Design, Assessment, and Modeling of Multi-Input Single-Output Neural Network Types for the Output Power Estimation in Wind Turbine Farms

Abstract

The use of renewable energy, especially wind power, is the most practical way to mitigate the environmental effects that various countries around the world are suffering from. To meet the growing need for electricity, wind energy is, nevertheless, being used more and more. Researchers have come to understand that a near-perfect output power estimate must be sacrificed. Variations in the weather influence wind energy, including wind speed, surface temperature, and pressure. In this study, the wind turbine output power was estimated using three approaches of artificial neural networks (ANNs). The multilayer feed-forward neural network (MLFFNN), cascaded forward neural network (CFNN), and recurrent neural network (RNN) were employed for estimating the entire output power of wind turbine farms in Egypt. Therefore, each built NN made use of wind speed, surface temperature, and pressure as inputs, while the wind turbine’s output power served as its output. The data of 62 days were gathered from wind turbine farm for the training and efficiency examination techniques of every implemented ANN. The first 50 days’ worth of data were utilized to train the three created NNs, and the last 12 days’ worth of data were employed to assess the efficiency and generalization capacity of the trained NNs. The outcomes showed that the trained NNs were operating successfully and effectively estimated power. When analyzed alongside the other NNs, the RNN produced the best main square error (MSE) of 0.00012638, while the CFNN had the worst MSE of 0.00050805. A comparison between the other relevant research studies and our suggested approach was created. This comparison led us to the conclusion that the recommended method was simpler and had a lower MSE than the others. Additionally, the generalization ability was assessed and validated using the approved methodology.

1. Introduction

1.1. Background

The present surge in the use of renewable energy sources (RESs) to meet the world’s electrical energy needs and end the dire consequences of fossil fuels has made this a promising area for research into the development of new industrial innovations to overcome their many difficulties [1]. Operating safety will be an important priority for the entire energy industry soon because of the expanding incorporation of RESs [2]. Among the many RESs are solar, tidal, wave, geothermal, and wind energy. Of these, wind energy requires a few financial costs [3]. According to an Economics Times article that appeared on energyworld.com, China is the biggest wind energy user, with 221 GW of power, followed by the United States with 96.4 GW of output capacity, and then Germany with 59.3 GW [4]. With 35 GW of wind power produced, India is the second-highest wind producer in Asia and the fourth in worldwide production. Other notable nations that use wind energy include Brazil with 14.5 GW installed capacity, Spain with 23 GW established capacity, the United Kingdom with 20.7 GW, France with 15.3 GW, and Canada with 12.8 GW. Italy has an installed capacity of 10 GW [4]. However, atmospheric conditions such as wind speed, air temperature, surface pressure, and humidity directly affect power generation, system reliability, and performance.

These conditions are also critical for the control of the grid operator that must prioritize wind turbine substations, improve the entrance of electrical power into the grid, and foresee future energy requirements and issues [5,6]. Two options are used in various studies to preserve the utility grid’s performance indices within permitted limitations, depending on changes in the climate and violent interruptions of RESs in grid-connected or islanded modes [7]. At first glance, using large-capacity energy storage devices, such as batteries, escalates the initial cost of deployment and negatively affects the utility grid’s power quality. Secondly, the use of new energy storage components must be eliminated by creating accurate models for estimating energy output based on climate conditions [8]. Several ANNs are employed to estimate, evaluate, and moderate the negative effects of weather conditions on wind turbine generation power for the purpose of trying to estimate the maximum storage ability of the grid during the adoption rates of RESs, specifically wind turbine systems, and preserve the utility grid’s performance indices within achievable limits, model meteorological factors for minimizing the generation negative aspects, and estimate the output power [9].

1.2. Related Work

Numerous techniques and approaches implemented for wind turbine power estimation have been reviewed in several scientific publications. The wind power estimating approaches are categorized as probabilistic (also known as intermediate estimating), that delivers a range of potential outcomes at specific times, or deterministic (commonly known as point forecasting), which generates one output for a certain time horizon [10]. A comparative study of tree-based learning algorithms with a six-month forecast was presented in [11], where the average and standard deviation of the wind speed were used to train various models. These models performed excellently in estimating wind power. In-depth examinations of the latest probabilistic wind power estimation techniques have been published in [12], where the LSTM model was employed to anticipate wind turbine power based on wind speed data which was used as input data. When estimating the wind turbine power time series two days in advance, the LSTM model performed effectively and was most accurate when forecasting one-to-five-time steps ahead. In [13], the study provided a thorough analysis of the most recent developments in the estimation of wind power from the viewpoints of physical, statistical (time series and artificial neural networks), and hybrid techniques. It also examined variables that affect computing time and accuracy in computational estimation. The predestined power estimation was categorized in [14] regarding input data, estimation output, timescale, and forecasting method. Biblical weather records, involving wind direction and speed, pressure, temperature, humidity, and radiation detected at multiple heights and intervals, were generally employed as input data. Wind data created at lower heights can be extrapolated to the turbine height in instances where the necessary data at a wind turbine height are not available because of the lower height of the meteorological station anemometer towers [15]. The wind speed data at 20 m and 30 m was used as input data. Power density and empirical methods were found to be the most effective approaches for which the Weibull distribution fitted the real wind data, based on RMSE studies.

Deterministic wind power prediction techniques can be sorted into the five denominations of persistence, physical, statistically significant, machine learning, and hybrid methods [16].The estimated error is produced by using the Gaussian mixture model. This method resolves the gap between the actual, complex wind power forecasting error and the widely used Gaussian error assumption in many forecasting models. Statistical techniques use existing data usually operate well over a short period of time [17]. The results of estimation performance showed that the recommended approach outperformed other widely used techniques, involving Laguerre neural networks, hybrid Laguerre networks, and singular spectrum evaluation. Physical approaches often work effectively over long-term time horizons and are built on numerical models for weather forecasting [18]. Machine learning is the ability to identify features in data and make estimations based on those features [19]. In this paper, the accuracy of the proposed NARNN and NARXNN for wind speed estimation was improved via the following statistical indicators such as MAE, MAPE, and RMSE. The results indicated that the average value of NARNN (MAE 0.0082, MAPE 11.39%, and RMSE 0.86) had more potential than the average value of NARXNN (MAE 0.10, MAPE 15.40%, and RMSE 1.16).

Ultimately, hybrid approaches use scoring, selecting features or enhancement, subsequent processing, deconstruction, and other strategies to combine different forecasting methods to produce superior forecasts [20]. The meteorological data consisting of wind speed and ambient temperature were used as the inputs to the mathematical model [21] and the outcomes indicated that the suggested strategy could estimate the output wind power based on the wind speed and the temperature with a MAPE of 3.513%. A variety of methods for estimating wind speed including the long short-term memory (LSTM), discrete-time univariate econometric model, support vector machine (SVM), random forest (RF), decision tree (DT), multilayer perceptron (MLP), and convolutional neural network (CNN) were suggested in [22]. The same metallurgical data were used as inputs for the above approaches, the findings in this study demonstrated that the SVM algorithm improved cost time series estimating performance, whereas the Wind Net model outperformed the SVM, RF, DT, MLP, CNN, and LSTM architectures in terms of lower MAE and RMSE values. Wind power estimation has also made use of deep learning techniques consisting of neural and deep learning networks [23,24]. This study used historical meteorological data and the power generation outputs of a wind turbine from the Scada wind power station in Turkey to execute a temporal convolutional network (TCN); LSTM, RNN, and gated recurrence unit (GRU) methods were used in comparison. According to the experimental findings, the mean absolute percentage error (MAPE) wind power estimation was 5.13%. The TCN model performed better than the other three models in terms of estimate accuracy and data input volume.

In [25], machine learning algorithms were utilized to perform wind power estimation according to daily wind speed data. To determine whether the algorithms may produce outcomes that were as good as those in the trained place, the efficiency of the suggested method was tested in various areas. Results showed that the Random Forest (RF), extreme Gradient Boost (XGBoost), and Support Vector Regression (SVR) algorithms demonstrated adequate estimating ability for long-term daily total wind power [26]. Furthermore, in past research [27], machine learning (ML) techniques such ANN, SVM, most comparable neighbor search, and RF have been implemented for defect identification. The actual power output was calculated from the wind data generated via the numerical weather prediction. The average and standard deviation values of daily wind speed were used as input and the results presented the possibility of substituting the wind data collection method at the hub height to that of a substantially lower height, decreasing the cost of wind data monitoring [28]. A short-term wind power forecasting method constructed around a wavelet-based NN was published by Abhinav et al. [29] and was suitable for all seasons of the year. In [30], the authors focused on the application of machine learning techniques for indirect regression of wind power a year ahead of time. These algorithms depended on the daily mean wind speed and standard deviation, which were measured at a height of 10 m and extrapolated to a height of 50 m. Hosravi et al. [31], using data collected at 5 min, 10 min, 30 min, and 1 h intervals, investigated a multilayer feed-forward neural network, an assistance vector regression, and an adaptive neuro fuzzy interpretation system for 24 h ahead for indirect power estimation.

Because the NN can be generalized under many conditions, wind turbine power estimation based on its approaches was achieved in [32,33] and the results showed that the proposed approach can be used to learn the variances in wind power data more effectively and that a competitive performance was generated. The suggested ensemble approach has been carefully evaluated using actual wind farm data from China. Within the context of the TILOS (Technology Innovation for the local Scale) project in Horizon 2020 in [34] where a framework incorporating a solar power source, wind generator, and load demand has been researched, an advanced modeling system was built. They delivered an impartial forecast of load demand as well as the power of distributed generators (solar and water). For assessing load demand, the ANN and SVR methods were applied. The estimation model was assessed using descriptive examination criteria like the coefficient of determination and the oriented mean absolute percentage error; this study’s results indicated that the prediction models had exceptionally excellent performance and impressive anticipating adequacy. The restricted amount of monitored systems and relevant data allowed for assessment and forecasting of a geographical output power with the employment of upscaling methodologies. Furthermore, in many situations, the most significant drawback is a shortage of historical data accessible to train the ML algorithms [35]. VOLKMER et al. [36] presented the two-stage feature selection model as an essential component of the hybrid iterative forecasting method (HIFM). While the methods mentioned previously are straightforward and robust forecasting techniques that are achievable, most predictors are linear, therefore, the wind power output is nonlinear and irregular.

1.3. Challenge and Main Contribution

According to previous researches, wind speed and weather parameters data such as temperature and pressure are the main factors that influence the performance of regression. These factors can be improved by combining different machine learning (ML) approaches, taking into consideration variables like training error, input layer size, and the ability to generalize ML techniques, particularly NN systems, under multiple scenarios. The main challenge was to design and develop a model with less inputs to reduce the complexity of the model. Furthermore, the error or the mean squared error should be very small, therefore the method should correctly estimate the power of the wind.

In this study, evaluation, verification, and contrast of multiple ANN models applying distinctive training datasets were analyzed. This study also assessed the regression score of the several ANN types using validated data on wind speed and meteorological variable data (temperature and pressure) as inputs of wind turbine power. Three different types of NNs (MLFFNN, CFNN, and RNN) were used to estimate the output power of the Gabal El-Zeit wind turbine farm located in the North-Eastern Desert, on the western coast of the Suez Gulf, Egypt, as presented in Figure 1 [37] and

Table 1. Description of the study area [38].

Study Area Location
Location	Gabal El-Zeit, Red Sea, Egypt
Latitude	28.009 N
Longitude	33.32 E

[38] under various weather variables (temperature, pressure, and wind speed). The dataset was collected in the period from 31 October 2023 to 31 December 2023) (62 days) [39]. The training of the three ANN types was validated, and the training approach was executed with acquired data of 50 days from the Gabal El-Zeit wind turbine. The training-error (TE) and mean squared error (MSE) metrics were used for examining the three ANN types and training procedures. Other distinct data (12 days) were used to assess the three trained ANN algorithms’ capacity for generalization and regression. From the training data that was applied, the outcomes indicated how well the three ANN approaches were trained, as evidenced by their extremely low TE and MSE values. Furthermore, they could generalize across numerous scenarios and datasets. As a result, the three trained ANN models estimated wind turbine power and other weather factors, such as temperature and pressure, as well as wind speed. A contrast to the outcomes of the three different trained ANN types and other approaches is emphasized in recently released studies.

The subsequent sections of the present study are laid out as follows: Section 2 delivers an equation for determining the wind turbine’s output power. The suggested model architecture as well as the design and equations of the three NN techniques is presented in Section 3. Section 4 presents the results from two different stages; the first stage is the training and testing of the NNs’ models, and the second stage is the generalization ability and effectiveness of the NNs’ models. Comparison with earlier research and discussion between the employed NNs and other recently published papers is displayed in Section 5. Section 6 presents the conclusion of this study.

2. Wind Turbine Power Calculation

Three metrics that describe a wind turbine’s efficiency that fluctuates with wind speed are power, torque, and thrust. The rotor’s power is determined by the total amount of energy it detects, the gearbox’s capacity determines its torque, and the rotor thrust greatly affects the tower’s skeletal design. A wind turbine generates power by harvesting the energy of moving air. The physical definition of kinetic energy is [40]:

$$KE=0.5m{V}^2$$

(1)

where $m$ is the mass of air and $V$ is the wind velocity ($m/s$).

In contrast, power can be described as the quantity of kinetic energy per unit of time.

$$P=0.5\frac{dm}{dt}{V}^2$$

(2)

$$\frac{dm}{dt}=\rho S_{a}V$$

(3)

where $\rho$ is the air density, $S_a$ is the swept area of blades, $\mathit{r}$ is the rotor radius (40$m$) and $(S_a=\pi r^2$).

A wind turbine needs some wind to flow out of the back to function. The turbine’s blades will not rotate if it harvests all the wind energy because there will not be sufficient wind for it to absorb. For this reason, the maximum volume of air that a wind turbine may produce is limited. The Betz Limit is the maximum value of power coefficient$C_P$.

The following equation demonstrates how the factors of air density, power coefficient, and turbine-swept area influence the extracted energy [40].

$$P=0.5\rho C_P{S}_a{V}^3$$

(4)

The tip speed ratio and blade pitch angle both influence the turbine’s power coefficient ($C_p$). The superior value (0.48) of power coefficient was used in this study [41]. The air density is delicate to surface temperature and pressure. The mathematical representation of wind density is affected by temperature and air pressure is shown as the following equation [42]:

$$\rho \left(p_r,T\right)=\frac{p_r}{287.06T}$$

(5)

where $p_r$ is the air pressure, $T$is the surface temperature.

In this paper, we proposed an easy method to estimate the power of the wind turbine compared via the mathematical equations presented in Equations (1)–(5). We designed three models of ANNs to estimate directly the power of the wind by knowing their inputs which were the wind speed, surface temperature, and pressure. ANNs do not need rules to be created earlier or complex equations, they just require input data and output data that is calculated from the previous Equations (1)–(5).

3. The Suggested Structure of ANN Approaches

The model of neural network schemes has three inputs: wind speed, surface temperature, and pressure, while the output is the wind turbine output power. Three different types of neural networks based on the multi-input single-output modeling of the system to estimate the output power of wind farm.

It is evident from Equations (4) and (5) that the power output of a wind turbine was precisely estimated by establishing the instantaneous wind speed, surface temperature, and pressure as an input of NNs, which were collected from study area in this work. The machine learning algorithms implemented in this study for assessing wind power as an output of NNs are briefly described as follows and the architecture of suggested models is presented in Figure 2. The primary goals of the NN structure were to achieve excellent performance represented by an extremely small TE and MSE (approximate zero).

The proposed technique was developed by using the three suggested NN algorithms as shown in Figure 3 that can be categorized into the following stages:

• Procuring the true wind turbine data, including wind speed, pressure, and surface temperature from the Gabal El-Zeit wind farm.
• The deficient parameters were created, and the data were arranged using the data cleaning technique.
• The process-oriented strategy for ANN algorithms (MLFFNN, RNN, and CFNN) comprised validation process as well as processes for testing and training.
• Demonstrating data

3.1. Designing of MLFFNN

The MLFFNN design comprised three layers: the input layer, which stored wind speed, temperature and pressure as its inputs; the nonlinear hidden layer (which used a tangential hyperbolic stimulation function); and the output layer, which established the output power (P′) as presented in Figure 4. Equation (3) shows the estimated power as well as the actual power produced by the wind turbine power plant (P) contrasted to each other [43]. In

Table 2. The primary benefits and drawbacks of the MLFFNN.

Parameter	MLFFNN
Advantages	For optimizing the control parameters, the MLFFNN completed online training [44].
	Robust neural networks resembling MLFFNN are simply and effectively implemented in many different types of problem fields [45].
	Compared to other networks, they can obtain superior classification results with much stronger networks for classification issues [46].
	In multiple scenarios, MLFFNN operates successfully [47].
Disadvantages	Several input target combinations are needed for this kind of network throughout the training phase [47].

, the primary benefits and drawbacks of the MLFFNNs are listed.

$$O_j={\varphi }_j(h_j)={\varphi }_j({\sum }_{i=0}^3{w}_{ji}{I}_i)$$

(6)

where $I_i$ are the MLFFNN’s inputs $I_0=1,I_1=V,I_2=T,I_3=p$, $w$ is the weight between the input and the hidden neuron.

$${\varphi }_j(h_j)=tanh(h_j)$$

(7)

Equation (7) represents the activation function of hidden layers

The MLFFNN’s predicted power P′ is given by

$$P^{\prime }={\varphi }_k(0)={\varphi }_k({\displaystyle {\sum }_j^n{b}_{1j}{O}_j})=\tanh ({\displaystyle {\sum }_{j=0}^n{b}_{1j}{O}_j})$$

(8)

where, $b_{1j}$ is the weight between the hidden neuron $j$ and $P^{\prime }$ is the estimated output power provided by the MLFFNN

3.2. Designing of CFNN

While the layouts of CFNN and MLFFN are identical, each hidden layer in the network is connected to the input signal through a weight matrix [48]. The CFNN structure is displayed in Figure 5. The primary benefits and drawbacks of the CFNN are listed in

Table 3. The primary benefits and drawbacks of the CFNN.

Parameter	CFNN
Advantages	The input and output layers of CFNN are linked together immediately [49].
	In CFNN each neuron in the input layer is attached to each neuron in the
	Hidden layer and each neuron in the output layer [50].
	The adaptable nonlinear relationship between input and output provides the CFNNs’ efficiency [49].
Disadvantages	Throughout the training stage, this type of network requires several input target pairs [47] because it is like MLFFNN.

.

Through the exception of the first hidden layer in CFFN, each hidden layer in the network has two weight matrices that manage the input and output signals of the upper layer of the NN, respectively [51].

$$O_j={\displaystyle {\sum }_{i=1}^3{A}^i{w}_i^i{I}_i+A^o({\displaystyle {\sum }_{j=1}^k{w}_j^k{A}_j^h({\displaystyle {\sum }_{i=1}^n{w}_{ji}^h{I}_i}))}}$$

(9)

where $A^i$ is an input layer to output layer activation function, $I_i$ is input sample $I_0=1,I_1=V,I_2=p,I_3=T$, $w_j^k$ is the weight that passes from input layers to output layers, $A^o$ is an activation function of an output layer, and $A_j^h$ is an activation function of the hidden layers. Equation (7) is produced as a result of adding bias $w^b$ to the input layer and activation function for every neuron in the hidden layer $A^h$ [51].

$$O_j={\displaystyle {\sum }_{i=1}^3{A}^i{w}_i^i{I}_i+A^o(w^b+{\displaystyle {\sum }_{j=1}^k{w}_j^o{A}_j^h(w_j^b+{\displaystyle {\sum }_{i=1}^3{w}_{ji}^h{I}_i}))}}$$

(10)

When the CFNN is constructed, the training process can be completed. During the training process, the dataset is inputted into the network to produce the desired output. For beginning the training process, CFNN requires inputs, target result, weight, and bias as shown in the architecture.

3.3. Design of RNN

RNNs are neural models that have the ability to integrate data into their decision function [52,53]. The RNN, displayed in Figure 6, comprises at least one feedback loop, which distinguishes it from FFNN. In

Table 4. The primary benefits and drawbacks of the RNN.

Parameter	RNN
Advantages	A universal approximation property of RNNs allows them to achieve complex translations from input chains to output chains [53], which makes it possible for them to estimate unlimited nonlinear dynamical systems with indefinite precision [54].
	For creating attractions from input-output relationships, recurrent networks can be employed for associative memory [54].
	RNN is a dynamic neural network and computationally powerful. It has versatile models and applications for temporal processing [54].
Disadvantages	It is frequently challenging to determine the network stability because of the nonlinear nature of unit activation output properties and the weight adjustment procedures [44].

, the primary benefits and drawbacks of the CFFNNs are listed.

The output of hidden neuron $j$ found within the hidden layer of the NN is provided as [43]:

$$O_j={\varphi }_j(h_j)={\varphi }_j({\displaystyle {\sum }_i^3{w}_{ji}{I}_i}+{\displaystyle {\sum }_{n=1}^n{c}_{ji}{O}_n(k-1)})$$

(11)

where $I_i$ are the MLFFNN’s inputs $I_0=1,I_1=V,I_2=T,I_3=p$, $w_{ji}$ is the weight between the input and the hidden neuron and $c_{ji}$ is the weight between the input $O_n(k-1)$ and the hidden neuron j.

The activation function of the hidden layer is provided by

$$\varphi (h_j)=\tanh (h_j)$$

(12)

The prediction power that produced by RNN is shown as:

$$P^{\prime }={\varphi }_k(0)={\varphi }_k({\displaystyle {\sum }_j^n{b}_{1j}{O}_j})=\tanh ({\displaystyle {\sum }_{j=0}^n{b}_{1j}{O}_j})$$

(13)

where, $b_{1j}$ is the weight between the hidden neuron and is the estimated output power provided by the RNN.

The next part goes into details about the planned NN’s training strategy.

4. Results

This section presents the results from two different stages: the first stage was the training and testing of the NNs’ models, and the second stage was the generalization ability and effectiveness of the NNs’ models.

4.1. Results of the NNs’ Training and Testing for Wind Turbine Output Power

The NNs’ (MLFFNN, CFNN, and RNN) training was demonstrated by applying the use of the Levenberg–Marquardt (LM) technique. The characteristics of the LM algorithm are as follows:

• When compared to learning algorithms, LM learning needs to choose between the confirmed integration of gradient descent and the rapid learning speed of the traditional Newton’s method [54,55].
• Data can be processed quickly and easily by this algorithm [56].
• It can be considered as an approximation to Newton’s method and is a sort of second-order optimization algorithm with an excellent theoretical basis and extremely rapid implementation [57].

The three types of proposed neural networks were trained using data from wind turbine power plants in Egypt. The two months (62 days) comprising the dataset were detailed. The first fifty days’ worth (50 days) of data were used to train developed NNs, and the last twelve days’ worth (12 days) of data were employed for assessing the performance and generalization ability of the trained NNs. The dataset (wind speed, temperature, and pressure) that was used for training NNs (MLFFNN, CFNN, and RNN) is presented as Figure 7.

Table 5. The maximum, minimum, main, and standard deviation value of wind turbine inputs and output power.

Data	Main	Maximum	Minimum	Standard Deviation
Temperature (KV)	295.852	304.62	288.13	3.466112
Pressure (KPa)	99.711	100.4	99.07	0.2424
Wind speed (m/s)	4.951976	13.22	0.22	2.525675
Output Power (watt)	318,196.3	3,261,274	15.0867	434,720.7

presents the maximum, minimum, main, and standard deviation value of wind turbine inputs and output.

There were 1200 input-output pairings in the training set. A total of 70% of these data were adopted for training each type of NN, 15% were used for testing, and the last 15% was employed for the validation process. These processes were conducted on MATLAB software.

Table 6. The steps through the training and testing process.

Step	Behavior
1	Import the wind turbine data collection
2	Establish the design’s initial variables and choose the perfect number of hidden neurons.
3	Commence the process of training
4	When the training process is completed, check the MSE results to evaluate the NNs’ performance.
5	If the value of MSE is not satisfactory, start from step 2 and repeat the previous steps
6	If the value of MSE is satisfactory (very low), start the testing process of the NN and check the value of MSE.If the MSE value is very low(satisfactory), implement step 7If the value of MSE is high, start from step 2 again and repeat the same previous steps
7	Evaluate the NNs’ capacity for generalization by applying various data
8	The NN has the ability to estimate wind turbine output power.

lists the steps through the training and testing process. The structure of the three NNs from the MATLAB/SIMULINK program is presented in Figure 8.

After evaluating numerous initializations for the weights and number of hidden neurons, the technique of trial and error was implemented to determine the perfect parameters of the three constructed NNs that deliver a high level of efficiency;

Table 7. The perfect parameters of the three constructed NNs.

Features	MLFFNN	CFNN	RNN
Hidden neurons	40	15	10
Iteration	1000	1000	1000
Training time	35 s	36 s	2 min and 15 s
MSE	0.00017312	0.00050805	0.00012638
Training method	LM algorithm	LM algorithm	LM algorithm

contains a list of these specifications.

Figure 9 displays the MSE that emerged after the training of the designed NNs. The MSE obtained by training the anticipated RNN was more effective and lower than that of the other NN designs, as demonstrated by Figure 9. This meant that employing the RNN produced superior resolution and approximation, but the training time was longer than other NNs. Nonetheless, the MSE outcome of the MLFFNN and CFNN architectures was also low and acceptable. Note that the best validation efficiency is highlighted by the label in Figure 10. As seen in the figure, the NN with the lowest validation error epoch always produced the highest performance, or lowest MSE. The same collection of data used for the training phase was used to test the three trained NNs after the training was finished. Figure 11 displays the approximation error between the total output power from the wind turbine and the predicted total power by the three trained NNs. While utilizing the RNN, CFNN, and MLFFNN, the approximation error was close to zero as seen by the figure. Consequently, it may be argued that the NN had received comprehensive instruction and could accurately and efficiently predict the wind turbine output power.

It is visible in Figure 10 that when employing the RNN, the approximation error was better and lower than when utilizing other forms of NNs; in the case of using the CFNN as the higher one, it resulted in an approximation error.

Table 8. The absolute value of the approximation error (average, standard deviation, maximum, and minimum) of the trained MLFFNN, RNN, and CFNN.

Parameters	MLFFNN	CFNN	RNN
Mean absolute error (KW)	0.000180901	0.000668836	−1.02625 × 10−5
Standard deviation of absolute error	0.012832615	0.03484154	0.01168997
Maximum absolute error (KW)	0.0833	0.706595224	0.082086591
Minimum absolute error (KW)	−0.0849	−0.208697219	−0.078644149

displays additional instances of the absolute magnitude of this approximation error using the three trained NNs: average, maximum, minimum, and standard deviation (std.).

Figure 11 provides additional illustrations of the resolution and contrast between the estimated total power by the three trained NNs and the real total power from wind turbine. As presented in Figure 11, both their approximation and resolution were satisfactory and of superior quality. These outcomes corroborated the data demonstrated in Figure 10.

4.2. Results of the Trained NNs’ Generalization Ability and Efficiency

The present portion demonstrates the generalization capabilities and accuracy of the three trained NNs employing nontraining data that was different to the training data. The last of the accessible/collected data, which was the data for 12 days, was employed for this objective. In this instance, the inputs (temperature, wind speed, and pressure) to the NN are depicted in Figure 12. Figure 13 and Figure 14 compare and display the error between the predicted total power from the three trained NNs (MLFFNN, RNN, and CFNN) and the actual total power from wind turbine.

Table 9. The absolute error (averages, std., maximum, and minimum) values between the two total powers using the last of the accessible/collected data, which was the data for 12 days to demonstrate the generalization capabilities.

Parameters	MLFFNN	CFNN	RNN
Mean absolute error (KW)	−3.07958 × 10−5	0.002469069	0.000551047
Stander deviation of absolute error	0.012392692	0.019690275	0.011829579
Maximum absolute error (KW)	0.0483	0.050212881	0.051843358
Minimum absolute error (KW)	−0.0761	−0.170007531	−0.066207257

also shows the absolute error (averages, std., maximum, and minimum) values between the two total powers.

Table 9 and Figure 13 and Figure 14 demonstrate that there was a very excellent approximation between the predicted total power by the NNs and the true total power, and the variation between them was minimal. This indicated that under various data and environments, the three NNs were properly trained and capable of accurately and effectively forecasting the wind turbine output power. Additionally, the results proved that the trained RNN and MLFFNN performed better than the trained CFNN.

5. Comparison with Earlier Researchs

The suggested NN types were contrasted with other relevant earlier methods that are discussed in references [7,58,59,60]. This comparison aimed to clarify the influence of the NN in estimating output power under different conditions. The designed approach, the numbers of user inputs, the resulting MSE, and the examination of the generalization ability under various conditions, and additionally, the number of hidden neurons and epochs were all taken into consideration when establishing this comparison. As shown in

Table 10. The comparison of the suggested method for estimating wind turbine power with other previously published methods.

Paper	Year	NN Approaches	No. Inputs	MSE	Generalization Ability	Hidden Neurons	Epochs	Training Time
Currently suggested methods	2024	MLFFNN	Three inputs (Temperature, pressure, and wind speed)	0.000173	yes	40	1000	35 s
		CFNN	Three inputs (Temperature, pressure, and wind speed)	0.0050805	yes	15	1000	36 s
		RNN	Three inputs (Temperature, pressure, and wind speed)	0.00012638	Yes	10	1000	2 min and 15 s
KANNAN, S., et al. [58]	2023	RNN	Three inputs: Average Temperature, Minimum and Maximum Hourly Air Temperature	0.1041	No	Not mentioned	Not mentioned	28.84 s
		CNN	Three inputs: Average Temperature, Minimum and Maximum Hourly Air Temperature	0.1059	No	Not mentioned	Not mentioned	15.32 s
		LSTM	Three inputs: Average Temperature, Minimum and Maximum Hourly Air Temperature	0.0867	No	Not mentioned	Not mentioned	8.94 s
SHARKAWY, Abdel-Nasser, et al. [7]	2023	MLFFNN	Two inputs: Temperature and solar radiation	0.2753	Yes	50	42	16 s
		RNN	Two inputs: Temperature and solar radiation	0.6125	Yes	25	13	49 s
		NARXNN	Two inputs: Temperature and solar radiation	0.8873	Yes	70	50	9 min and 47 s
MADHIARASAN, Manogaran [60]	2021	MLPN	Five inputs: Wind Direction Temperature Relative Humidity, Precipitation of Water Content and Wind speed	2.0476 × 10−9	No	3	2000	Not mentioned
		RBFN	Five inputs: Wind Direction Temperature Relative Humidity, Precipitation of Water Content and Wind speed	2.9525 × 10−4	No	3	2000	Not mentioned
		Elman Network	Five inputs: Wind Direction Temperature Relative Humidity, Precipitation of Water Content and Wind speed	0.0012	No	3	2000	Not mentioned

, our suggested NNs approached Manogaran’s [60] record of the lowest results from MSE compared with the other two previous methods. This indicated that employing our suggested structures improved both the accuracy and the closeness between estimated and true power. While it was not stated and was not explored with others, the generalization ability under various scenarios and conditions was evaluated with our suggested approach by Abdel-Nasser, et al. [7].

Figure 15 shows the difference between suggested methods and the other approaches mentioned in Table 10 by displaying the accuracy percentage (%) that could be calculated by the difference between 100 and MSE% (100-MSE%). The accuracy of the NNs depends on the percentages of MSE. We can summarize the comparison of Table 10 and Figure 15 that the suggested method successfully accomplished the challenge of achieving high accuracy in power estimation under various condition with less volume of data inputs. Manogaran’s strategies, despite achieving good performance similar to the suggested model, was considered more complex as the large number of inputs data compared with suggested strategy.

6. Conclusions

To mitigate power outages and utility grid disturbances driven by changes in the environment, it is imperative to enhance the predictability of the NNs used for estimating and foreseeing wind turbine output power. Three trained ANN types (MLFFNN, CFNN, and RNN) were suggested in this work for establishing wind turbine power. As this implies, the surface temperature, wind speed, and pressure were the input for these NNs, and its output was the wind turbine power. Data for 62 days were gathered from actual wind farms in Egypt. The LM learning algorithm was employed to train the data from the first 50 days to the training procedure. The remaining data, which spanned 12 days, were employed to evaluate the trained NNs’ performance and capacity for generalization. The developed NNs produced excellent and adequate performance (extremely low MSE), according to the training procedure results. This indicated that the NN was capable of accurately and efficiently estimating the power generation of wind turbines. These outcomes indicated that, when compared to MLFFNN and CFNN, the RNN performed the best MSE (0.00126). When employing the intended CFNN, the MSE and approximation error were the highest (0.00508) when compared to the other NNs. The process of training outcomes was confirmed by results derived from assessing the trained NNs’ capacity for generalization using data that was not used during training. Each trained NN can operate with various datasets and circumstances. Furthermore, when compared to the other NNs, the trained MLFFNN and RNN executed most effectively, while the trained CFNN operated lowest. A comparison was created between our suggested strategy and other related research studies. We concluded from this comparison that the suggested approach had a low MSE and was more straightforward than the others. Also, the suggested approach was used to check and evaluate the generalization ability.