Comparison of the Wind Speed Estimation Algorithms of Wind Turbines Using a Drive Train Model and Extended Kalman Filter

Abstract

To compare and validate wind speed estimation algorithms applied to wind turbines, wind speed estimators were designed in this study, based on two methods presented in the literature, and their performance was validated using the NREL 5MW model. The first method for wind speed estimation involves a three-dimensional (3D) look-up table-based approach, constructed using drive train differential equations. The second method involves applying a continuous–discrete extended Kalman filter. To verify and compare the performance of the algorithms designed using these different methods, feed-forward control algorithms, available power estimation algorithms, and a linear quadratic regulator, based on fuzzy logic (LQRF) control algorithms, were selected and applied as verification means, using the estimated wind speed as the input. Based on the simulation results, the performance of the two methods was compared. The method using drive train differential equations demonstrated superior performance in terms of reductions in the standard deviations of rotor speed and electrical power, as well as in its prediction accuracy for the available power.

1. Introduction

The control algorithm of a wind turbine plays a crucial role in determining its operational performance. Control algorithms can be classified into the two following types: power control and load reduction control. Power control can be further divided into generator torque control and blade pitch control, depending on the type of control command signal. Generator torque control refers to the maximum power point tracking (MPPT)-based torque command adjustment to produce maximum power in the operating region with wind speeds lower than the rated wind speed, known as Region II. Blade pitch control, on the other hand, refers to the pitch angle command adjustment to maintain the rated rotor speed and power in the operating region with wind speeds higher than the rated wind speed, known as Region III [1,2,3]. Load reduction control is a control strategy aimed at reducing thrust and moments acting on the wind turbine, and algorithms based on it can be designed through the application of additional control logic for specific purposes [4]. Recently, control strategies that consider the dynamic behavior of the wind turbine drive train have been introduced, addressing issues related to fatigue damage in wind turbines [5]. Typically, wind turbine control algorithms include basic power control algorithms supplemented with classical single-input–single-output (SISO) control algorithms, such as proportional (P), proportional–integral (PI), and proportional–integral–derivative (PID) control techniques, for objectives including vibration or load reduction. Additionally, modern multi-input–multi-output (MIMO) control algorithms have been proposed to improve the performance of multi-loop SISO-based classical control logic [6,7,8,9,10,11,12,13,14,15,16,17]. Classical control-based vibration and load reduction techniques include drive train dampers [4], feed-forward control algorithms [6,7,8], individual pitch control algorithms [9,10], peak shaving [11], and tower dampers [12]. Modern control techniques based on MIMO algorithms include optimal control [14,15] and robust control [16,17].

Some classical control-based algorithms with SISO, as well as modern control algorithms, utilize wind speed obtained through wind speed estimation algorithms as essential parameters [13,14,15,16]. Wind speed estimation algorithms for wind turbines refer to algorithms that estimate the equivalent wind speed acting on the current target wind turbine, using parameters measured from the wind turbine and a simplified wind turbine model [8,18]. Wind speed estimation is generally performed via the wind turbine controller, and the estimated wind speed is used for various purposes depending on the algorithm; for instance, it can be used to calculate the available power at individual wind turbines for wind farm control, as parameters for feed-forward control algorithms to improve operational performance, and as one of the input parameters for modern control algorithms based on MIMO. The prediction accuracy of thusly estimated wind speed can influence control performance, necessitating research to investigate and improve prediction accuracy [19,20,21,22].

There are two primary methods for estimating wind speed within wind turbine control algorithms using measured parameters to integrate and apply wind turbine control algorithms. The first method is a 3D look-up table-based estimation method, constructed using the aerodynamic torque calculation formula and drive train differential equations, which estimates wind speed using generator torque, blade pitch angle, and rotor speed as inputs [8,18]. The second method employs an extended Kalman filter, designed based on a 3D wind field model and a nonlinear rotor model, as applied in the recently presented reference open-source controller (ROSCO) [23].

The drive train model-based estimation method has been applied as an input parameter in several control algorithm cases presented in the literature. Nam designed a wind speed estimation algorithm and a feed-forward control algorithm for a multi-MW wind turbine and performed a simulation based on a numerical model. The analysis results indicated that the feed-forward control algorithm effectively reduced the standard deviations of both rotor speed and generator output by approximately 50% [8]. Jeon designed an LQR controller based on fuzzy logic for the NREL 5MW model and conducted simulations using the Bladed program. Additionally, the same algorithm was applied to a scaled-down wind turbine model, and experimental verification was conducted in a wind tunnel. The experimental results showed that the standard deviations of rotor speed and generator output were reduced by approximately 36.39% and 38.94%, respectively [14].

In recent research on available power estimation for the application of wind farm control algorithms, a comparative analysis of various wind speed estimation algorithms based on simplified wind turbine models was conducted [18]. In this study, a wind speed estimation algorithm based on a drive train model was compared with a simpler model-based wind speed estimation algorithm that excludes the time derivative term of the drive train model. The comparison results indicated that the simpler model-based wind speed estimation algorithm is more advantageous for available power estimation.

Some of the literature has proposed Kalman filter-based methods that do not use the drive train model of wind turbines. Song et al. proposed a wind speed estimation algorithm using a non-standard extended Kalman filter to enhance wind turbine performance, confirming improved maximum power control performance through optimal tip speed ratio (TSR) tracking. According to simulation results, applying the proposed wind speed estimation algorithm to optimal TSR tracking control could increase annual energy production by approximately 0.8% [24]. Abbs et al. proposed a wind speed estimation algorithm based on the extended Kalman filter and applied it to a floating wind turbine control algorithm. Simulation results under average 11 m/s conditions indicated a root mean square error (RMSE) of approximately 0.48 m/s for estimated wind speed based on average rotor speed. The estimated wind speed was utilized for optimal TSR tracking control, torque control, and minimum pitch angle calculation for peak shaving, the application of which reduced rotor thrust in the Region II-1/2 area by approximately 20% [23].

As previously described, various studies have been presented in the literature on the application and validation of wind turbine controllers using either drive train model or Kalman filter-based estimated wind speeds. However, there is a lack of research comparing and validating the differences in wind speed prediction accuracy and controller performance between these two methods. There is a need for research that results in selecting the most suitable wind speed estimation method for control algorithms in order to enhance the operational performance of wind turbines.

Therefore, this study aims to compare the prediction accuracy of the drive train model-based wind speed estimation algorithm with that of the Kalman filter-based wind speed estimation algorithm, proposed in the literature for application in wind turbine control, and to compare their performance when applied to the same controller. Performance comparisons were conducted focusing on feed-forward control algorithms for classic control, available power estimation algorithms for pitch control, and the linear quadratic regulator based on the fuzzy logic (LQRF) control algorithm. The aforementioned algorithms, previously proposed in other studies, were applied and validated on the selected NREL 5MW model, specifically chosen for this research. The originality and contribution of this study, compared to existing research, can be summarized as follows.

Firstly, a quantitative comparison was conducted to assess the prediction accuracy of two representative wind speed estimation algorithms widely used in previous studies, the drive train model-based method and the Kalman filter-based method, both applied to the same wind turbine; this comparison enabled our determination of the preferable wind speed estimation algorithm.

Secondly, the performance comparison of these wind speed estimation algorithms not only evaluated their prediction accuracy, but also assessed their applications to control algorithms intended for actual wind turbines. The evaluation aimed to determine which method offers superior control performance through the application of control algorithms utilizing estimated wind speed as an input parameter; this included both classical and modern control algorithms, such as feed-forward control, available power estimation algorithms, and LQRF algorithms [8,13,14,15,16,19,20].

Thirdly, the Bladed program, a validated aeroelastic simulation tool typically used for wind turbine certification, was utilized instead of a simple Matlab-based wind turbine model to compare the control algorithms, which were implemented as external controllers in dynamic link library (DLL) format, and performance analysis was conducted under 3D turbulent wind conditions, simulating environments closely resembling those encountered by actual wind turbines.

2. Wind Turbine and Control Algorithm

2.1. Target Wind Turbine

The NREL 5MW model was selected as the target wind turbine for the design and performance verification of algorithms based on two wind speed estimation methods; designed by the National Renewable Energy Laboratory (NREL) for simulation research purposes, it was modeled using commercial software based on publicly available specifications [25]. Furthermore, we designed and applied feed-forward control algorithms, available power estimation algorithms, and LQRF control algorithms for performance validation of the wind speed estimation algorithms targeting the NREL 5MW model. As indicated in

Table 1. Specifications of the target wind turbine.

Specification	Unit	Value
Wind Turbine Type	-	HAWT, VSVP, Upwind
Rated Power	MW	5
Rotor Diameter	m	162
Hub Height	m	90
Rated Wind Speed	m/s	11.4
Rated Rotor Speed	rpm	12.1
Fine Pitch Angle	deg	0
Optimal Tip Speed Ratio	-	7.8
Max-Cp	-	0.48
Gear Ratio	-	1:97

, which presents its specifications, the NREL 5MW wind turbine is a large-scale turbine with a rated power of 5 MW, a rated wind speed of 11.4 m/s, and a rated rotor speed of 12.1 rpm [25].

2.2. Control Algorithm

The overall control algorithm of the target wind turbine consists of basic power control, feed-forward control, available power estimation, and wind speed estimation algorithms, with the LQRF control algorithm implemented separately. Figure 1 illustrates the schematic overview of the control algorithm, while Figure 2 shows the schematic overview of the LQRF control algorithm. The designed algorithms for the target wind turbine were structured as external controllers in DLL format and designed to interface with the Bladed program. The following section presents the design details of the feed-forward control, available power estimation, and LQRF control algorithms for verifying the performance of the wind speed estimation algorithm.

2.2.1. Feed-forward Control Algorithm

The feed-forward control algorithm adds additional pitch commands as feed-forward terms to the basic closed-loop pitch control of the wind turbine, aimed at reducing the standard deviations of rotor speed and output [8]. Typically, pitch control in wind turbines is used to maintain rated power output, even when wind speeds exceed the rated speed. In other words, pitch control calculates pitch commands based on generator speed to maintain rated power control by adjusting the generator speed. However, conventional pitch control based on generator speed fails to promptly respond to momentary changes in variable wind speeds. The feed-forward control algorithm addresses this limitation by compensating for instantaneous wind changes, rapidly adjusting pitch angles in response to wind variations. Figure 3 illustrates the schematic of the designed feed-forward control algorithm, indicating the use of rotor speed and estimated wind speed as control parameters. Rotor speed uses measured values as inputs, while estimated wind speed utilizes the output from the embedded wind speed estimator.

As shown in the figure, the feed-forward control algorithm calculates the feed-forward pitch angle command using the rotor speed and estimated wind speed. The feed-forward pitch angle command consists of compensation for pitch angle changes due to variations in wind speed and rotor speed, with each compensation value calculated based on the relationships among pitch angle, wind speed, and rotor speed. The required pitch angle change, $d{B}_{FF}$, to maintain rated power output for changes in wind speed, $dV,$ and rotor speed, $d{\Omega }_r,$ in a steady state is obtained with Equation (1) [8]. The feed-forward control algorithm was implemented by adding the feed-forward command to the pitch controller command of the target wind turbine, as shown in Figure 1.

$$d{\beta }_{FF}=\left({\displaystyle \frac{\partial \beta }{\partial V}}\right)dV+\left({\displaystyle \frac{\partial \beta }{\partial {\Omega }_r}}\right)d{\Omega }_r$$

(1)

2.2.2. Available Power Estimator

Available power refers to the maximum power that can be generated under given wind conditions, and an available power estimation algorithm is used to predict this value. Available power serves as a control parameter in situations for which turbine output needs to be intentionally reduced, such as control that generates less power than the planned output, and it is used as a parameter for upstream turbines in wind farm control strategies, including active induction control’s demanded power point tracking (DPPT) control [18,26,27]. DPPT control is one method of output control aimed at following output commands, operating based on a specific proportion of available power as the output command. Available power can be expressed as shown in Equation (2), where $C_p$ represents the power coefficient of the target wind turbine, adjusted to correspond to wind speed $V$ [18]. Standard air density is applied, and mechanical losses are set at 94.4%. The available power estimation algorithm is integrated into the control logic of the target wind turbine as an additional module, as depicted in Figure 1.

$$P_{avail}={\displaystyle \frac{1}{2}}{\rho }_{a}A{V}_{est.}^3{C}_p\left(V\right){\eta }_m{\eta }_e$$

(2)

2.2.3. Linear Quadratic Regulator Based on Fuzzy Control Algorithm

LQRF is a proposed algorithm for the optimal control of wind turbines through enhancing the traditional LQR control algorithm, which is vulnerable to uncertainties in the turbine’s state, by integrating fuzzy logic [14]. The target trajectories of LQR control, fuzzy logic, and gain scheduling are determined by the estimated wind speed, thus requiring high wind speed estimation accuracy. The time derivative of the state–space vector $\dot{x}$ can be expressed in terms of the matrices $A$ and $B$, the state–space vector $x$, and the input vector $u$. The output vector $\mathrm{y}$ can be represented as a relationship between the matrix $C$ and the state–space vector. Equation (3) represents the wind turbine in state–space form, with matrices $A$, $B$, and $C$ considered in the LQR control design. Equation (4) represents the state, input, and output vectors of the linear system, respectively. The inputs include the nacelle fore–aft displacement $d$, nacelle fore–aft velocity $\dot{d}$, rotor speed ${\Omega }_r$, pitch angle $\beta$, pitch rate $\dot{\beta }$, generator torque $T_g$, and the time integral of rotor speed. The outputs are the pitch angle command ${\beta }_{CMD}$ and the generator torque command $T_{CMD}$.

$$\begin{gathered} \dot{x}=A_{matrix}x+B_{matrix}u \\ \mathrm{y}=C_{matrix}x; \end{gathered}$$

(3)

$$\begin{gathered} x={\left[\begin{array}{ccc}d& \dot{d}& {\Omega }_r\end{array} \begin{array}{cc}\beta & \dot{\beta }\end{array} \begin{array}{cc}{T}_g& \int {\Omega }_{r}dt\end{array}\right]}^T \\ u={\left[\begin{array}{cc}{\beta }_{CMD}& T_{CMD}\end{array}\right]}^T; y={\Omega }_r \end{gathered}$$

(4)

The optimal state feedback gain for minimizing the objective function, provided in quadratic form of the output and input in Equation (4), can be obtained by solving the algebraic Riccati equation [13]. Additionally, fuzzy logic was applied for the purpose of interpolating nonlinear systems and control inputs. As shown in Figure 1, the LQRF control algorithm was applied to the target wind turbine control algorithm, replacing the existing power control algorithm to perform power control. Detailed information on the design of the LQRF control algorithm can be found in the literature, published through previous research [14].

3. Wind Estimation Algorithms

3.1. Method Based on Drive Train Model for Wind Estimation

One method for estimating wind speed involves applying the estimated wind speed using a 3D look-up table. The input variables of the 3D look-up table are rotor speed, pitch angle, and rotor torque. Rotor speed and pitch angle, used as input variables, are based on feedback from operational data. Additionally, rotor torque can be obtained through two methods, the first of which involves dividing the measured generator torque by the gear ratio; the second method involves calculating and applying aerodynamic torque, using the formula shown in Equation (5), where $J_r$ is the rotor inertia, $N$ is the gear ratio, $J_g$ is the generator inertia, $T_g$ is the generator torque, $B_r$ is the damping coefficient of the rotor shaft, $B_g$ is the damping coefficient of the generator shaft, and ${\Omega }_r$ is the rotor speed. For implementation of the simplified model without time derivative terms, $J_r$ and $J_g$ are assumed to be 0. Additionally, $B_r$ and $B_g$ are assumed to be very small and are considered as 0 in this study [3].

$$T_a=\left(J_r+N^2{J}_g\right){\displaystyle \frac{d{\Omega }_r}{dt}}+N{T}_g+\left(B_r+N^2{B}_g\right){\Omega }_r$$

(5)

3.2. Method Based on Extended Kalman Filter for Wind Estimation

Another method for estimating wind speed utilizes an extended Kalman filter proposed by NREL [21] and currently applied in ROSCO to calculate and provide estimated wind speeds. The extended Kalman filter leverages a covariance matrix based on the anticipated 3D wind field and defines a nonlinear rotor model to predict wind speed. For wind speed estimation, the nonlinear continuous time state–space model used in the continuous–discrete extended Kalman filter can be defined as shown in Equations (6) and (7). Here, ${\eta }_s$ represents system noise defined as white noise, and ${\eta }_{me.}$ denotes measurement noise assumed to be constant white noise.

$$x_k=f\left(x_{k-1}\right)+{\eta }_s$$

(6)

$$y_k=h\left(x_{k-1}\right)+{\eta }_{me.}$$

(7)

The wind speed estimation based on the extended Kalman filter proceeds through the steps outlined in Figure 4; this process is divided into state prediction, covariance prediction, Kalman gain computation, result prediction, and covariance error computation. In Step 1, state prediction of the nonlinear wind field model is performed, expressed as Equation (8), in which ${\widehat{x}}_k^{-}$ denotes the predicted value of $x_k$, which is subsequently used in the wind speed estimation step. In Step 2, the covariance error is predicted, expressed as Equation (9), where $P_k^{-}$ represents the predicted value of the error covariance $P$, used in the Kalman gain computation step$, J_f$ represents the Jacobian of the process, and $Q$ denotes the process noise covariance. In Step 3, the Kalman gain is computed, expressed as Equation (10), where $K_k$ represents the Kalman gain, $J_h$ denotes the Jacobian of the observation, and $R$ signifies the measurement noise covariance. In Step 4, the result based on previously predicted and computed values is predicted using Equation (11), where $\widehat{x}$ represents the predicted result; $Z_k$ denotes the measurement values including rotor speed, generator torque, and pitch angle; and $h$ signifies the rotor system model. Through the above-described steps, the final wind speed estimation is obtained, whereafter, in Step 5 the covariance error is computed, expressed as Equation (12). The computed covariance error is fed back to Step 1, iterating the entire process for each $k,$ as previously described [20,28,29]. In this study, we designed and applied the method described above to assess prediction accuracy based on different wind speed estimation methods.

$${\widehat{x}}_k^{-}=f\left({\widehat{x}}_{k-1}\right)$$

(8)

$$P_k^{-}=J_f{P}_{k-1}{J}_f^T+Q_{k-1}$$

(9)

$$K_k=P_k^{-}{J}_h^T{\left(J_h{P}_k^{-}{J}_h^T+R_k\right)}^{-1}$$

(10)

$${\widehat{x}}_k={\widehat{x}}_k^{-}+K_k(z_k-h({\widehat{x}}_k^{-}\left)\right)$$

(11)

$$P_k=P_k^{-}-K_k{J}_h{P}_k^{-}$$

(12)

4. Simulation Validation

The control algorithms of the target wind turbine, including the feed-forward control, available power estimation, LQRF control algorithms, and wind speed estimation algorithm, were designed using Matlab/Simulink (R2024b) and finalized in DLL format. The DLL format external controller was integrated with the Bladed dynamic simulation program for control performance verification. Bladed simulation, while less reliable than experimental validation, is a performance verification method that can be considered before applying control algorithms to actual wind turbines. Although it may differ slightly from real-world conditions, it is commonly used in research for verifying control algorithms. Figure 5 provides a brief overview of the procedural steps involved in the simulation utilized in this study, the process of which can be divided into control algorithm design, DLL file creation, and simulation using the Bladed program. Specifically, the Bladed simulation involved several detailed stages, including wind turbine modeling, wind condition setting, controller application, and analysis.

Figure 6 presents the comparison between the wind speed estimation results and the rotor mean wind speed under average wind speed conditions of 18 m/s and normal turbulence model (NTM) Class A. The rotor mean wind speed represents the equivalent wind applied across the rotor plane of the wind turbine, assumed as the reference value for comparison in this study. The black line denotes the rotor mean wind speed, the blue line shows the wind speed estimation results based on the 3D look-up table method, and the red line indicates the wind speed estimation results based on the Kalman filter method. Both wind speed estimation methods exhibit similar trends to the estimated wind speeds, and the validation of wind speed prediction was conducted by comparing mean wind speeds and standard deviation values.

Table 2. Comparison of rotor averaged wind speed and results of estimated wind speed.

Condition	Wind Speed [m/s, %]
	Mean	Error	Std.	Error
Rotor Averaged	17.80	-	1.94	-
DTM	18.26	2.58	2.05	5.67
EKF	18.29	2.75	2.01	3.61

quantitatively presents the rotor mean wind speed and wind speed estimation results under the condition of an average wind speed of 18 m/s. For the 3D look-up Table method, the errors in mean wind speed and standard deviation are approximately 2.58% and 2.75%, respectively; meanwhile, for the Kalman filter method, they are approximately 5.67% and 3.61%, respectively.

To compare the wind speed estimation algorithms, one algorithm each from SISO-based classical control, algorithms applicable to wind farm control, and MIMO-based modern control was selected and simulated. The following section presents the simulation conditions and results, and compares the performance results of the two wind speed estimation methods.

4.1. Validation 1: Feed-forward Control Algorithm

The dynamic simulation was conducted using the NREL 5MW model as the target wind turbine. The simulation conditions involved wind speeds higher than the rated wind speed (18 m/s) with a Class A standard turbulence model, and each condition was simulated for 600 s.

The results of performance verification on the feed-forward control algorithm using estimated wind speeds according to the wind speed estimation methods are shown in Figure 7. The simulation results display rotor speed, pitch angle, generator torque, and output values, where the solid black line represents the baseline output control algorithm, and the blue and red solid lines depict the simulation results of the feed-forward control algorithm with different wind speed estimation methods. While operational performance appears similar, differences in rotor speed and output standard deviations can be observed.

Table 3. Comparison of simulation results with the application of the feed-forward control algorithm.

Condition	Rotor Speed [rpm, %]				Electrical Power [MW, %]
	Mean	Diff.	Std.	Diff.	Mean	Diff.	Std.	Diff.
Baseline	12.10	-	0.2482	-	5.00	-	0.1035	-
DTM	12.10	0	0.2332	−6.04	5.00	0	0.0945	−8.70
EKF	12.09	−0.08	0.2431	−2.05	5.00	0	0.1015	−1.93

presents the comparison results of the means and standard deviations of rotor speed and generator output and confirms that the application of the feed-forward control algorithm improved operational performance compared to the baseline output control algorithm. With the feed-forward control using the 3D look-up table method, the standard deviations of rotor speed and generator output decreased by approximately 6.04% and 8.70%, respectively. For the Kalman filter method, these reductions were approximately 2.05% and 1.93%, respectively. According to the simulation results, the feed-forward control using the 3D look-up table method demonstrated slightly superior performance, indicating that, although the feed-forward control algorithm was applied identically, differences in wind speed estimation methods resulted in varying operational performance of the wind turbine. Therefore, since the accuracy of wind speed estimation can affect the control performance of wind turbines, it is necessary to choose a more accurate or suitable method.

4.2. Validation 2: Available Power Estimator

The simulation employing the available power estimation algorithm was conducted using the same model, under simulation conditions of wind speeds lower than the rated wind speed (8 m/s) with a Class A standard turbulence model. The analysis was performed for 600 s in a dynamic simulation environment with different wind speed estimation algorithms applied.

Figure 8 illustrates the results of the dynamic simulation, presenting rotor speed, pitch angle, generator torque, generator output, and available power. Additionally, Figure 9 displays a representation of generator output and available power. Available power functions as a function of estimated wind speeds, exhibiting trends similar to those of estimated wind speeds.

Table 4. Comparison of power output and available power using wind speed estimation method.

Method	Electrical Power (MW, %)
	Mean	Error	Std.	Error
Generator Power	1.9041	-	0.6533	-
Available Power-DTM	1.8930	−0.58	0.6799	4.07
Available Power-EKF	2.0429	7.29	0.7080	8.37

shows the comparison results between generator output and estimated available power, indicating mean errors of −0.58% and 7.29%, and standard deviation errors of 4.07% and 8.37%, respectively. Furthermore,

Table 5. Comparison of RMSE, MSE, and MAE for estimated available power.

Method	Electrical Power (MW)
	RMSE	MSE	MAE
Available Power-DTM	0.2061	0.0425	0.1672
Available Power-EKF	0.2332	0.0544	0.1818

presents the comparison results of root mean square error (RMSE), mean square error (MSE), and mean absolute error (MAE) between generator output and available power. The drive train model method shows lower RMSE compared to the Kalman filter method, and similar trends are observed in MSE and MAE. Specifically, for the drive train model method, the RMSE, MSE, and MAE values are 0.2061 MW, 0.0425 MW, and 0.1672 MW, respectively. For the extended Kalman filter method, the same values are 0.2332 MW, 0.0544 MW, and 0.1818 MW, respectively. The simulation results indicate a slight advantage of the drive train model method in estimating available power, additionally demonstrating that the accuracy of available power estimation varied depending on the applied wind speed estimation methods, leading to the conclusion that more accurate wind speed estimation is needed to improve the estimation accuracy for available power.

4.3. Validation 3: Linear Quadratic Regulator Based on Fuzzy Control Algorithm

The dynamic simulation was performed using the NREL 5MW model as the target wind turbine. The simulation conditions involved above-rated wind speeds (18 m/s) with a Class A standard turbulence model, and winds from different seeds were applied for wind estimation in the validation of the feed-forward control algorithm. Each condition was executed for 600 s in a dynamic simulation environment.

The results of the validation on the LQRF control algorithm using estimated wind speeds according to different wind speed estimation methods are shown in Figure 10. The simulation results depict rotor speed, pitch angle, generator torque, and output. The black line represents the simulation results of the LQRF control algorithm based on the drive train model method, while the red line denotes the simulation results based on the extended Kalman Filter method. Although operational performance appears similar, differences in the standard deviations of rotor speed and output can be observed.

Table 6. Comparison of simulation results with the application of the LQRF control algorithm.

Condition	Rotor Speed [rpm, %]				Electrical Power [MW, %]
	Mean	Diff.	Std.	Diff.	Mean	Diff.	Std.	Diff.
DTM	12.11	-	0.1104	-	5.00	-	0.0482	-
EKF	11.96	−1.24	0.1356	22.83	4.94	−1.20	0.0582	20.75

presents the comparison results of mean and standard deviation for rotor speed and generator output. Slight differences in operational performance can be observed depending on the applied wind speed estimation method. For the LQRF control algorithm using the drive train model method, the standard deviations of rotor speed and generator output are found to be 22.83% and 20.75% lower, respectively, compared to when the Kalman Filter method is applied. According to the simulation results, the performance of the LQRF control algorithm using the drive train model method appears relatively superior. According to the simulation results, although the same control algorithm was applied, the drive train model method showed greater reductions in the standard deviations of rotor speed and generator output, leading to the conclusion that the accuracy of the estimated wind speed is crucial, even when modern control algorithms are applied.

5. Conclusions

In this study, wind speed estimation algorithms employing two methods were designed for the NREL 5MW turbine. To validate the designed wind speed estimation algorithms, comparative verifications were conducted using the feed-forward control, available power estimation, and LQRF control. The first method is based on the drive train model, using measured rotor speed, pitch angle, and generator torque as inputs. The second method utilizes a continuous–discrete extended Kalman filter designed based on the Kalman filter.

To validate the algorithms, dynamic simulations based on the Bladed program were performed, and wind speeds estimated using the two different methods were compared. The comparison results indicated that the wind speed estimation performances were similar; however, considering the design phase of the wind speed estimator, the Kalman filter-based wind speed estimation involves a more complex process, due to the use of relatively more variables.

Firstly, according to simulation of the feed-forward control algorithm results, the algorithm based on the drive train model method reduced the standard deviations of rotor speed and output by 6.04% and 8.70%, respectively, while the Kalman filter-based feed-forward control algorithm reduced them by 2.05% and 1.93%, respectively. The reductions in standard deviation for rotor speed and output performance were relatively superior when the drive train model-based method was applied.

Secondly, additional simulations were conducted using the available power estimation algorithm. The results were evaluated using the means and standard deviations of generator output and estimated available power. The mean errors were −0.58% and 7.29%, and the standard deviation errors were 4.07% and 8.37%, respectively. Furthermore, according to the comparison of the RMSE, MSE, and MAE values, the drive train model-based method showed RMSE, MSE, and MAE values of 0.2061 MW, 0.0425 MW, and 0.1672 MW, respectively, while the Kalman filter method showed RMSE, MSE, and MAE values of 0.2332 MW, 0.0544 MW, and 0.1818 MW, respectively. The simulation results confirmed that the drive train model-based method exhibited relatively superior performance in estimating available power.

Lastly, according to the simulation of the LQRF control algorithm results, the LQRF control algorithm using the Kalman filter-based method showed higher standard deviations of rotor speed and output, by 22.83% and 20.75%, respectively. Therefore, the performance of the LQRF control algorithm using the drive train model-based method was relatively superior. This study’s results, although based on simulations, confirmed that applying different wind speed estimation methods led to varying performance outcomes for the target algorithms. It was found that the drive train model-based method had a more favorable impact on wind turbine control compared to the other method. Consequently, it was concluded that wind speed prediction accuracy must be considered to optimize wind turbine operational performance.

For future research, experimental validation is planned using the wind speed estimation algorithms verified in this study, applied to a 100 kW medium-sized wind turbine, currently under development for reliability- and accuracy-related improvements on the research findings. Additionally, expanding research on performance validation by applying the estimated wind speeds to other control algorithms will be pursued.