1. Introduction
The rotor effective wind speed (REWS), defined as the average wind speed on the rotor surface [
1], is useful for designing advanced control strategies of wind turbines [
2]. REWS can be estimated by the estimation methods that have been widely studied, such as power balance estimator [
3], extended-Kalman-filter-based estimator [
4], Kalman-filter-based estimator [
5], disturbance-accommodating control [
6], unknown input observer [
7], immersion and invariance estimator [
8]. Through these estimation methods, an accurate estimate of REWS has been achieved. However, the estimated REWS is only a reflection of wind speed information at this moment, and the advanced control algorithms relying on this estimated value fail to solve the contradiction between the slow response of rotor rotation and the rapid change of wind speed.
For such contradiction, some researchers have proposed predictive control methods, which can greatly promote the power production [
9,
10] and reduce the operational cost [
11] of wind turbines. Facing the difficulty in obtaining accurate previewed wind speed information with common measurements, the development of wind lidar measurement technology has promised a solution. Lidar is capable of proactively measuring wind speed within a certain range in front of the wind turbine, independent of the influence of aerodynamic shape and wake [
12], previewing wind information in advance [
13]. Since lidar can provide multi-point and multi-plane measurements with high accuracy, its measurement information could be used by the intelligent predictive control, improving the control performance of wind turbines. In this context, accurately predicting the REWS with lidar measurements is vital, but the relevant research is lacking.
The existing approach, mechanism modeling, generally estimates the effective wind speed on the virtual rotor surface first, and then deduces the REWS at the hub according to the Taylor frozen turbulence hypothesis [
14]. To be specific, the horizontal wind speed at different heights in front of the wind turbine can be obtained through lidar measurement. Then, the REWS on the virtual rotor surface can be calculated through the geometric relationship of the horizontal wind speed of each height. This method requires a quantity of multi-beam lasers to obtain an accurate REWS. Meanwhile, the influence of distance weighting and wind evolution is hardly modeled by the mechanism-modeling method [
15]. Thus, it is difficult to achieve a high-precision prediction of the REWS by the mechanism modeling method.
According to the best knowledge of the authors, data-driven methods have not fully been used in the prediction of REWS but have been well developed in wind speed prediction in the general space [
16,
17]. The data-driven method can realize reliable prediction through extracting mathematical relationships and nonlinear features hidden in historical data or samples [
18,
19]. This type of method mainly includes two parts: data extraction and prediction modeling. The former generally refers to data selection and information acquisition [
20], while the latter refers to algorithm selection and extrapolation prediction [
21]. Differently from general wind speed prediction, the prediction of REWS needs to establish a complex spatiotemporal mapping between inputs and output. Therein, the input information is the wind measurements at different heights in front of the wind turbine, and the output information is the REWS. This will weaken the correlation between input and output and increase the difficulty of prediction.
Motivated by the above discussions, this study attempts to build a data-driven model to predict the REWS using lidar measurement information and proposes a REWS prediction framework based on empirical mode decomposition (EMD) and gated recurrent unit (GRU) neural networks. EMD overcomes the problem of no adaptive basis function and can directly start decomposition without conducting advance analysis and research [
22]. GRU solves the problem of gradient disappearance by introducing a gating mechanism. With a simple structure, GRU can process large-size datasets and is widely used in complex time series prediction [
23]. Consequently, the prediction framework combined with EMD–GRU is expected to obtain high precision results of REWS.
Differently from wind speed prediction in the general space, the prediction of REWS based on lidar measurement information can use the multi-beam measurement information of lidar together with the mechanism-modeling knowledge of REWS. By combining the measurement information with the modeling knowledge, different prediction schemes could be designed. Thereby, three EMD–GRU schemes are proposed: one with mechanism modeling as the input, one with lidar data as the input, one with the combined input. Considering the influence of independent decomposition frequency from EMD, classification prediction based on GRU is carried out. To reduce the accumulation of prediction errors, the weighted aggregation based on an intelligent equilibrium optimizer (EO) is carried out. The innovations and contributions are as follows.
The novel data-driven prediction framework based on lidar measurement information is put forward to predict the REWS, enabling advanced predictive controls of wind turbines.
Three prediction models based on the proposed EMD–GRU prediction framework are designed and compared based on professional BLADED software V4.8.
The frequency classification and intelligent aggregation are presented to optimize the EMD–GRU models so as to reduce the prediction error and simplify the modeling complexity.
The remainder of this paper is constructed as bellow: the REWS calculation through lidar measurement is introduced in
Section 2; the EMD–GRU prediction schemes with three different inputs are thoroughly described in
Section 3; the results and discussions are provided in
Section 4. Finally,
Section 5 concludes the paper.
2. Lidar Measuring and REWS Calculation
The lidar for the control utilization is usually installed on the nacelle of the wind turbine. The lidar emits laser pulses into the atmosphere, receives the backscattering signals of atmospheric particles, and calculates the wind speed in line of sight at measuring point by analyzing the Doppler frequency shift of the emitted laser and the scattered laser. The lidar has a speed range of 50 m.
The REWS calculation can adopt the mechanism modeling, mainly including two aspects. For one thing, the horizontal wind speed at different heights in front of the wind turbine should be obtained through lidar measurement. For the other, the REWS of the virtual rotor surface should be calculated based on the horizontal wind speed of each height.
For the first aspect, the calculation of horizontal wind speed at different heights is shown in
Figure 1. In
Figure 1a,
and
respectively represent the wind speed measured by each laser beam, and the direction of wind speed is laser direction. Project
and
to obtain the horizontal wind speed at that height first.
Figure 1b takes
as an example to introduce the geometric relationship of the projection.
In
Figure 1, the projection of
on
can be described as:
where
represents the angle between the laser beam and the horizontal plane.
Similarly, the projection of on can also be described.
Thus, at the height of
and
, the horizontal wind speed perpendicular to the rotor surface is described as:
where
represents horizontal wind speed at that height, and
indicates the angle between
and
.
The horizontal wind speed at the height of and can also be obtained. Due to the scanning characteristics of lidar, this method can be extended to the calculation of horizontal wind speed at various heights.
For the other aspect, to calculate the REWS at a virtual rotor surface, it can assume that there is a virtual wind turbine at the wind speed measuring point. The area of the virtual wind turbine is subdivided into multiple horizontal sections, taking 5 parts as an example. See
Figure 2 for details.
Figure 2a shows the sector area, and
Figure 2b shows the REWS calculation.
The calculation for the sector area of the shaded part in
Figure 2 is as follow. According to
Figure 2b, the top (
) and bottom areas (
) of the circular area can be directly calculated by:
where
,
, and
represent the sector area, the radius of the rotor, and the height of the sector area, respectively.
To calculate the area of
, the areas
and
can be seen as a whole sector area, and the area of
can be subtracted.
where
represents the area of
.
The area
can be obtained using:
where,
refers to the REWS;
indicates the number of divided areas of the virtual rotor surface;
and
are the area and horizontal wind speed of the
zone, respectively;
refers to the gross area.
The above calculation of REWS only represents the effective wind speed faced by the virtual rotor at the measuring spot. To improve the calculation accuracy, the number of lidar measuring points should be increased. Otherwise, the prediction accuracy will be affected. Moreover, the influence of wind evolution is hard to include in the mechanism modeling.
3. EMD–GRU Prediction Schemes
The proposed data-driven prediction framework based on EMD–GRU is shown in
Figure 3, including three parts: the data processing based on EMD, the classification prediction based on GRU, and the weighted aggregation based on EO.
In the data processing phase, the EMD decomposition and delay processing are included. The input data are decomposed into intrinsic mode functions (IMF) and residual by EMD, and then time delay is processed for each decomposition part.
In the GRU predicting phase, each IMF component is divided into high-, medium-, or low-frequency groups according to its frequency characteristics. Together with the residuals, the four groups are predicted through the same GRU neural network. The GRU parameter is determined by EO.
In the aggregating phase, after optimizing the weight of each IMF and residual by EO algorithm, all the predicted values are aggregated to obtain the predicted REWS.
3.1. Data Processing Based on EMD
3.1.1. Determination of Input Data
In order to ensure a strong correlation between the input information and output REWS, three schemes with different inputs are proposed:
Scheme 1: there is only one input, that is, the wind speed measured by four laser beams is first processed through mechanism modeling, and then the calculated REWS is taken as the input of the EMD–GRU model.
Scheme 2: the input of the EMD–GRU model to predict the REWS is the wind speed measured by four laser beams.
Scheme 3: the wind speed measured by four laser beams and the REWS calculated by mechanism modeling are used as the input of the EMG-GRU model.
3.1.2. Empirical Mode Decomposition
EMD, as a flexible method for non-stationary and nonlinear data decomposition, shows better adaptability and usability compared to traditional decomposition methods (like Wavelet analysis). Complex wind speed input sequences can be decomposed using EMD to obtain components with different characteristic scales, which are more regular than the original input sequence. Although there are still different degrees of non-stationarity among these components, the difficulty of non-stationarity for prediction is reduced. Since EMD decomposition has a high signal-to-noise ratio, it can improve the prediction accuracy of REWS.
All the raw data sequences of the input are decomposed into sub-sequences by EMD. For the original wind speed series
X(
t) measured by lidar, through EMD decomposition, it can be described as the following equation:
where
denotes the decomposed IMF, and
is the residual of EMD.
3.1.3. Delay Processing
Since there is a certain distance between the measuring spot of lidar and the blade rotor, the decomposed input data cannot be directly put into the GRU neural network for prediction. Thus, it is necessary to consider time shift of the wind, and the Taylor frozen turbulence hypothesis [
24] is introduced to perform delay processing for each IMF. Time delay
under different average wind speeds can be calculated using:
where
represents the distance between the lidar measurement spot and the lidar, while
represents the average wind speed.
3.2. Prediction Modeling Based on GRU Neural Network
3.2.1. Frequency Classification Preparation
Due to insufficient sampling rate and spline interpolation, there are some frequency components in each IMF component spectrum that are independent of the target signals. If each IMF component is modeled, it will not only reduce work efficiency but also cause error accumulation and reduce prediction accuracy because of too many models.
Therefore, during frequency grouping, the sample entropy algorithm [
25] is used to calculate the entropy of each sequence of IMF to represent the complexity of each sequence. Firstly, the entropy values of IMFs under different average wind speeds are calculated. Then, at each average wind speed, the maximum entropy value is taken as the reference value. Finally, according to 1/5 and 1/10 of the maximum entropy value, all IMF subsequences are divided into three groups: high-, medium-, and low-frequency.
3.2.2. GRU Neural Network
GRU is a variant proposed by Greff et al. on the basis of long short-term Memory (LSTM), with simple structure and easy calculation [
23].
GRU contains two gating units, namely update gate
and reset gate
. The update gate controls the degree to which the state information
of the previous moment is introduced into the current state through activation function
, while the reset gate controls the degree to which the state information
of the previous moment is introduced into the candidate set through activation function
. The specific calculation formulas of GRU are as follows:
where
and
refer to input vector and output vector, respectively;
refers to candidate activation vector;
and
represent the parameter matrices and vectors, respectively.
3.2.3. EO Algorithm
EO is an optimization algorithm inspired by the physical phenomenon of dynamic balance of mass in control volume [
26]. Compared to other optimizers, EO has higher optimization efficiency and fewer iterations.
The main steps of EO optimization are as follows:
Step 1: Initialization and function evaluation.
where
is initial concentration;
and
are the lower limit and upper limit of variables to be optimized, respectively;
is the random vector between 0 and 1; and
is population number.
Step 2: Equilibrium pool and candidates (
).
where,
, respectively, are the optimal solutions found in the current iteration and are mainly used to improve the global exploration ability;
is the average value of the above four solutions and is mainly used to improve local development ability.
Step 3: Exponential term (
).
where
is a random number between 0 and 1; time,
, stands for the initial time; time,
, is defined as a function of iteration.
Step 4: Generation rate (
).
where
is the initial value and
indicates a decay constant.
Step 5: Update the solution (
).
where
is the control volume.
3.2.4. GRU Prediction Based on EO
It can be learned from
Figure 3 that four GRU neural networks are adopted in total. If the learning rate is set separately for each neural network, although the prediction effect can be improved, the process of adjusting the parameters will become complicated and the feasibility of the model could be reduced. Therefore, each GRU neural network sets the same parameters and uses EO to find the optimal learning rate.
The learning rate of GRU determines whether the fitness function can converge to the minimum, which is optimized by EO. The index RMSE taken as the fitness function of EO optimization is shown as Equation (20), in which refers to the prediction value of REWS obtained through the GRU neural network and refers to the actual REWS. In order to obtain , the four component quantities (including high-, medium-, and low-frequency groups as well as the residual) under all average wind speeds are used as the input of the GRU neural network, and the first 3/4 of the input is used for training.
The optimization process of GRU is shown in
Figure 4. First, according to Equation (13), particles are evaluated for their fitness function, and then Equation (14) is used to determine the equilibrium candidates and construct the equilibrium pool. If the fitness function has not yet converged or reached the number of iterations, loop Equations (14)–(17).
3.3. Aggregation Computing Based on EO
3.3.1. Aggregation Computing
Aggregation computing is conducted by:
where
is REWS, and
are weights of
(high-frequency group),
(medium-frequency group),
(low-frequency group) and
(residual), respectively.
There are always some errors when GRU predicts the components obtained through EMD decomposition. The prediction accuracy could be improved by optimizing the weight of the predicted values, which is performed using EO.
3.3.2. Aggregation Weight Optimization with EO
EO is used to determine the weight coefficients of each frequency group and residual. The evaluation indicator RMSE Equation (20) is taken as the fitness, where and refer to the aggregation computing value calculated from Equation (18) and the actual REWS, respectively. The minimum fitness function should be found in EO optimization.
The procedure of aggregation weight optimization with EO is shown in
Figure 5. First, after function initialization Equation (13), the result of aggregation computing Equation (18) is calculated. Both the aggregation result and the actual REWS are used to calculate the EO fitness. Then, the current balance pool state is determined according to Equation (14). After updating the exponential term Equation (15) and generation rate Equation (16), recalculate the current solution Equation (17) to find the next population of the weight. In the process of optimization, if the EO fitness converges, it indicates that the optimization is effective, and vice versa.
5. Conclusions
In this paper, a data-driven approach has been proposed to predict the REWS with lidar measurements. Three EMD–GRU schemes are proposed to improve the reliability of the REWS prediction. Accordingly, the main conclusions can be summarized as follows:
- ➢
Among three EMD–GRU schemes with different input, the prediction accuracy, stability, and effectiveness of Scheme 3 exhibit obvious superiority compared to those of the other two schemes.
- ➢
The EO and PSO algorithms could effectively optimize the prediction performance of EMD–GRU model, and the optimization effect of EO algorithm is better than that of PSO. The RMSE of the EMD–GRU model after EO optimization is reduced by 0.0592, which is about 0.03 lower than that of PSO.
- ➢
Compared to the traditional mechanism model and the single GRU model, the prediction performance of the proposed EMD–GRU model is significantly improved. Relative to the mechanism model, the EMD–GRU model demonstrates MAE improvements of 49.18%, 53.43%, 52.10%, 65.95%, 48.18%, and 60.33% across the six datasets.
Compared to some traditional models, the proposed EMD–GRU model, which includes data processing steps and neural network training processes, may require more computational resources and time to complete the prediction task. In real-time control applications, this method has some limitations and room for improvement. The future work focuses on using REWS prediction with lidar measurement to further optimize the control systems and achieve smarter and more sensitive control strategies to improve the performance and efficiency of wind turbines.