A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia

Citation: Habtemariam, E.T.; Kekeba, K.; Martínez-Ballesteros, M.; Martínez-Álvarez, F. A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia. Energies 2023,16, 2317. https://doi.org/ 10.3390/en16052317 Academic Editor: Michele La Rocca Received: 30 November 2022 Revised: 8 February 2023 Accepted: 20 February 2023 Published: 28 February 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article A Bayesian Optimization-Based LSTM Model for Wind Power Forecasting in the Adama District, Ethiopia Ejigu Tefera Habtemariam 1, Kula Kekeba 1, María Martínez-Ballesteros 2and Francisco Martínez-Álvarez 3,* 1Big Data and HPC Center of Excellence, Department of Software Engineering, Addis Ababa Science & Technology University, Addis Ababa P.O. Box 16417, Ethiopia 2Department of Computer Science, University of Seville, ES-41012 Seville, Spain 3Data Science & Big Data Lab, Pablo de Olavide University, ES-41013 Seville, Spain *Correspondence: [email protected] Abstract: Renewable energies, such as solar and wind power, have become promising sources of energy to address the increase in greenhouse gases caused by the use of fossil fuels and to resolve the current energy crisis. Integrating wind energy into a large-scale electric grid presents a significant challenge due to the high intermittency and nonlinear behavior of wind power. Accurate wind power forecasting is essential for safe and efficient integration into the grid system. Many prediction models have been developed to predict the uncertain and nonlinear time series of wind power, but most neglect the use of Bayesian optimization to optimize the hyperparameters while training deep learning algorithms. The efficiency of grid search strategies decreases as the number of hyperparameters increases, and computation time complexity becomes an issue. This paper presents a robust and optimized long-short term memory network for forecasting wind power generation in the day ahead in the context of Ethiopia’s renewable energy sector. The proposal uses Bayesian optimization to find the best hyperparameter combination in a reasonable computation time. The results indicate that tuning hyperparameters using this metaheuristic prior to building deep learning models significantly improves the predictive performances of the models. The proposed models were evaluated using MAE, RMSE, and MAPE metrics, and outperformed both the baseline models and the optimized gated recurrent unit architecture. Keywords: Bayesian optimization; deep learning; LSTM; time series; forecasting 1. Introduction Nowadays, reliable and sufficient energy is essential for human comfort. With the growing population and increasing energy-intensive industries, the demand for energy continues to rise. Renewable energy sources such as solar, geothermal, and wind energy have gained significant attention globally for their environmental benefits and contributions to the green economy [1]. Generating energy from renewable sources has become a promising solution to support sustainable economic growth and provide a healthier world for future generations [ 1 , 2 ]. Wind energy, in particular, is abundant and renewable, and its growth has the potential to reduce pollutant gas emissions from the use of fossil fuels [ 3 , 4 ]. The number and energy generation capacity of wind generation plants have increased annually as countries place a greater emphasis on renewable energy sources [ 5 ]. According to the World Wind Energy Association (WWEA), wind energy generation capacity has reached 650.8 GW globally. Ethiopia, in Eastern Africa, has the largest share of abundant renewable energy resources, including hydroelectric power, but has yet to fully tap into this potential. The potential for wind energy in Ethiopia is estimated to be about 1350 GW, with an annual installed capacity of approximately 1676 GW [6]. However, the integration of wind energy with a large-scale electric grid presents a major challenge due to the highly intermittent and nonlinear nature of wind power. Energies 2023,16, 2317. https://doi.org/10.3390/en16052317 https://www.mdpi.com/journal/energies Energies 2023,16, 2317 2 of 22 Additionally, wind power generation is greatly impacted by complex atmospheric factors such as wind speed, temperature, and air pressure, which can affect wind power generation and grid operation. To address this, accurate wind power forecasting is crucial for safely connecting wind power to the grid system and ensuring efficient grid operation [ 7 ]. Accurate forecasting of wind power generation helps keep the energy supply and demand in the grid system stable and is useful for appropriate wind farm site selection and making informed investment decisions [ 8 ]. However, the highly variable and intermittent behavior of wind power due to complex atmospheric variables makes wind power forecasting a difficult task. In recent years, the generation of time series data from sources such as sensors and smart meters has led to the availability of large volumes of data. Time series is a sequence of observations taken at defined time intervals, which could be hourly, daily, weekly, monthly, or yearly. Time series forecasting has been widely studied in many application areas, including finance, environment, energy, and climatology. Similarly, wind power forecasting depends on uncertain wind power time series data, and accurate wind power forecasting is essential for the planning and reliable execution of power systems to ensure a continuous supply [9]. Deep learning algorithms have become popular in various research fields, such as health care, natural language processing, time series forecasting [ 10 , 11 ], computer vision, and image recognition [ 12 ], due to their flexible structure and effective feature learning abilities. In the energy sector, deep learning algorithms have demonstrated exceptional performance in energy consumption and wind power forecasting. They effectively capture nonlinear time series and high-variation data, resulting in higher prediction accuracy for solar and wind energy compared to conventional methods [13–15] . Long short-term memory (LSTM) and gated recurrent unit (GRU) are two widely used deep learning algorithms in the field of wind power forecasting, energy consumption forecasting [16] , peak load forecasting, and fault identification [13]. Hyperparameter tuning is a critical aspect of deep learning and machine learning algorithms. Hyperparameters are configurable parameters that can be adjusted to achieve optimal model performance [ 17 ]. They determine the parameters of the model during training and have a significant impact on its predictive performance [ 18 , 19 ]. However, manual hyperparameter tuning can be difficult and the results may not be consistent [ 12 , 20 ]. Automatic optimization techniques, such as grid and random search, have drawbacks, including time-consuming for larger parameter sets and a lack of optimal discovery, respectively [ 21 ]. On the other hand, Bayesian optimization (BO) is an informed approach that uses a surrogate model to evaluate only the most promising models [ 12 , 22 ]. It computes the posterior distribution of the objective function using the Bayes theorem, allowing for fewer sampling points and faster computation time. Furthermore, optimizing hyperparameters while training deep learning algorithms, such as LSTM and GRU significantly improves their predictive performance [ 19 , 23 ]. Although numerous wind power forecasting models have been proposed [ 24 – 26 ], most of them have not utilized optimization strategies to reach desired performance levels. In other words, the use of BO in combination with LSTM models (BO-LSTM) is limited in enhancing wind power forecasting. Additionally, wind power forecasts are often specific to a single location, and the complexity and variability of wind power cannot be generalized across all sites. Thus, the aim of this paper is to apply BO to develop a robust wind power prediction model using LSTM. BO is a global optimization technique that can be used to optimize the hyperparameters of machine learning models. It uses a probabilistic model to guide the search for the global minimum by constructing a model of the objective function being optimized. Using BO with LSTM networks offers several benefits, including more efficient discovery of the optimal hyperparameter values compared to other optimization methods, such Energies 2023,16, 2317 3 of 22 as grid search or random search. This is particularly useful when training deep learning models, which can be expensive optimization problems. Another advantage of BO is its ability to handle complex and multimodal objective functions, which can arise when training LSTM networks. Unlike fixed search strategies such as grid search, Bayesian optimization uses a probabilistic model to guide the search, enabling it to handle complex optimization problems. In conclusion, the advantages of using BO with LSTM networks include increased efficiency in finding optimal hyperparameters, the ability to handle complex and multimodal objective functions, and applicability to expensive optimization problems, such as deep learning model training. In light of the information presented, the contribution of this paper can be summarized as follows: 1. Bayesian optimization (BO) was employed to identify optimal hyperparameters, such as the number of neurons and activation function, for the purpose of enhancing wind power forecasting. 2. The BO-LSTM model proposed in this paper was evaluated using real wind power data and found to outperform baseline methods in terms of statistical error metrics. 3. The paper presents a robust BO-LSTM model for day-ahead wind power forecasting, utilizing actual wind power data. 4. A wind power dataset was created for the first time in the Adama district of Ethiopia, following a comprehensive and arduous data collection process. The rest of this paper is organized as follows. Section 2provides a comprehensive overview of related works in the field. The methodology, including its theoretical foundations, the steps taken in data preparation, and exploratory analysis, is described in detail in Section 3. In Section 4, we present the results of our hyperparameter tuning efforts and engage in an in-depth discussion of the findings. Finally, the conclusion and suggestions for future work are presented in Section 5. 2. Related Works This section aims to review previous studies on wind power generation forecasting that employed machine learning and deep learning models. Various methods have been utilized to predict wind power production for the purpose of making the integration of wind power with the grid system easier and more effective [ 27 , 28 ]. These methods can be broadly categorized into: 1. Physics-based methods: This approach predicts desired variables using real-time atmospheric variables, such as temperature, pressure, surface roughness, and obstacles. However, it is computationally intensive and may not be suitable for shortterm forecasting tasks due to the high computation time and computing resources required [29,30]. 2. Traditional statistical methods: Autoregressive (AR), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) models are conventional statistical methods for time series forecasting, and they are effective in capturing linear mathematical relationships in time series data. However, their prediction accuracy decreases for longer forecast horizons, and they struggle to model complex seasonal patterns and exogenous variables [ 31 – 33 ]. Nevertheless, the combination of ARIMA and LSTM techniques has resulted in successful approaches in recent years [34]. 3. Machine learning methods: Machine learning is a data-driven approach that maps between dependent and independent variables and is widely used for classification and prediction tasks [ 29 ]. This category includes feed-forward neural networks, support vector regression (SVR), k-nearest neighbor, fuzzy neural networks, extreme learning machines, and others. For example, Ahmed et al. [ 35 ] proposed using gradient boosting machines (GBMs) and support vector machines (SVMs) to predict wind Energies 2023,16, 2317 4 of 22 power over medium to long-term time frames and found that the SVM model performed better with some computational run-time concerns. Another study proposed a wind turbine power generation prediction model using linear regression, k-nearest neighbor regression, and decision tree regression algorithms to predict one-minute time resolution data [ 36 ]. Shabbir et al. [ 37 ] used an SVM-based algorithm to predict wind energy production one day ahead, and they found that the proposed algorithms had better forecasting results with the lowest root mean square error (RMSE) values. However, conventional machine learning algorithms may struggle to capture temporal information effectively and produce more accurate forecasts for complex and nonlinear wind power data [ 38 ]. In [ 39 ], a method was proposed to predict power generation by exploiting wind speed data from different heights in the same area and achieved a 3.1% improvement in accuracy compared to the traditional support vector machine method. Gao proposed an approach based on grey models and machine learning for monthly wind power forecasting using data from China [ 40 ]. A hybrid model based on Laguerre polynomials and the multi-objective Runge-Kutta algorithm was proposed in [ 41 ] for wind power forecasting, and the effectiveness of the method was demonstrated using wind power data from a Chinese wind farm. Due to the focus of this paper, this section only reviews deep learning-based strategies for wind power forecasting. Wind power is a promising energy source that can help address current environmental issues. Accurate wind power prediction is critical for the stable and optimal operation of the electric grid in power systems. Many novel models have been proposed, such as [ 42 – 44 ]. Reference [ 45 ] proposes an efficient wind power forecasting model using an LSTM network. A hybrid model of a convolutional neural network and multilayer perceptron network was developed for day-ahead wind power generation forecasting in [46] . Reference [ 47 ] introduces a hybrid method for ultra-short-term wind power prediction, taking into consideration wind power, wind direction variables, and factors from the environment and turbine disturbance. Reference [ 48 ] proposes a hybrid of convolutional neural network and informer model to predict average wind power over a period of time, effectively extracting time series features and trend information using a 2-D convolutional neural network. Reference [ 49 ] uses a sparse machine learning technique to predict next-hour wind power by combining real-time observation data with data from physical model forecast results. Reference [ 50 ] proposes a new model to forecast the electricity production of wind farms in Manisa, Turkey, using a univariate sequence-to- sequence learning model, with promising results. The accurate prediction of wind power is important for stable and reliable power grid operation and effective integration of wind power into the electricity grid. A wavelet decomposition-based method was developed to improve the accuracy of wind power forecasting [ 51 ]. The role of wind speed forecasting in wind power generation is critical, and a hybrid model based on a GRU neural network and variation mode decomposition has been shown to effectively capture the intermittent and fluctuating behaviors of wind power [ 24 ]. LSTM is capable of accurately learning data patterns and providing results for longer temporal dependency data, such as monthly predictions [ 25 ]. A novel method based on an improved stacked GRU-RNN and multiple monitoring parameters has been used to reduce the complexity of the model, saving computational costs and requiring fewer training data [52]. RNN, a class of deep learning, is composed of sequence-based architectures that model the temporal correlation between past and current information [ 26 ]. LSTM networks, an improvement of RNN, have an internal state that can propagate data through multiple time steps, allowing them to effectively process time series data. Putz et al. introduced a novel model based on neural expansion analysis for time series wind power forecasting in [ 53 ]. This model outperforms other statistical and classical machine learning methods and requires little to no data preprocessing. Yu et al. proposed an improved LSTM forget-gate network in [ 45 ] that uses Spectral Clustering to enhance the model’s training speed and accuracy. Mishra et al. studied a comparative analysis of Energies 2023,16, 2317 5 of 22 five deep learning models including Deep Feed Forward, Deep Convolutional Network, RNN, Attention mechanism, and LSTM in [ 4 ]. Lin et al. used Temporal Convolutional (TCN) Network for wind power prediction in [ 54 ] and found that TCN outperforms LSTM, RNN, and GRU in terms of the data input volume, stability of error reduction, and forecast accuracy. Prema et al. proposed a wavelet decomposition-based prediction model with LSTM learning in [ 55 ] and found that wavelet decomposition improved the capture of the intermittent variations in wind data. Duan et al. developed a hybrid forecasting model using decomposition and two deep learning models in [ 29 ] and employed variational mode decomposition to extract local features of the data. A wind power prediction model based on deep learning feature extraction and genetic algorithms was proposed in [ 56 ]. A novel genetic LSTM framework was presented in [ 9 ] to predict short-term wind power and the LSTM structure’s window size and the number of neurons were determined by genetic algorithms. In [ 57 ], a deep learning-based approach was developed for modeling and prediction of wind turbine output power and was found to be more stable and robust compared to genetic algorithms and particle swarm optimization algorithms. Akash et al. conducted a study on long-term wind speed forecasting using machine learning and time series analysis, as reported in [ 58 ]. The results, based on evaluations of MAE and RMSE, indicated that LSTM outperformed ARIMA and the artificial neural network (ANN). In [ 59 ], a Bayesian-optimized artificial neural network was proposed to forecast hourly wind speed, with improved results over the ANN and SVM models as a result of the optimization strategy. Saini et al. in [ 60 ] proposed various machine learning algorithms to enhance wind speed forecasting and energy generation estimation. GRU performed exceptionally well compared to other machine learning approaches for the given dataset. In [ 28 ], Lin and Zhang presented a novel hybrid model for accurate wind speed prediction. 3. Materials and Methods This section discusses the theoretical framework, exploratory analysis, and data preprocessing approaches for the proposed study. In addition, model training along with hyperparameter tuning have been addressed in this section. After data refinement as discussed in Section 3.4, the data set was partitioned into a training set and a test set in which the training data contains the first three years (70%) and the test set contains the last year ( 30% ) wind power data in order to keep the importance time order. As the main part of the methodology of this paper, building the LSTM model on the training set by defining hyperparameter space and fine-tuning the model is implemented by using Bayesian optimization to search for the best hyperparameters combination with minimum loss values. Based on the optimal hyperparameter configuration, the proposed wind power forecasting model was trained on the wind power dataset of the three sites (groups) and the performance of each model was evaluated on the test dataset. Meanwhile, to ensure whether the proposed BO-LSTM outperforms other algorithms or not, different baseline models were studied with each dataset. The methodology of this paper is detailed in Figure 1. Energies 2023,16, 2317 6 of 22 Wind power Dataset Data Preprocessing Exploratory Analysis Data Transformation Validation set Training set Test set Train /Test Split Initialize Hyperparameters is lower MSE value? Build Model Train LSTM with Training and validation set Select optimal Hyperparameters Yes Update Hyperparameters Train LSTM Model on full data Model Testing Model Evaluation using MAE, RMSE and MAPE No Prediction Data reshaping Figure 1. Proposed methodology for wind power forecasting. 3.1. Deep Learning Architectures RNN is a type of deep learning algorithm commonly utilized in speech recognition, emotional analysis, and text analysis. Unlike deep feed-forward neural networks (DFFNNs), RNNs incorporate feedback loops and internal connections between hidden units. These internal connections enable RNNs to effectively use past data to predict future data [ 61 ]. As a result, RNN is capable of processing sequential data and identifying both short-term and long-term dependencies. It is particularly useful for time series modeling and forecasting of data with temporal correlations. Training of RNNs typically involves back-propagation through time to learn the temporal correlations in sequence data. However, RNNs can suffer from the vanishing gradient problem, where the stability of gradient propagation across time steps decreases, leading to an inability to learn long-term dependencies between inputs and predictions [ 62 ]. This occurs when the weight updates are proportional to the gradient, but small or vanishing gradients result in minimal changes to the weight values. LSTM and GRU were developed to address the limitations of RNNs by allowing for the learning and storage of longer sequence data, and effectively handling high volatility and seasonal variation in time series data. Energies 2023,16, 2317 7 of 22 3.1.1. Long-Short Term Memory Network LSTMs are better equipped to handle information with longer temporal dependencies and lag features in sequence data processing [ 63 ]. Unlike standard DFFNNs, which operate in a forward learning style, LSTMs have a specialized memory unit [ 64 ] to store previous operation values for use in dealing with temporally dependent data. LSTMs consist of a cell unit and gate modules, as illustrated in Figure 2[ 65 ]. The gates include a forget gate, an input gate, and an output gate, which regulate the flow of data into and out of the cell state during processing [ 66 ]. The input gate controls updates to the memory cell from the input and the forget gate decides which information to keep and which to discard [ 64 ], while the output gate determines the information to pass to the next state. LSTMs have been widely used in time series forecasting and have achieved remarkable performance [ 67 , 68 ]. Their main advantage lies in their memory cell, which serves as a specialized neuron structure for storing information over long time gaps [ 15 ]. The mathematical representation of the LSTM cell can be defined in Equations (2)–(6). ft=σ(wf×[ht−1,xt] + bf)(1) it=σ(wi×[ht−1,xt] + bi)(2) ˜ Ct=tanh(wc×[ht−1,xt] + bc)(3) Ct=ft∗Ct−1+it∗˜ Ct(4) Ot=σ(wo×[ht1,xt] + bo)(5) ht=Ot∗tanh(ct)(6) where ft , it , and ˜ Ct denote the forget gate, the input gate, and the candidate cell state, respectively; Ot represents the output gate; Ct and ht are the cell output at the current time t ; Ct−1 and ht−1 are the cell outputs at the previous time xt−1 , and xt is the input to the LSTM cell. wis the weight of neurons, and bis the bias for each weight. Figure 2. LSTM architecture. The LSTM network’s ability to learn more complex tasks is due to the use of nonlinear activation functions, namely the sigmoid function σ and the hyperbolic tangent function tanh . The sigmoid function is a nonlinear activation function that maps data to values between 0 and 1, while the hyperbolic tangent function maps data to values between − 1 and 1. The sigmoid and hyperbolic tangent activation functions can be expressed mathematically in Equation (7) and Equation (8), respectively. Energies 2023,16, 2317 8 of 22 σ(x) = 1 1+e−x(7) tanh(x) = ex−e−x ex+e−x=1−e−2x 1+e−2x(8) There are several advantages of using LSTM networks for wind energy forecasting compared to other methods: 1. Handling long-term dependencies: One of the main challenges in wind energy forecasting is capturing long-term dependencies in the data. LSTMs are particularly well suited for this task because they are designed to handle long-term dependencies by selectively forgetting or retaining information from previous time steps. 2. Handling non-linear relationships: Wind energy is affected by many non-linear factors, such as temperature, humidity, and pressure. LSTMs are capable of capturing non-linear relationships in the data, making them a good choice for wind energy forecasting. 3. Handling multivariate time series: LSTMs can handle multiple inputs, making them well suited for multivariate time series data, such as wind energy data, which often includes multiple sources of information. 4. Good performance: LSTMs have shown good performance in wind energy forecasting tasks, outperforming traditional time series forecasting methods, such as ARIMA and SARIMA. 5. Robustness to noise: LSTMs are less sensitive to noise in the data compared to traditional time series methods, making them a good choice for wind energy forecasting where data quality can be a challenge. Overall, LSTMs offer several advantages in wind energy forecasting, making them a popular choice among researchers and practitioners in the field. 3.1.2. Gated Recurrent Unit Neural Network GRU is a newer version of LSTM and is capable of learning temporal dependencies in data to avoid the long-term dependency-learning problems of RNN [ 69 ]. Compared to LSTM, GRU has a simpler architecture with two gates, the update gate and the reset gate, as illustrated in Figure 3. In GRU, there is no cell state and the update gate combines the input and forget gates. The update gate determines what information from the previous hidden state to bring into the current state [ 70 ] and decides the amount of previous information to be memorized in the current state. The reset gate determines the aggregation of the previous information with the current input [ 71 ]. The reset gate also decides which information to discard from the previous states. The reset gate controls the capture of short-term dependencies in the sequence data, while the update gate is responsible for activating and filtering the long-term sequence data. GRU has a faster training time due to its fewer parameters compared to LSTM. The mathematical representation of GRU operations can be defined as in Equations (9)–(12): rt=σ(Wr[ht−1,xt]) (9) zt=σ(Wz[ht−1,xt]) (10) ˜ ht=tanh(Wh[rt◦ht−1,xt]) (11) ht=(1−zt[rt◦ht−1,xt]) (12) where rt and zt are the reset and update gates, respectively, in a GRU operation. Additionally, x is the input vector, while ˜ ht and ht denote the candidate output and the output vector, respectively. Energies 2023,16, 2317 9 of 22 Figure 3. GRU architecture. 3.2. Bayesian Optimization The performance of machine learning algorithms, especially deep learning-based predictive models, can be improved through hyperparameter optimization. Grid search and random search are the most commonly used methods for finding the optimal combination of hyperparameters to produce more accurate models. However, the efficiency of grid search decreases with the increasing size of the number of hyperparameters, and its computational time complexity is high due to the exponential increase in the number of evaluations required with each additional parameter [ 19 ]. On the other hand, random search uses a combination of randomly sampled parameters based on a statistical distribution, which can be ineffective in finding optimal hyperparameter points for some complex models [ 72 ]. Bayesian optimization (BO) is an efficient strategy for solving computationally expensive functions without a closed-form expression [ 73 ]. It builds a probability model of the objective function to determine the optimal hyperparameters in an informed manner, reducing the number of times the objective function needs to be run by choosing only the most promising set of hyperparameters. The BO approach consists of two basic components: • Surrogate (probabilistic) model: BO is guided by Bayes’ theorem, and in each iteration, it uses a surrogate model to approximate the objective function, which can be sampled efficiently. A Gaussian process is the most effective surrogate model for selecting the promising set of hyperparameters to be evaluated in the true objective function [74] . The surrogate model estimates the objective function, which is used to guide future sampling. • Acquisition function: BO uses an acquisition function [ 75 ] to determine which points in the search space should be evaluated and to provide information on the optimal value of f . The purpose of the acquisition function is to use posterior information to find the best sample point in each iteration and to propose a new sampling point to identify the most promising set of hyperparameters to be evaluated next. The acquisition function balances exploitation and exploration. Exploitation involves focusing on the search space with a higher likelihood of improving the current solution based on the current surrogate model, while exploration is the strategy of moving towards less explored regions of the search space. BO solves problems by finding the parameters that minimize the objective function in a finite domain, with lower and upper bounds on every variable, as given by Equation (13) . x∗=argmin x∈Xf(x)(13) Energies 2023,16, 2317 16 of 22 Table 3. Comparison of six forecasting models on three Sites data. Data Models MAE RMSE MAPE (%) Site I ANN 0.1009 0.1310 0.916 XGBoost 0.1312 0.1664 1.3737 ARIMA 0.1939 0.2277 1.8680 LSTM 0.1070 0.1264 2.0642 BO-GRU 0.0651 0.0826 1.1470 BO-LSTM 0.0621 0.0793 1.1353 Site II ANN 0.1024 0.1307 2.4062 XGBoost 0.1489 0.1926 1.7796 ARIMA 0.1844 0.2214 2.2057 LSTM 0.1137 0.1399 1.1725 BO-GRU 0.0707 0.0910 1.1621 BO-LSTM 0.0708 0.0893 1.2275 Site III ANN 0.1440 0.1791 1.9741 XGBoost 0.1452 0.1878 1.6768 ARIMA 0.1748 0.2106 2.1963 LSTM 0.1137 0.1401 1.1903 BO-GRU 0.0972 0.1247 1.0896 BO-LSTM 0.0948 0.1220 1.0674 Moreover, hyperparameter tuning has a significant effect on the performance of these nonlinear models and BO-LSTM and BO-GRU outperform the standard LSTM and GRU. It can be observed that the performance of BO-LSTM is better than all benchmark algorithms such ANN, XGBoost, ARIMA, standard LSTM, and BO-GRU according to all error indices and for the three wind farm sites dataset, except the slightly lower MAE error value of the competitive BO-GRU for Site II. Specifically, while comparing with standard LSTM and BO-GRU in all three cases, BO-LSTM obtained lower MAE, RMSE, and MAPE error with values of 0.0621, 0.0793, and 1.1353, respectively, for Site I. However, the differences in prediction accuracy between BO-LSTM and BO-GRU are not very large. Hence, Table 3 shows the viability of a Bayesian Optimization algorithm in tuning the LSTM model by searching for the best hyperparameter combination which significantly improves the proposed BO-LSTM performance. Table 4shows the error indices of the optimized deep learning frameworks, namely BO-LSTM and BO-GRU models, and the standard LSTM and GRU on both the training and test data. The MAE and RMSE error values for all three cases are very much closer and lower than that of the use of untuned deep learning models. It can be observed that by applying the hyperparameter tuning prior to building deep learning models, they learn nonlinear features from wind power and reduces the overfitting problems that have been experienced with the use of standard LSTM and GRU implementation. Moreover, from the analysis of Table 4 , it is worth mentioning that BO-LSTM achieves superior performance than that of the standard LSTM and BO-GRU models, both on training and test MAE and RMSE metrics for all three cases. As shown, the BO-LSTM model outperforms the BO-GRU model. Both BO-LSTM and BO-GRU models were applied to the data from the three wind farm sites or groups, as indicated in Table 3. It can be concluded that Bayesian optimization is a suitable strategy for this context, as both deep learning models show competitive results when optimized in this way. Despite using the same optimization strategy to search for optimal parameters in the same hyperparameter spaces, as shown in Tables 1and 2, the prediction errors still varied, which could be due to the variability of the data recorded at each wind generation plant. The BO-LSTM-based prediction results are presented in Figures 10–12 for the actual and predicted data of Site I, Site II, and Site III, respectively. These figures show a good resemblance between the actual and predicted data, as confirmed in Table 4. The Supplementary Material, including the actual and predicted values for these figures, can Energies 2023,16, 2317 17 of 22 be found at https://github.com/DataLabUPO/AdamaWindPowerResults, accessed on 19 February 2023. Table 4. Forecasting performances of competitive deep learning models on training and test data. Dataset Models Training Testing MAE RMSE MAE RMSE Site I LSTM 0.0909 0.1167 0.1118 0.1371 GRU 0.0825 0.1046 0.1004 0.1205 BO-GRU 0.0611 0.0807 0.0693 0.0881 BO-LSTM 0.0590 0.0782 0.0627 0.0800 Site II LSTM 0.0848 0.1104 0.0950 0.1146 GRU 0.0875 0.1142 0.0970 0.1163 BO-GRU 0.0714 0.0967 0.0775 0.0989 BO-LSTM 0.0689 0.0956 0.0741 0.0930 Site III LSTM 0.1167 0.1461 0.1095 0.1386 GRU 0.1219 0.1505 0.1088 0.1363 BO-GRU 0.1063 0.1377 0.0993 0.1274 BO-LSTM 0.1032 0.1352 0.0986 0.1258 8/13/2021 10/2/2021 11/21/2021 1/10/2022 3/1/2022 4/20/2022 6/9/2022 Time (days) 0 50000 100000 150000 200000 250000 Wind power Actual value Predicted value Figure 10. Prediction vs. actual plot for Site I. 8/13/2021 10/2/2021 11/21/2021 1/10/2022 3/1/2022 4/20/2022 6/9/2022 Time (days) 50000 100000 150000 200000 250000 Wind power Actual value Predicted value Figure 11. Prediction vs. actual plot for Site II. Energies 2023,16, 2317 18 of 22 8/13/2021 10/2/2021 11/21/2021 1/10/2022 3/1/2022 4/20/2022 6/9/2022 Time (days) 0 50000 100000 150000 200000 250000 Wind power Actual value Predicted value Figure 12. Prediction vs. actual plot for Site III. 5. Conclusions In this paper, we use the Bayesian optimization algorithm to find the optimal hyperparameter values that result in a higher level of model accuracy. We search for impactful hyperparameter values and use them to develop deep LSTM and deep GRU models on a real wind power dataset. For each selected wind farm site, we propose and test wind power forecasting models. Our experimental results and comparative analysis show that the proposed model, which combines Bayesian Optimization and deep LSTM, outperforms the benchmark models in terms of error metrics. Hyperparameter tuning with Bayesian Optimization is a feasible method that finds the optimal combination of parameters within a reasonable computation time. It also helps to minimize model overfitting issues. The results in Table 4 show that the training and test error variance for the BO-LSTM model is much lower than for the standard LSTM network. Additionally, conventional machine learning models and ANNs cannot discover the temporal information hidden in wind power time series data, leading to inaccurate estimations. However, despite the difficulty and time consumption of training deep learning models, the combination of Bayesian Optimization and deep LSTM is found to be efficient and effective in learning nonlinear time series data. In comparison to the baseline ANN, XGBoost, and ARIMA models, the BO-LSTM model achieves better results. Additionally, it outperforms tuned GRU models in terms of performance on training and test data with good learning convergence. In wind power forecasting, time is an important feature to predict future sequence values and future work should address this parameter through automatic hyperparameter tuning, which is not covered in this work. The proposed BO-LSTM model can also be tested with a particular location’s exogenous variables, such as temperature, wind speed, and wind direction in addition to the wind power variable in future work. Supplementary Materials: The following supporting information can be downloaded at: https: //github.com/DataLabUPO/AdamaWindPowerResults, accessed on 19 February 2023. Author Contributions: E.T.H. designed the methodology, wrote the article, and conducted the experimentation. F.M.-Á. supervised and was involved in writing and editing the article. K.K. supervised the topic selection and conceptual development. M.M.-B. wrote the literature, designed the models, and edited the methodology. All authors have read and agreed to the published version of the manuscript. Funding: The authors would like to express their gratitude to the Spanish Ministry of Science and Innovation for their support through projects PID2020-117954RB and TED2021-131311B-C22. They would also like to thank the European Regional Development Fund and Junta de Andalucía for their support through projects PY20-00870 and UPO-138516. Energies 2023,16, 2317 19 of 22 Data Availability Statement: Data are available upon request to the Ethiopian Electric Utility company. Conflicts of Interest: The authors declare no conflict of interest regarding the publication of this paper. 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