi (Step S7), proceed to Step S9.

[0056]

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[0057] On the other hand, if "No" is determined in step S6, the processor 4 sets the rotational torque T in the equation of motion shown in equation (8) to 0 (step S8) and proceeds to step S9.

[0058] After step S9, the processor 4 determines that the rotational speed ω is equal to the speed threshold ω start It is determined whether or not the value exceeds the limit (step S10). If it is determined to be "No" in step S10, the processor 4 returns to step S4.

[0059] Processor 4 repeatedly executes the loop of steps S4 to S10 with a time step Δt of wind condition data, while numerically integrating the equation of motion in equation (8) using Euler's method. Note that numerical integration may be performed using methods other than Euler's method.

[0060] If the result in step S10 is "Yes", then processor 4 determines whether n=N or not (step S11). If the result in step S11 is "No", then processor 4 adds 1 to n (step S12) and returns to step S3.

[0061] If the result in step S11 is "No", then processor 4 determines whether m = M (step S13). If the result in step S13 is "No", then processor 4 adds 1 to m (step S14) and returns to step S2.

[0062] If "Yes" is determined in step S13, the processor 4 estimates the startup time of the floating-axis wind turbine 100 (step S15). Specifically, the processor 4 numerically integrates the equation of motion in equation (8) over time and calculates the velocity threshold ω start The time when this value is exceeded is estimated as the start time. In step S15, for each initial rotational speed ω0 from n=1 to N, and for each static mechanical loss torque T from m=1 to M, Mech0 Each startup time is estimated. Additionally, since the initial time t0 is set to 0:00, 6:00, 12:00, and 18:00 each day using a year's worth of continuous wind condition data, a statistical value of the startup time using a year's worth of wind speed data is obtained.

[0063] [Regarding the calculation results] Next, we will explain the calculation results using the startup time estimation method. Figure 7 shows an example of calculation results using the startup time estimation method. Specifically, Figure 7 shows the calculation results when the startup time estimation method was applied to a 20kW class floating-axis wind turbine. In particular, Figure 7 shows the startup time on the horizontal axis and the cumulative distribution function (CDF) on the vertical axis. Figure 7(a) shows the case where the initial rotational speed ω0 is 0 rad / s and the static mechanical loss torque T is... Mech0 The relationship between startup time and CDF is shown for values ​​of 0, 20, 40, 60, 80, and 100 Nm. Figure 7(b) shows the static mechanical loss torque T Mech0 The relationship between startup time and CDF is shown for cases where the torque is 100 Nm and the initial rotational speed ω0 is 0, 0.1, 0.2, 0.3, 0.4, or 0.5 rad / s.

[0064] In Figure 7, the gentler the curve showing the relationship between startup time and CDF, the longer the startup time, and the slower the floating-axis wind turbine 100 takes to rotate. In other words, as can be seen from Figure 7, the static mechanical loss torque T Mech0 It was confirmed that the smaller the value and the larger the initial rotational speed ω0, the shorter the startup time tends to be. In particular, static mechanical loss torque T Mech0 This has a significant impact on the startup time, and the static mechanical loss torque T Mech0 The goal is to minimize this. Furthermore, if an acceptable startup time can be defined, the startup rate (for example, guaranteeing 95% startup in 10 hours (Figure 7(a))) can also be set.

[0065] According to the embodiment described above, the following effects are achieved. In the startup time estimation method according to this embodiment, the processor 4 numerically integrates the equation of motion for the rotation of the floating-axis wind turbine 100 over time and estimates the point in time when the rotational speed exceeds a specific cut-in wind speed as the startup time of the floating-axis wind turbine 100. Therefore, according to the startup time estimation method of this embodiment, the startup time of the floating-axis wind turbine 100 can be easily estimated. When matching the specifications of the wind turbine with the installation site, wind power generation operators can use the startup time estimated in this way to predict the expected values ​​of the operating rate and capacity factor, and carry out appropriate design.

[0066] (Other embodiments) While embodiments for carrying out the present invention have been described so far, the present invention should not be limited to the embodiments described above. In the above-described embodiment, a floating-axis wind turbine 100 was adopted as the wind turbine according to the present invention, but it is not limited to this, and configurations in which the floating body 200 does not rotate, or fixed-bottom type wind turbines, etc., are also used, including friction loss torque T Fric A configuration in which this value is 0 is acceptable. Furthermore, a horizontal-axis wind turbine may be used instead of the vertical-axis wind turbine 300.

[0067] Figure 8 is a flowchart showing a modified example of the embodiment. In the above-described embodiment, the initial rotational speed ω0 for each n=1 to N, and the static mechanical loss torque T for each m=1 to M are Mech0 While the startup time was estimated for each operation, it is not limited to this; it also depends on a specific initial rotational speed ω0 and a specific static mechanical loss torque T. Mech0 A configuration that estimates the startup time corresponding to this can be adopted. If this configuration is adopted, the flowchart for the startup time estimation method will be the flowchart shown in Figure 6, with steps S1, S2, and S11-S14 omitted (Figure 8). [Explanation of Symbols]

[0068] 1. Startup time estimation device 2 Input section 3 Storage section 4 processors 100 Floating Axis Wind Turbines 200 floating bodies 300 vertical axis wind turbine 301 Rotation axis 302 Blade 303 Support arm 400 Support bearing

Claims

1. A startup time estimation method performed by the processor of a startup time estimation device, The aforementioned processor, A method for estimating the startup time of a wind turbine, which involves numerically integrating the equation of motion for the rotation of a wind turbine over time and estimating the point in time when the rotational speed exceeds a specific cut-in wind speed as the startup time of the wind turbine.

2. The aforementioned processor, The method for estimating the startup time according to claim 1, which involves numerically integrating the equation of motion over time using wind condition data relating to wind speed at the wind turbine installation site observed over a specific period in the past, and wind condition data created artificially, to obtain a statistical amount of the startup time.

3. The aforementioned processor, The startup time estimation method according to claim 1, wherein the equation of motion is numerically integrated over time using the initial rotational speed of the wind turbine which has been set in advance.

4. The aforementioned processor, The startup time estimation method according to claim 1, wherein the moment of inertia of the wind turbine is I, the rotational speed of the wind turbine is ω, time is t, and the rotational torque of the wind turbine is T, and the equation of motion in the following equation (1) is numerically integrated over time. [Math 1]

5. The aforementioned wind turbine, This is a floating-axis wind turbine in which a floating body that floats on the ocean and a vertical-axis wind turbine are rigidly connected and rotate relative to a support bearing. The aforementioned processor, A method for estimating the start-up time according to claim 4, which calculates the rotational torque T based on the driving torque of the vertical-axis wind turbine, the frictional loss torque in the floating body with respect to seawater, and the mechanical loss torque generated in the support bearing that maintains the posture of the generator connected to the transmission system that transmits rotational force from the floating body and the vertical-axis wind turbine to the generator and the mooring line when the floating body and the vertical-axis wind turbine rotate relative to the support bearing.

6. A startup time estimation program to be executed by a computer, The startup time estimation program instructs the computer to perform the following: A startup time estimation program that numerically integrates the equations of motion for the rotation of a wind turbine over time and estimates the point at which the rotational speed corresponding to a specific cut-in wind speed is reached as the startup time of the wind turbine.

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