Compared with conventional power grids, a smart grid (SG) can provide a more intelligent, efficient, reliable, and sustainable power service by utilizing advanced structure and information technology . Therefore, the nature of industrial utility and users will be greedy. Conventional grids cannot satisfy both parties simultaneously to address the latest grid difficulties such as robustness, reliability, and so on. The novel and intellectual idea of the SG renovates conventional grids through the integration of modern communication technology. In this context, consumers are involved in the trade of energy . The bidirectional transmission or energy flow benefits the industrial utility and the users. Notably, consumers do not remain just consumers; they also become “prosumers” who are capable of accessing the electricity market as both buyers and sellers . Concurrently, the smart industrial utility is able to efficiently manage its sources. To maximize SG performance, mainly in terms of dispersal, a decision-making entity is required. Proper decision making results in electricity cost reductions for users, together with the reduction of overall energy losses and mitigation of the peak-to-average ratio . Considering these objectives, recent research in SG has primarily focused on the optimized methods of power scheduling. However, before scheduling, a precise short-term load forecasting (STLF) method is required to properly plan the ongoing grid functioning needed for effective resource management . A high degree of randomness and non-linearity in historical load curves make STLF very challenging. In this study, several STLF techniques were proposed. However, the accuracy of such techniques was either not satisfying or their convergence rates were slow.
Load prediction is a crucial outcome of an SG mechanism. It predicts the long-term, short-term, and medium-term demand for electrical energy from consumers . Deep learning (DL) can be broadly utilized for load prediction in SGs. Though a subset of machine learning (ML), DL is highly useful compared with other conventional ML techniques. Moreover, it eases the utility of other ML techniques combined with ANN for superior outcomes . Several methods are integrated with ANN for smart grids, which include K-nearest Neighbor (KNN), Random Forrest (RF), other ML methodologies, Support Vector Machine (SVM), and Decision Tree (DT), achieving superior outcomes for load forecasting, power management, and other purposes . Power distribution firms especially benefit from SGs through the determination of superior power distribution between the clients or consumers (corporate office, home, and industry) . Presently, diverse electrical power consumption data can be aggregated centrally. DL can perform load prediction from this vast amount of information, therefore enabling power distributors to estimate demand for power distribution .
For load forecasting, this study focused on the development of a new wild horse optimization method with a deep learning-based STLF scheme (WHODL-STLFS) for SGs. The presented WHODL-STLFS technique was initially used to design a WHO algorithm for the optimum selection of features from the electricity data. The WHO algorithm mimics horse behavior in which they leave their group and join another group before becoming adults to prevent mating between siblings or fathers and daughters. The WHO algorithm was chosen because it properly balances the exploration and exploitation phases and achieves the optimal global solution. In addition, attention-based long short-term memory (ALSTM) was exploited to learn the energy consumption behaviors in order to forecast load. Finally, an artificial algae optimization (AAO) algorithm was applied as the hyperparameter optimizer of the ALSTM model. The experimental validation of the WHODL-STLFS technology was carried out under several measures. In short, the key contributions of the paper are as follows:
In ref. , mid-term and STLF (MTLF and STLF) were modeled with the use of smart-metered data obtained from a real-time distribution grid at the NIT Patna campus using various traditional and ML approaches. Data preprocessing can be carried out to transform the raw data into a suitable form through the removal of the outliers presented in the data. Moreover, the influential weather-related parameters acquired by correlation analysis, including the past load, can be utilized for training the load forecasting method. In ref. , an accurate and fast hybrid electric load forecasting (FA-HELF) structure was modeled. Firstly, RF and relief-F techniques were compiled together to devise a hybrid feature selection method for eliminating redundancy. Secondly, kernel-related PCA was presented for extracting features to overcome the issue of dimension reduction. Lastly, for execution, an FA-HELF optimizer was compiled with an SVM forecaster.
Syed et al.  modeled a new hybrid clustering-related DL technique for STLF at the distribution transformer levels with boosted scalability. The study examined the benefit of training duration and the presentation relating to accuracy when clustering-related DL modeling was used for STLF. A k-Medoid-related technique was leveraged for clustering, whereas predictive techniques were generated for various clusters of load profiles. In ref. , a novel hybrid STLF was devised. The data preprocessing and feature-selection elements depend upon the modified mutual information (MMI) method, which is an enhanced version of the mutual information method, utilized for selecting abstractive attributes from historical data. The training and forecasting element depends upon factored conditional restricted Boltzmann machines (FCRBMs), known as a DL technique, empowered through learning to predict the future electric load. The optimized method relies upon this modeled genetic wind-driven (GWDO) optimized technique, which was employed for fine-tuning the adaptable variable of the method.
An enhanced STLF was modeled in . Initially, the load was decomposed into distinct frequency elements, changing from lower to higher levels comprehended by the ensemble empirical-mode decomposition method. Following this, the smooth and periodic lower-frequency element was predicted through a multivariate linear regression model while sustaining computation ability, while the higher-frequency element with a high degree of randomness was predicted by LSTM-NN techniques. In ref. , a new DL-related technique was applied for electricity load forecasting. A three-step method was applied with feature selections utilizing a hybrid feature selector (DT and XGboost), a redundancy removal utilizing a feature-extracting method (Recursive Feature Elimination), and forecasting or classification through an enhanced Extreme Learning Machine (ELM) and SVM. Ünal et al.  proposed an advanced pre-processing system combined as a hybrid sequential learning-related energy forecasting system, which utilized a CNN and BLSTM in a unified structure for an accurate energy-consumption forecast. The new hybrid DL technique related to data feature decoding and coding was enforced in the forecasting phase.
In this study, new WHODL-STLFS technology was developed for accurate and timely load forecasting for SGs. The presented WHODL-STLFS technique encompasses a three-stage process. At the initial level, the WHODL-STLFS technique used the WHO-based feature-selection process. Next, the ALSTM model was exploited for predicting load in SGs. Lastly, the AAO algorithm was employed as the hyperparameter optimizer of the ALSTM model. Figure 1 illustrates the working process of the WHODL-STLFS system.
Firstly, the WHODL-STLFS technique used the WHO-based feature selection process. The WHO approach is a metaheuristic technique inspired by the social behavior of wild horses . In the presented method, various efficiencies are established using the behaviors of wild horses, such as mating, leading, chasing, grazing, and hunting. The horses were classified into two social groups, namely non-territorial and territorial. However, the WHO approach focuses on non-territorial groups that encompass group leaders (stallions), various mares, and their offspring. Moreover, if the foals exceed the age of puberty, they leave their group and incorporate into others. The WHO technique was defined in the following phases.
In this phase, the variable needed for the WHO algorithm is determined to estimate the initial solution:
This phase introduces the grazing performance of foals before they reach puberty. The stallion is regarded at the center of the grazing region, while the residual group members neighbor the center of the region as follows:
This stage provides the performance of foals after reaching the age of puberty. As noted above, foals leave the group and integrate with other groups to mate and prevent fathers from marrying their sisters and daughters. Foal performance can be determined as follows:
The group stallion leads the group member to the waterhole for food in this phase. Similarly, the stallion fights with other stallions to dominate the waterhole, which is determined by the following:
Eventually, the group leader was carefully chosen to obtain optimal fitness values. In each iteration, the group leader was carefully chosen, while an optimal leader could be identified among all the leaders from the iteration:
In the presented method, the termination criteria were used to implement the enhanced procedure up to the maximum iteration count (Max. It) as explained in Algorithm 1 below.
At this stage, the ALSTM model was exploited for predicting load in SGs. The RNN is a type of NN, whereas the outcome of a feed-forward typical ANN is offered as a novel input to neurons depending on the new input value . The outcome value at any neuron relies on its input at moment . This enhances the dynamism of the network system. Assuming there is a connection between two input values, this technique is resolved as a memory-network approach. In RNN, input data are supposed to connect to everyone. The LSTM is the best-known RNN network approach, but the infrastructure has been introduced to address the vanishing gradient problem. At present, refers to the input value at time , and signifies the outcome value at time .
The infrastructure of the LSTM network node comprises three basic gates: output gate , forget gate , and input gate . However, the input and output gates represent the data that entered and data that exited the node at time , respectively. The forget gate selective data that were forgotten were connected to previous status data and current input . These three selected gates upgraded the current memory cell and current latency value. In the LSTM node, the links between the gates were calculated mathematically, employing the following equation:
The LSTM network infrastructure processed the representation vector obtained as an input from the initial to the final data. Let stand for the matrix containing the hidden vector that LSTM created, whereas the size of hidden state is defined as and the length of provided data is represented by . Furthermore, denotes the vector of ls and embedded vector. Figure 2 showcases the infrastructure of the ALSTM technique.
Lastly, an AAO algorithm was employed as the hyperparameter optimizer of the ALSTM model. Uymaz et al.  developed the AAO technique as a biologically stimulated metaheuristic optimization approach to overcome the problems of continuous and real-time optimization. This is a motivation for the search activity of microalgae. The life cycle included mitotic reproduction, which alters the environmental adaptation, and dominant species. The helical motion phase, adaptation stage, and the reproduction or evolutionary stage are the three stages of the AAO algorithm. The reproduction or evolutionary phase are exploited to replenish the community cell by resurrecting algae by mitotic partition once they have sufficient sources of nutrients and light in the environment. Algae perform a movement called helical movement . Algae cells employ their flagellum (organelle) for helical motion and they exist in a liquid atmosphere and congregate near to the liquid surface where there exists an adequate light source as explained in Algorithm 2.
The AAO approach derives an objective function according to the mean square error (MSE) and it is utilized for predicting the testing output of the ALSTM approach. It is determined by the following equation:
This section examines the load forecasting performance of the WHODL-STLFS model under two aspects: an FE grid and a Dayton grid. Figure 3 shows the MAPE examination of the WHODL-STLFS model on the applied FE grid. The figure indicates that the WHODL-STLFS model obtained reduced MAPE values during the training and testing phases.
Figure 4 depicts the MAPE examination of the WHODL-STLFS approach on the applied DAYTON grid. The figure demonstrates that the WHODL-STLFS technique attained decreased MAPE value during the training and testing stages.
Table 1 and Figure 5 provide the load-prediction outcomes of the WHODL-STLFS model with existing models on an FE grid. The experimental values indicated that the WHODL-STLFS model demonstrated enhanced outcomes with minimal differences between the actual and predicted values. For instance, under the conditions of a 1 h duration and 672 kW actual load, the WHODL-STLFS model predicted a load of 671 kW. Likewise, under the conditions of a 10 h duration and 735 W actual load, the WHODL-STLFS approach predicted a load of 733 kW. Similarly, under the conditions of a 24 h duration and 673 kW actual load, the WHODL-STLFS method predicted a load of 672 kW.
Table 2 and Figure 6 offer the load-prediction outcomes of the WHODL-STLFS method with present approaches on the DAYTON grid. The experimental value indicates that the WHODL-STLFS method demonstrated improved outcomes with minimal differences between the predicted and actual values. For example, under the conditions of a 1 h duration and 175 kW actual load, the WHODL-STLFS approach predicted a load of 174 kW. Similarly, under the conditions of a 10 h duration and 213 W actual load, the WHODL-STLFS technique predicted a load of 213 kW. Likewise, under the conditions of a 24 h duration and 179 kW actual load, the WHODL-STLFS approach predicted a load of 178 kW.
Table 3 and Figure 7 demonstrate the comparative EXET analysis of the WHODL-STLFS model on two grids. The experimental values indicated that the Bi-level model exhibited poor performance with increased EXET values. FCRBM, AFC-ANN, and LSTM models exhibited slightly decreased EXET values. Although the MI-ANN model achieved reasonable EXET values, the WHODL-STLFS model exhibited enhanced performance with minimal EXET values of 12.11 s and 10.54 s on the FE grid and Dayton grid, respectively.
Table 4 and Figure 8 illustrate the comparative average error rate (AERR) examination of the WHODL-STLFS method on two grids. The experimental values indicated that the LSTM approach demonstrated poor performance with improved AERR values. Comparatively, the Bi-level approach demonstrated slightly reduced AERR values. Although the AFC-ANN technique accomplished reasonable AERR values, the WHODL-STLFS method illustrated improved performance with minimal AERR values of 4.13 and 2.88 on the FE grid and the Dayton grid, respectively.
Table 5 and Figure 9 illustrate a comparative MAPE inspection of the WHODL-STLFS method compared with other existing methods. The results infer that the WHODL-STLFS technique reached minimal MAPE values. For instance, in 60 samples, the WHODL-STLFS model reached a lower MAPE of 0.164%, whereas the LSTM-AFC-ANN and Bi-level models resulted in increased MAPE of 3.306%, 0.715%, and 2.813%, respectively. Additionally, in 720 samples, the WHODL-STLFS technique reached a lower MAPE of 0.059% while the LSTM-AFC-ANN and Bi-level models resulted in improved MAPE of 2.485%, 0.458%, and 2.392%, respectively.
Table 6 and Figure 10 show a comparative EXET examination of the WHODL-STLFS approach compared with other current techniques. The results showed that the WHODL-STLFS method obtained minimum EXET values. For example, in 60 samples, the WHODL-STLFS technique attained lower EXET of 9.19 s while the LSTM-AFC-ANN and Bi-level methods resulted in improved EXET of 65.56 s, 57.96 s, and 105.79 s, respectively.
Moreover, in 720 samples, the WHODL-STLFS technique obtained a lower EXET of 14.58 s while the LSTM-AFC-ANN and Bi-level methodologies resulted in improved EXET of 72.85 s, 64.93 s, and 111.49 s, respectively. Finally, these results confirmed the enhanced load-prediction results of the WHODL-STLFS model on the SGs.
In this study, a new WHODL-STLFS technique was developed for accurate and timely load forecasting for SGs. The presented WHODL-STLFS technique encompassed a three-stage process. At the initial level, the WHODL-STLFS technique used the WHO-based feature selection process. Next, the ALSTM model was exploited to predict load in SGs. Lastly, the AAO algorithm was employed as the hyperparameter optimizer of the ALSTM model. The experimental validation of the WHODL-STLFS technique was undertaken and the results indicated its promising forecasting performance compared with recent models. Thus, the WHODL-STLFS technique can be applied as a proficient approach for load forecasting in real time. In the future, we will extend the WHODL-STLFS technique to validate real-time large-scale SG data to assure its consistent performance. In addition, advanced DL models can be employed to improve the prediction outcome. Moreover, statistical results and ablation studies need to be performed in the future. Author Contributions
Conceptualization, A.M. and E.A.; methodology, A.G.; software, A.S.Z.; validation, E.A., A.G. and R.M.; formal analysis, M.I.E.; investigation, A.A.A.; resources, N.M.S.; data curation, N.M.S.; writing—original draft preparation, E.A., A.G., R.M. and A.M.; writing—review and editing, A.G., E.A. and R.M; visualization, R.M.; supervision, E.A.; project administration, A.M.; funding acquisition, E.A. All authors have read and agreed to the published version of the manuscript.
This article does not contain any studies with human participants performed by any of the authors.
Load-prediction outcome of the WHODL-STLFS system with distinct timeslots under the FE grid.