# Application of Fuzzy-RBF-CNN Ensemble Model for Short-Term Load Forecasting

Authors: Mohini Yadav; Majid Jamil; Mohammad Rizwan; Richa Kapoor
Journal: Journal of Electrical and Computer Engineering
 (2023)

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## Abstract

Accurate load forecasting (LF) plays an important role in the operation and decision-making process of the power grid. Although the stochastic and nonlinear behavior of loads is highly dependent on consumer energy requirements, that demands a high level of accuracy in LF. In spite of several research studies being performed in this field, accurate load forecasting remains an important consideration. In this article, the design of a hybrid short-term load forecasting model (STLF) is proposed. This work combines the features of an artificial neural network (ANN), ensemble forecasting, and a deep learning network. RBFNNs and CNNs are trained in two phases using the functional link artificial neural network (FLANN) optimization method with a deep learning structure. The predictions made from RBFNNs have been computed and produced as the forecast of each activated cluster. This framework is known as fuzzy-RBFNN. This proposed framework is outlined to anticipate one-week ahead load demand on an hourly basis, and its accuracy is determined using two case studies, i.e., Hellenic and Cretan power systems. Its results are validated while comparing with four benchmark models like multiple linear regression (MLR), support vector machine (SVM), ML-SVM, and fuzzy-RBFNN in terms of accuracy. To demonstrate the performance of RBF-CNN, SVMs replace the RBF-CNN regressor, and this model is identified as an ML-SVM having 3 layers.


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## Body

## 1. Introduction

Load forecasting [1] is a technique to predict the future load demands to attain equilibrium between the energy supply and consumption while considering different variables such as historical loads and weather conditions (temperature, pressure, humidity, etc.). With time series variations of nonlinear loads and different seasonal conditions, it is difficult to achieve short-term load forecasts with accuracy as the main consideration in different economical factors [2].Accurate load forecasting will reduce the cost of electricity generation and improve trading advantages [3], especially during peak hours. Load forecasting shows the significance of a continuous demand rise, which leads to two prediction terms: overestimated and underestimated demands. This overestimated prediction incurs extra charges on the production cost of generation to maintain the large storage reserves as a backup supply. On the other hand, the underestimation affects the demand response. Accurate load forecasting plays a vital role in an industrial sector, a deregulated economy, and the coordination of the functioning of the entire power network, especially in smart grids [4–11]. Different energy companies try to calculate the forecast demand [12] more precisely and efficiently using an artificial neural network (ANN). As per the Mckinsey Global Institute, artificial intelligence (AI) should be considered for the prediction of power demand and supply [13]. As an example, the UK-based National Grid and the Google-owned team “DeepMind” [14, 15] enable the future demand forecast using smart meters and AI techniques. Furthermore, retailers also calculate the energy prices based on the forecast. With the new exposure to smart metering, many researchers have been exploring STLF in the residential sector [16–19].Previously, the studies were based on manual methods that rely on particular datasets, which is not sustainable for utilities as the complexity of the network increases. For STLF, the researchers have used different regression methods [20] and presented exponential stabilities in mixed mode-dependent time delays [21], neural networks [22], clustering approaches [23], and support vector machine-based methods [24]. In the last years, researchers also used the Kalman filtering approach in forecasting applications and discussed the reduced order filtering approaches [25, 26]. All these methods are simple, but they are unable to reach to higher accuracy level when compared with artificial intelligence techniques. The authors [27] have presented the switched delay PSO technique for STLF.Better performance has been achieved with the integration of different computational methods. Some references are briefly explained here. A multitask regression approach is used to predict the load recorded from residential and industrial smart meters [28]. Feature selection is done using additive models [29]. Recursive support vector regression (R-SVR) is integrated with empirical mode decomposition (EMD), where EMD is categorized as principal and behavioral, and then R-SVR is employed to provide prediction [30]. RBFNN and neural-based fuzzy models are utilized to tune their parameters using a penalty function [31]. To overcome the load forecasting problem, a fuzzy neural network is developed using a bilevel optimization algorithm [32].It seems [33–35] that RBFNN presents an incredible response for the evaluation of demand forecasting. Although its prediction is based on the width of the radial basis function in the hidden layer, in the case of highly complicated problems like load forecasting, it deals with the “curse of dimensionality,” as usual for every kernel approach. To ease this drawback, a composite RBF is accompanied by a deep learning (DL) approach. DL includes an automation process with a decision-making feature [36]. DL has a more complex architecture than other neural network architectures, including more layers and mathematical formulation. CNN used in this paper is one of the techniques of DL. DL serves as a great application in load forecasting [37]. Long-short-term memory recurrent neural network (LSTM-RNN) [38] and 3-filter CNN [39] are showing promising results in this field. CNN selects the input feature when the input is transformed into a graphical representation [40]. The input is accumulated into clusters by applying the k-means technique [41], subsequently, CNN is used for prediction purposes in each cluster [42]. The authors [43] have trained the neural network with a deep learning process, including convolution and pooling techniques, to extract the feature maps and forecast the load demand data for days ahead.The main contribution of this study is to generate ensemble predictions from multiple local regressors, and this regression variable activates the forecast process using the data clustering method to assign the input to different clusters. The presented work defines its novelty that comes with an introduction of:(1)
New technique based on the fuzzy clustering approach, which clusters the input vector to generate ensemble predictions.(2)
Creative neural network architecture consists of RBF, convolution, and pooling in a fully connected two-layer network. This is termed as fuzzy-RBF-CNN. This proposed approach divides the input dataset into input subsets, which are used to develop the ensemble of RBF-CNN regressors. Each of these regressors is trained in two phases using the functional link artificial neural network (FLANN) optimization method with a deep learning framework.(3)
Using the RBFNN training procedure, RBF-CNN regressor widths and RBF centers are optimized. The above-mentioned hidden layer outputs from RBFNN are received by the corresponding CNN, which then executes the load prediction. In this way, the final prediction is determined as an average of ensemble load predictions. CNN is used to extract the input feature when input is transformed into a graphical representation. CNN used in this paper is one of the techniques of DL. DL serves as a great application in load forecasting.(4)
In the case of highly complicated problems like load forecasting, RBFNN deals with the “curse of dimensionality,” which is usual for every kernel approach. To ease this drawback, a composite RBF is accompanied by a deep learning approach. RBFNN presents an incredible response for the evaluation of demand forecasting. Although its prediction is based on the width of the radial basis function in the hidden layer.In this paper, a fuzzy-based prediction framework integrated with a deep learning network has been presented for STLF. This hybrid approach can capture hidden characteristics of load pattern and gain accuracy in results of load forecasting. On the basis of the obtained results and complete analysis, the following conclusions are being drawn: firstly, in comparison to the LSTM method (generally for RBFNN second layer) activations performed by CNN on RBF give around 9% improvement in forecasting accuracy. It indicates that higher forecast accuracy is attained by RBF-CNN regressors. Secondly, the application of CNN on the RBFNN hidden layer gives high robustness. Third, the proposed model (Fuzzy-RBF-CNN) performs better than ML-SVM and results in a 14% improvement on average. Fourth, in comparison of MAPEs of 24 h-SVM and fuzzy-RBFNN, the fuzzy clustering approach is more successful, as it provides 39% and 34% better performance with reference to 24 h-SVM. Thus, it shows the effectiveness of the fuzzy clustering method and the improvement in RBFNN response by CNN.The rest part of this paper is explained in given Sections: Section2 presents the relevant and recent literature for study. Section 3 explains the proposed hybrid model. Section 4 discusses the complete training procedure of the proposed model structure. Section 5 illustrates the case study in both interconnected and isolated power systems. Section 6 shows the outcome of training the system with different methods, and Section 7 concludes the proposed work.


## 2. Related Work

STLF defines the load prediction horizon from an hour to one week, which is significant for large-scale decision-making operations of power grids where group of countries have a single power system, such as the European Union. To clearly understand the new approach for the STLF model, the whole literature involves both the statistical model and machine learning models. Both of these models are subdivided into individual models and hybrid models. Hybrid models involve feature extraction, forecasting, and different optimization approaches, unlike individual models that involve only forecasters.


### 2.1. Individual Forecasting Models

In this STLF, the forecaster predicts the load consumption. Distributed methods are proposed [44] to forecast load using weather information. Auto regression integrated moving average (ARIMA) and Grey [45] are individual forecasting models used for subnetworks (which are formed by dividing power systems as per weather conditions). To determine the performance of adapted methods with respect to traditional models, two performance metrics, i.e., the root mean square error (RMSE) and the mean square error (MSE), are used. Here, the MSE checks whether the value of the forecast is close to the actual value, and its lower value indicates a better fit. RMSE will exaggerate the large errors, which is helpful when compared with other methods. A deep recurrent neural network (DRNN) is used to predict energy consumption [46]. This method outperforms other methods in terms of RMSE like convolution RNN, ARIMA, and SVR by 5.9%, 18.5%, and 12.1%, respectively. In [47], the author has proposed LSTM-RNN that mainly concentrates on accuracy while ignoring the convergence rate and calculation complexity. In [48], the author has tested the recency effect experienced in LF to improve prediction accuracy at the level of high model complexity. The author has presented a long-term forecasting model by conducting an analysis on western US energy utility. It is done for both peak and normal load usage. These aforementioned techniques are more robust with fast convergence but lag in the accuracy level of the forecast.


### 2.2. Hybrid Forecasting Model

In these models, techniques of feature extraction and optimization are used along with forecasters to improve forecasting accuracy. The author in [49] analyzes the complete power system structure on the basis of hourly load and weather conditions by applying a polynomial regression model. It has presented a model to predict the load on the distributed generation side using SVM and the fruit fly immune (FFI) algorithm. In [50], the author has proposed an IoT-based deep neural network for high precision. In addition, factors like temperature, humidity, and weather conditions [12] are taken into consideration. The author in [51] has presented a hybrid learning model to forecast the intensity of solar radiation [52]. The dynamic behavior of data is analyzed using a genetic algorithm (GA), back propagation (BP), and neural network. This model outperforms both in STLF and long-term load forecasting. To harvest the solar energy, it is necessary to optimally forecast its generation. For this purpose, the author in [53] has proposed a regression technique called least absolute shrinkage and selection operator (LASSO), which enhances forecast accuracy. ARIMA, wavelet neural network (WNN), and improved empirical mode decomposition (EMD) used to forecast load and FFI optimization is done. Its simulation results outperform those of existing methods when compared. The ANN model forecasts hourly energy consumption, and its model is trained using Levenberg–Marquardt (LM) and BP techniques [54]. Different parameters, like temperature, hourly/weekly energy usage, and dry bulb data, are taken as input. The accuracy of the model is tested on the basis of RMSE. An AI-based hybrid model [55] is proposed to predict the 24 hr load of polish grid and it is validated on offline data of Poland. EMD-based ensemble model using deep learning approach is used to forecast load, and it is tested on the Australian energy grid. In this paper, the data is broken up into intrinsic mode functions (IMFs), and each IMF is used to improve accuracy. The author in [56] presented the fully automated machine learning structure for forecasting the load. In [57], a hybrid incremental learning technique is used that combines discrete WT, EMD, and a random vector functional link network (RVFLN). The simulation result is evaluated on Australian energy data, and this model outperforms eight benchmark models. In [58], load forecasting is done using an extreme learning machine model (ELM), and the proposed study is validated by half hour resolution data of Australia. Its result outperforms existing methods such as RBF-ELM and mixed ELM. In [59], the author has applied hybrid of particle swarm optimization approach (PSO) and ELM where tanh function is used as activation function and avoids unwanted hidden nodes and overtraining. This proposed approach is better than RBFNN, according to the obtained results. In [60], to forecast the hotel building demand, i.e., highly irregular, the online modifier forecaster is proposed. This paper uses a clustering-based hybrid model, i.e., a combination of SVR and wavelet decomposition techniques. It results in higher accuracy than traditional methods. In [61], STLF is done using deep learning approach and tested on energy consumption of year 2014 of China cities. The simulation results show a significant impact of parameters like temperature and other weather conditions on energy usage. It also highlights the better prediction accuracy of the deep learning model in comparison to the random forecast and gradient boosting models. To improve efficiency and relative prediction accuracy, this study [62] will feed the output of the forecaster module to the optimization module. It improves the prediction accuracy at the cost of calculation complexity. To improve forecasting accuracy using dynamic mode decomposition and an extreme value constraint approach, the author [63] has presented the STLF model. The authors [64] presented STLF for distribution feeders. To improve both the stability and prediction accuracy of the model, the author has developed an integrated model of VMD, LSTM, and Bayesian techniques. The author [65] developed a hybrid approach to forecast the energy generation from solar panel-microgrid. This model used GA, PSO, and neuro-fuzzy approaches is tested on real-time power generation data. This prediction module forms the historical load profile by analyzing the stochastic load pattern of consumer demand and then forecasting the future load demand.Due to ease in the implementation of electric load forecasting, ANN is mostly used as a machine learning approach. Number of layers, number of neurons, and learning rate are the most promising parameters to define the performance of ANN. Mainly, learning algorithms such as gradient descent, BP algorithm, etc. suffer from premature convergence and overfitting. In order to overcome this disadvantage, hybrid forecasting approaches have been discussed. Overfitting is reduced by data augmentation, feature selection, and creating ensemble load predictions. Hybrid techniques have enhanced model capabilities, but the problems of slow convergence and large computational time still persist compared to nonhybrid techniques.All the aforementioned techniques produce satisfactory results for small data size only and their performance is highly dependent on knowledge and experience. Using a clustering approach on smaller data size leads to the problem of overfitting and creates a high generalization error. In a practical scenario, the data size is invariable, and there is no technique that can handle large data. This proposed study outperforms in comparison to present ANN methods and linear regression models. Table1 presents a summary of related work.Table 1
Relevant work summary report in terms of techniques, aim, drawbacks, and remarks.
TechniquesAimDrawbackRemarksLoad forecasting based on weather information for bulk power systemImprovement in forecasting accuracySuitable for bulk power system onlyIncorporating exogenous variables, the performance of bulk and distributed power systems improvesResidential forecasting using DRNNEnhance the user’s comfort level by reliable electricity availabilityModel complexity increasesResidential energy forecasting is possible by sharing the load data of consumers to energy regulation commissionLSTM-RNN for residential forecastingImproved accuracyIncreased in accuracy only for meter level forecastImprovement in accuracy not in convergence rateIoT-based load forecastingImproved operation of power system with accuracyLarge complex frameworkImpact on convergence rateForecasting based on big data approachAccuracy improved for scalable modelsComplex structure with less convergenceHigh complexity with improved accuracyWeek ahead forecasting using deep model with denoising auto encodersImproved accuracyModel performance is affected with reduced data sizeConvergence rate is affected, but accuracy improved with large data sizeArtificial intelligence-based load forecastingReduction in MSE with improved accuracyAccuracy with high convergence rateSigmoid function reduced convergence rateIntelligent hybrid model for load forecastingDay-ahead load forecastingEffective management of grid operationReliability is improved with high model complexityConclusions are figure out from above relevant literature survey: (1) no forecasting method is perfect in all respects; however, it depends on the application; (2) suffers from overfitting problem where model performs better in training but not in forecasting; and (3) compromise between forecasting accuracy and convergence rate. In this respect, a novel hybrid approach is proposed, which is integrated with three processes: (i) hybrid architecture composed of RBF, convolution, and pooling in a fully connected two-layer network; (ii) fuzzy clustering algorithm after data preprocessing; and (iii) FLANN algorithm-based optimization technique.


## 2.1. Individual Forecasting Models

In this STLF, the forecaster predicts the load consumption. Distributed methods are proposed [44] to forecast load using weather information. Auto regression integrated moving average (ARIMA) and Grey [45] are individual forecasting models used for subnetworks (which are formed by dividing power systems as per weather conditions). To determine the performance of adapted methods with respect to traditional models, two performance metrics, i.e., the root mean square error (RMSE) and the mean square error (MSE), are used. Here, the MSE checks whether the value of the forecast is close to the actual value, and its lower value indicates a better fit. RMSE will exaggerate the large errors, which is helpful when compared with other methods. A deep recurrent neural network (DRNN) is used to predict energy consumption [46]. This method outperforms other methods in terms of RMSE like convolution RNN, ARIMA, and SVR by 5.9%, 18.5%, and 12.1%, respectively. In [47], the author has proposed LSTM-RNN that mainly concentrates on accuracy while ignoring the convergence rate and calculation complexity. In [48], the author has tested the recency effect experienced in LF to improve prediction accuracy at the level of high model complexity. The author has presented a long-term forecasting model by conducting an analysis on western US energy utility. It is done for both peak and normal load usage. These aforementioned techniques are more robust with fast convergence but lag in the accuracy level of the forecast.


## 2.2. Hybrid Forecasting Model

In these models, techniques of feature extraction and optimization are used along with forecasters to improve forecasting accuracy. The author in [49] analyzes the complete power system structure on the basis of hourly load and weather conditions by applying a polynomial regression model. It has presented a model to predict the load on the distributed generation side using SVM and the fruit fly immune (FFI) algorithm. In [50], the author has proposed an IoT-based deep neural network for high precision. In addition, factors like temperature, humidity, and weather conditions [12] are taken into consideration. The author in [51] has presented a hybrid learning model to forecast the intensity of solar radiation [52]. The dynamic behavior of data is analyzed using a genetic algorithm (GA), back propagation (BP), and neural network. This model outperforms both in STLF and long-term load forecasting. To harvest the solar energy, it is necessary to optimally forecast its generation. For this purpose, the author in [53] has proposed a regression technique called least absolute shrinkage and selection operator (LASSO), which enhances forecast accuracy. ARIMA, wavelet neural network (WNN), and improved empirical mode decomposition (EMD) used to forecast load and FFI optimization is done. Its simulation results outperform those of existing methods when compared. The ANN model forecasts hourly energy consumption, and its model is trained using Levenberg–Marquardt (LM) and BP techniques [54]. Different parameters, like temperature, hourly/weekly energy usage, and dry bulb data, are taken as input. The accuracy of the model is tested on the basis of RMSE. An AI-based hybrid model [55] is proposed to predict the 24 hr load of polish grid and it is validated on offline data of Poland. EMD-based ensemble model using deep learning approach is used to forecast load, and it is tested on the Australian energy grid. In this paper, the data is broken up into intrinsic mode functions (IMFs), and each IMF is used to improve accuracy. The author in [56] presented the fully automated machine learning structure for forecasting the load. In [57], a hybrid incremental learning technique is used that combines discrete WT, EMD, and a random vector functional link network (RVFLN). The simulation result is evaluated on Australian energy data, and this model outperforms eight benchmark models. In [58], load forecasting is done using an extreme learning machine model (ELM), and the proposed study is validated by half hour resolution data of Australia. Its result outperforms existing methods such as RBF-ELM and mixed ELM. In [59], the author has applied hybrid of particle swarm optimization approach (PSO) and ELM where tanh function is used as activation function and avoids unwanted hidden nodes and overtraining. This proposed approach is better than RBFNN, according to the obtained results. In [60], to forecast the hotel building demand, i.e., highly irregular, the online modifier forecaster is proposed. This paper uses a clustering-based hybrid model, i.e., a combination of SVR and wavelet decomposition techniques. It results in higher accuracy than traditional methods. In [61], STLF is done using deep learning approach and tested on energy consumption of year 2014 of China cities. The simulation results show a significant impact of parameters like temperature and other weather conditions on energy usage. It also highlights the better prediction accuracy of the deep learning model in comparison to the random forecast and gradient boosting models. To improve efficiency and relative prediction accuracy, this study [62] will feed the output of the forecaster module to the optimization module. It improves the prediction accuracy at the cost of calculation complexity. To improve forecasting accuracy using dynamic mode decomposition and an extreme value constraint approach, the author [63] has presented the STLF model. The authors [64] presented STLF for distribution feeders. To improve both the stability and prediction accuracy of the model, the author has developed an integrated model of VMD, LSTM, and Bayesian techniques. The author [65] developed a hybrid approach to forecast the energy generation from solar panel-microgrid. This model used GA, PSO, and neuro-fuzzy approaches is tested on real-time power generation data. This prediction module forms the historical load profile by analyzing the stochastic load pattern of consumer demand and then forecasting the future load demand.Due to ease in the implementation of electric load forecasting, ANN is mostly used as a machine learning approach. Number of layers, number of neurons, and learning rate are the most promising parameters to define the performance of ANN. Mainly, learning algorithms such as gradient descent, BP algorithm, etc. suffer from premature convergence and overfitting. In order to overcome this disadvantage, hybrid forecasting approaches have been discussed. Overfitting is reduced by data augmentation, feature selection, and creating ensemble load predictions. Hybrid techniques have enhanced model capabilities, but the problems of slow convergence and large computational time still persist compared to nonhybrid techniques.All the aforementioned techniques produce satisfactory results for small data size only and their performance is highly dependent on knowledge and experience. Using a clustering approach on smaller data size leads to the problem of overfitting and creates a high generalization error. In a practical scenario, the data size is invariable, and there is no technique that can handle large data. This proposed study outperforms in comparison to present ANN methods and linear regression models. Table1 presents a summary of related work.Table 1
Relevant work summary report in terms of techniques, aim, drawbacks, and remarks.
TechniquesAimDrawbackRemarksLoad forecasting based on weather information for bulk power systemImprovement in forecasting accuracySuitable for bulk power system onlyIncorporating exogenous variables, the performance of bulk and distributed power systems improvesResidential forecasting using DRNNEnhance the user’s comfort level by reliable electricity availabilityModel complexity increasesResidential energy forecasting is possible by sharing the load data of consumers to energy regulation commissionLSTM-RNN for residential forecastingImproved accuracyIncreased in accuracy only for meter level forecastImprovement in accuracy not in convergence rateIoT-based load forecastingImproved operation of power system with accuracyLarge complex frameworkImpact on convergence rateForecasting based on big data approachAccuracy improved for scalable modelsComplex structure with less convergenceHigh complexity with improved accuracyWeek ahead forecasting using deep model with denoising auto encodersImproved accuracyModel performance is affected with reduced data sizeConvergence rate is affected, but accuracy improved with large data sizeArtificial intelligence-based load forecastingReduction in MSE with improved accuracyAccuracy with high convergence rateSigmoid function reduced convergence rateIntelligent hybrid model for load forecastingDay-ahead load forecastingEffective management of grid operationReliability is improved with high model complexityConclusions are figure out from above relevant literature survey: (1) no forecasting method is perfect in all respects; however, it depends on the application; (2) suffers from overfitting problem where model performs better in training but not in forecasting; and (3) compromise between forecasting accuracy and convergence rate. In this respect, a novel hybrid approach is proposed, which is integrated with three processes: (i) hybrid architecture composed of RBF, convolution, and pooling in a fully connected two-layer network; (ii) fuzzy clustering algorithm after data preprocessing; and (iii) FLANN algorithm-based optimization technique.


## 3. Detailed Hybrid Framework

The proposed model comprises 3 layers: fuzzy clustering, RBF-CNN regressor, and composite layer. Initially, the novel method aggregates the input data into multiple clusters using the fuzzy clustering method. Each cluster shares its position with other clusters in the neighborhood for ensemble prediction at the second layer. These clusters are generated as per the fuzzy rule, and this given clustering method needs very variable sets represented as membership function sets. These function sets depends on variables required for the problem [44], also on required cluster which split up input dataset. As per the proposed clustering method, the inputs are assigned to a second layer, where for each cluster the RBF-CNN regressor is applied. At the first layer, a corresponding cluster (fuzzy rule) creates the dataset, which is received by the RBF-CNN regressor. The training of these regressors requires kernel numbers, centres, and widths. These are assumed by the RBFNN training procedure. RBF kernels with optimized values convert the input data into higher-dimensional space, and CNN is trained with the implementation of this converted input data at the second stage. This process performs a detailed analysis of the relation between a kernel element and its neighbor, compared to RBFNN. With this above-mentioned 2 stage training procedure, RBF-CNN works as one neural network that comprises an RBF, a convolutional layer, an averaging pooling layer, and two fully connected layers. At the third layer, the average of ensemble predictions of the RBF-CNN regressor is done; this is the final prediction stage of the proposed model and corresponds to activated clusters in the clustering layer. A proposed model structure with three clusters that corresponds to the final load forecast is presented in Figure 1. Here, input x (i) actuate fuzzy rules 1, 2, 3, …, k and RBFCNNs to provide an independent prediction. Figure 2 shows the basic flowchart diagram of the hybrid forecasting fuzzy-RBFNN model.Figure 1
Fuzzy architecture for the proposed model.Figure 2
Basic flowchart diagram of the hybrid forecasting fuzzy-RBFNN model.


## 4. Training of Model Structure

### 4.1. Fuzzy Clustering Approach

To model the fuzzy-RBF-CNN, the input dataset is grouped according to variables that carry significant information. Hence, the highly correlated one defines the shape and quantity of clusters in the first layer. Most important input variables to model the load forecast are temperature, hours/months/weekend, and current load status. The training process of the first layer hybrid model contains variables with fuzzy membership functions. For continuous input variables, the Gaussian membership function is preferred, whereas for definite variables, the trapezoidal membership functions. Each variable is classified into fuzzy sets having the same behavior and semantic description, which are denoted by the membership function. The “hour” variable is represented with multifuzzy sets for daytime hours, and for nighttime hours, it is represented with a single-fuzzy set. Variables not involved in clustering are initialized with a membership value equal to 1.During training cycle,xi input vector is chosen through dataset and forms fuzzy rules. The membership output M (xi) is determined per variable i using the xi input vector. Furthermore, the activation functions for each variable are calculated, which are denoted as S (i, k)(1)Si,k=ΠYMxin,where YM (xi): output of variable M contained in fuzzy rule k. n: most important input variable in numbers on which dataset is grouped.For activation of variables less the existing rules, next fuzzy rule is(2)is=argminifi,argmaxSi,k.Until the minimum activationfi,argmaxSi,k stops increasing, the training of the first layer of fuzzy-RBF-CNN continues till it reaches to the threshold value denoted by STH. The significance behind defining this threshold value is to reduce complexity of design framework by limiting number of clusters. The value of STH is 0.73, which is determined using the trial and error method.The algorithm behind this approach is defined in steps, as shown below in Table2.Table 2
Fuzzy clustering algorithm.
(1) Load the membership function for each variableM(2) Load input data set(3) Select input variablexi randomly(4) Determine output variableM (xi)(5) Chose membership function of maximum output(6) Develop first layer rule(7) CalculateS (i, k) for each variable using equation (1)(8) DetermineSmax (i) for each x (i)(9) Determinex (i′) for minima of Smax (i)(10) Determine output variableM (xi)(11) Chose membership function for each variable having maximum output(12) Develop next rule(13) From equation (1), calculate S (i, k) for each variable(14) MinSmax (i) < STH


### 4.2. Steps for RBFNN Training

In the case of RBF-CNN, kernels are associated with CNN while the training process is executed in dual phases: Initially, autonomous RBFNN is trained and different sets of RBFs are created through the cross-validation method. Secondly, input data is transformed into 3-dimensional arrays to train a CNN. By applying the permutation approach [45], the input variables that are least significant are removed from the set at the initial stage of the RBF-CNN process. In this process, the baseline is defined, and then a randomly selected variable is permuted using the random forest algorithm [46].Basically, RBFNN comprises a 2 layer neural network with a hidden layer consisting of nonlinear RBFs and linear output. Its hidden layer parameters are controlled by RBF numbers (control the model whether over or under fitting), RBF centers (plan the model characteristics), and radii of RBFs (compute activation function for RBF). The type of RBF is given by the following equation:(3)Sj2,k=1e∑xi−ci,j2,k/ri,j2,k2,where k: cluster. i: input variable. j: indices for RBF, j∈1,JmSj2,k,ci,j2,k, ri,j2,k2: activation, centers, and radii of RBFs corresponding the cluster k.Applyingk cluster with permutation approach and forming dataset, equation (3) presents the RBFNN hidden layer output, which is trained with the k-means algorithm to locate RBF centers and latter to evaluate RBF radii, FLANN algorithm is used. The FLANN approach is a higher order derivative optimization technique algorithm [47], which uses a single-layer feed forward network and is extensively used on account of its low computational complexity. Moreover, it overcomes nonlinearity in outputs due to the functional expansion feature.In the RBFNN training process, the objective function is the sum of squared error, which is determined using validation and testing sets. The RBF weights and biases are upgraded and compared with the forecasted value per iteration. Then, the mean of squared error on validation and testing are computed and continues till error value is minimized. At that optimal point, the radii value is determined. With the hyperparameter optimization approach, namely “coarse-to-fine” [48], the above procedure is carried out for different RBFs.Furthermore, a three-foldcross-validation is performed for each tested RBF that comprises validation and testing of sets. This testing deals with a continuous portion of the set, whereas the validation set is selected randomly. While averaging the cross-validation results, the optimal value of RBF’s hidden layer is obtained. This is the process of obtaining the corresponding RBFNNs.


### 4.3. Steps of CNN Training

RBFNN deals with the “curse of dimensionality” issue because of the summation of activation for each element, and to mitigate this issue, activations are computed individually for each RBF element using the following equations:(4)Sj2,k=1e∑xi−ci,j2,k/ri,j2,k2,j∈1,Jk.After performing the RBFNN training procedure, each input vector is converted to 3-dimensional arrays. Then, training, validation, and testing are employed in equation (4), and three arrays of four-dimensional sets are obtained as 3 × E × Jk × Dtrain,k, 3 × E × Jk × Dval,k and 3 × E × Jk × Dtest,k, where E: input variables. Jk: most appropriate value of RBF number. Dtrain,k, Dval,k, and Dtest,k: sizes of training, validation, and testing sets, respectively.In image processing applications, these datasets are used to establish CNN for deep neural network. CNN comprises input layer, output layer, and a number of hidden layers. This hidden layer involves convolution layers accompanied by a pooling layer with two coupled layers. The convolution layer takes out the features from images utilizing kernels and creates filters [19]. In the convolution layer, different images are obtained by applying weights to each filter. It is a deep neural network with feed forward propagation techniques. As compared with multilayer perceptrons, it provides the best accuracy in all nonlinear problems, such as load forecasting.In CNN training, the FLANN optimization algorithm is implemented, CNN parameters are updated, and mean square errors are computed to evaluate the performance. Convolution layer consists of 32 filters with a kernel of size 2 × 4 pixels. It is followed by a pooling layer that sums up the filters with a stride of 2 pixels, while the coupled layers have 2048 and 512 neurons, respectively.


## 4.1. Fuzzy Clustering Approach

To model the fuzzy-RBF-CNN, the input dataset is grouped according to variables that carry significant information. Hence, the highly correlated one defines the shape and quantity of clusters in the first layer. Most important input variables to model the load forecast are temperature, hours/months/weekend, and current load status. The training process of the first layer hybrid model contains variables with fuzzy membership functions. For continuous input variables, the Gaussian membership function is preferred, whereas for definite variables, the trapezoidal membership functions. Each variable is classified into fuzzy sets having the same behavior and semantic description, which are denoted by the membership function. The “hour” variable is represented with multifuzzy sets for daytime hours, and for nighttime hours, it is represented with a single-fuzzy set. Variables not involved in clustering are initialized with a membership value equal to 1.During training cycle,xi input vector is chosen through dataset and forms fuzzy rules. The membership output M (xi) is determined per variable i using the xi input vector. Furthermore, the activation functions for each variable are calculated, which are denoted as S (i, k)(1)Si,k=ΠYMxin,where YM (xi): output of variable M contained in fuzzy rule k. n: most important input variable in numbers on which dataset is grouped.For activation of variables less the existing rules, next fuzzy rule is(2)is=argminifi,argmaxSi,k.Until the minimum activationfi,argmaxSi,k stops increasing, the training of the first layer of fuzzy-RBF-CNN continues till it reaches to the threshold value denoted by STH. The significance behind defining this threshold value is to reduce complexity of design framework by limiting number of clusters. The value of STH is 0.73, which is determined using the trial and error method.The algorithm behind this approach is defined in steps, as shown below in Table2.Table 2
Fuzzy clustering algorithm.
(1) Load the membership function for each variableM(2) Load input data set(3) Select input variablexi randomly(4) Determine output variableM (xi)(5) Chose membership function of maximum output(6) Develop first layer rule(7) CalculateS (i, k) for each variable using equation (1)(8) DetermineSmax (i) for each x (i)(9) Determinex (i′) for minima of Smax (i)(10) Determine output variableM (xi)(11) Chose membership function for each variable having maximum output(12) Develop next rule(13) From equation (1), calculate S (i, k) for each variable(14) MinSmax (i) < STH


## 4.2. Steps for RBFNN Training

In the case of RBF-CNN, kernels are associated with CNN while the training process is executed in dual phases: Initially, autonomous RBFNN is trained and different sets of RBFs are created through the cross-validation method. Secondly, input data is transformed into 3-dimensional arrays to train a CNN. By applying the permutation approach [45], the input variables that are least significant are removed from the set at the initial stage of the RBF-CNN process. In this process, the baseline is defined, and then a randomly selected variable is permuted using the random forest algorithm [46].Basically, RBFNN comprises a 2 layer neural network with a hidden layer consisting of nonlinear RBFs and linear output. Its hidden layer parameters are controlled by RBF numbers (control the model whether over or under fitting), RBF centers (plan the model characteristics), and radii of RBFs (compute activation function for RBF). The type of RBF is given by the following equation:(3)Sj2,k=1e∑xi−ci,j2,k/ri,j2,k2,where k: cluster. i: input variable. j: indices for RBF, j∈1,JmSj2,k,ci,j2,k, ri,j2,k2: activation, centers, and radii of RBFs corresponding the cluster k.Applyingk cluster with permutation approach and forming dataset, equation (3) presents the RBFNN hidden layer output, which is trained with the k-means algorithm to locate RBF centers and latter to evaluate RBF radii, FLANN algorithm is used. The FLANN approach is a higher order derivative optimization technique algorithm [47], which uses a single-layer feed forward network and is extensively used on account of its low computational complexity. Moreover, it overcomes nonlinearity in outputs due to the functional expansion feature.In the RBFNN training process, the objective function is the sum of squared error, which is determined using validation and testing sets. The RBF weights and biases are upgraded and compared with the forecasted value per iteration. Then, the mean of squared error on validation and testing are computed and continues till error value is minimized. At that optimal point, the radii value is determined. With the hyperparameter optimization approach, namely “coarse-to-fine” [48], the above procedure is carried out for different RBFs.Furthermore, a three-foldcross-validation is performed for each tested RBF that comprises validation and testing of sets. This testing deals with a continuous portion of the set, whereas the validation set is selected randomly. While averaging the cross-validation results, the optimal value of RBF’s hidden layer is obtained. This is the process of obtaining the corresponding RBFNNs.


## 4.3. Steps of CNN Training

RBFNN deals with the “curse of dimensionality” issue because of the summation of activation for each element, and to mitigate this issue, activations are computed individually for each RBF element using the following equations:(4)Sj2,k=1e∑xi−ci,j2,k/ri,j2,k2,j∈1,Jk.After performing the RBFNN training procedure, each input vector is converted to 3-dimensional arrays. Then, training, validation, and testing are employed in equation (4), and three arrays of four-dimensional sets are obtained as 3 × E × Jk × Dtrain,k, 3 × E × Jk × Dval,k and 3 × E × Jk × Dtest,k, where E: input variables. Jk: most appropriate value of RBF number. Dtrain,k, Dval,k, and Dtest,k: sizes of training, validation, and testing sets, respectively.In image processing applications, these datasets are used to establish CNN for deep neural network. CNN comprises input layer, output layer, and a number of hidden layers. This hidden layer involves convolution layers accompanied by a pooling layer with two coupled layers. The convolution layer takes out the features from images utilizing kernels and creates filters [19]. In the convolution layer, different images are obtained by applying weights to each filter. It is a deep neural network with feed forward propagation techniques. As compared with multilayer perceptrons, it provides the best accuracy in all nonlinear problems, such as load forecasting.In CNN training, the FLANN optimization algorithm is implemented, CNN parameters are updated, and mean square errors are computed to evaluate the performance. Convolution layer consists of 32 filters with a kernel of size 2 × 4 pixels. It is followed by a pooling layer that sums up the filters with a stride of 2 pixels, while the coupled layers have 2048 and 512 neurons, respectively.


## 5. Case Studies

This proposed model is evaluated as per the customer consumption rate provided by the energy market. Iteratively, it runs on a daily basis as per recorded data, predicts the hourly loads for the current day, and then predicts the load for the next seven days ahead. While following data selection approach explained in [49], the input variables are historical load [50], data of temperature forecast [51], and calendar data (month/hour/year) along with special days indication. For the fuzzy clustering method, most significant variables are average value of previous day load, maximum temperature, and special days index with hour/month.To compute the performance of the proposed hybrid model, two case studies are examined. The first study is for the Hellenic interconnected power system, where time series load data [53] covers the period from 1 January 2015 to 30 June 2019, and temperature prediction data is acquired from the SKIRON meteorological model [54]. This presented model was trained with recorded data for the first four years and tested with recorded data during 2018. Secondly, it is applied to the Cretan power system, which is an isolated system and highly loaded during summer. The Hellenic power system considers period from 1 Jan 2017 to 31 Dec 2019. During the summer of 2019, the peak load was 660 MW and the minimum load was 135 MW. Then, in 2017, the yearly peak load was 665 MW, while in 2018, it was 610 MW. Also, the fuzzy membership functions of the first layer are applied to these two case studies. In the case of the fuzzy clustering approach, the significant input variables in the first layer are the average value of day-ahead loads, the maximum temperature on a daily basis, the maximum temperature of the forecasted day, and the “hour,” “month,” and special day index of forecasting time. For “hour/month,” three trapezoidal membership functions are applied, whereas for special days index, two trapezoidal membership functions are employed. The average value of day-ahead loads is modeled by employing 3 Gaussian membership functions, and the maximum temperature predicted on a daily basis is divided into 5 fuzzy sets presented by Gaussian membership functions. The performance of the proposed model is evaluated using the mean absolute error (MAE), mean absolute percentage error (MAPE), and the root mean squared error (RMSE).In the Hellenic power system, the clusters formed are 76 for first layer while in the Cretan power system it is 68. The historical loads are modeled by applying 3 Gaussian membership functions. Variables “such as hour/month/special day index” are modeled using a fuzzy membership function. Maximum temperature is split into five fuzzy sets and is designed with a definite membership function of 1.Clusters form subsets, which contain input samples that activate the fuzzy rule. Then, the training procedure of RBF-CNNs for each fuzzy rule is repeated. Further, ensemble predictions are produced for RBF-CNNs that indicate fuzzy initialized by the activation value more than the thresholdSactivation = 0.


## 6. Outcome of Proposed Framework

### 6.1. Standards

To certify the work of the presented hybrid model, two advances and a traditional forecasting model are developed. The shape of the first two models consists of 24 regressors with similar structures. Each regressor is trained to obtain prediction data for one hour a day. For the first standard model, regressors are developed using the MLR approach [55], while for the second model, SVMs [66] are employed. This standard model is marked as 24 hr MLR and 24 h-SVM. For validating the performance of the proposed fuzzy-RBF-CNN, the RBF-CNN regressors are being replaced by SVMs. This method is marked as ML-SVM, having 3 layers. SVM is a supervised learning algorithm that does very well in the classification of data into different datasets. MLR offers generic and extendable configurations for clustering, classification, regression, etc. Fuzzy-RBFNN is eminent from other techniques in terms of universal approximation and higher learning speed. These three techniques are widely used to address other research problems. The membership functions corresponding to all variables of the fuzzy-RBF-CNN first layer are designed once and applied to all presented case studies without fine tuning. Fuzzification of the input variables leads to the creation of fuzzy rules using the linguistic representations of the corresponding membership functions. Each fuzzy rule defines a data cluster of the fuzzy-RBF-CNN first layer to which an RBF-CNN regressor will be connected. The fuzzy rules are constructed using an iterative training procedure.Using the same technique as discussed in this proposed work, the input data is clustered in the first layer. Different SVMs are trained for each cluster to develop different forecasts, and the mean of the developed ensemble predictions gives rise to the final prediction value. The forecast values applied to the proposed model obtained from RBFNN are determined.For every activated cluster, these values first produce the mean of three RBFNN outputs and then all activated cluster predictions. This model is marked as fuzzy-RBFNN. Furthermore, the execution of the persistence method is evaluated and then compared with the proposed model and the two aforesaid models [56].


### 6.2. Hellenic Interconnected Network

During forecasting, the MAPEs of fuzzy-RBF-CNN and fuzzy-RBFNN have identical values in comparison to other benchmarks, which indicate less robustness. In Tables3 and 4, the MAPE and RMSE of the proposed model are shown. Initially, load time series data of a nonlinear and complex nature are demonstrated and compared for the accuracy obtained from 24 h-MLR and 24 h-SVM. The performance of 24 h-SVM and ML-SVM indicates less improvement by the proposed model. The proposed method achieves improvements in the range of 5% to 20% [56]. However, in comparison to the least square method (generally used for RBFNN second layer) activations performed by CNN on RBF gives around a 9% improvement in outcome.Table 3
MAPEs for the proposed model and standard models.
Day aheadPersistence methodMLRSVMML-SVMLSTMFuzzy-RBFNNFuzzy-RBF-CNN15.903.453.001.931.801.851.5727.723.783.252.191.901.951.6336.333.813.302.291.851.951.6546.703.943.502.452.201.971.6356.704.083.612.502.192.001.6866.014.113.682.542.172.011.6977.854.143.702.602.202.051.72Table 4
RMSEs for the proposed model and standard models.
Day aheadPersistence methodMLRSVMML-SVMFuzzy-RBFNNFuzzy-RBF-CNN11308710593583490460217717806626275114703190280168966051247141978852750731515475519088857827825204796183990179878852548071770888802800534487In this case study, comparing the execution of ML-SVM with that of 24 h-SVM, the structure developed from the fuzzy clustering approach shows remarkable improvement for the short horizon, whereas for the longer horizon (more than 4 days ahead), both ML-SVM and 24 h-SVM show similar performance. For this study, higher forecast accuracy is attained by RBF-CNN regressors.Table5 shows the calculated MAPEs for fuzzy-RBF-CNN and ML-SVM structures obtained while calculating forecast values for working and nonworking days. For a complete prediction scope including both working and nonworking days, this proposed model shows better performance than the standard model. On nonworking days, the MAPE of Fuzzy-RBF-CNN is 2.11% in the case of three and four days-ahead horizon.Table 5
Performance evaluation of the presented model and ML-SVM in the case of both normal and special days using MAPE values.
Day aheadML-SVMFuzzy-RBF-CNNWorking daysNonworking daysWorking daysNonworking days12.822.202.482.1023.153.402.701.0533.253.512.711.1143.483.582.691.1153.583.602.741.1563.603.622.751.1373.653.702.781.15Figure3 illustrates the accuracy of the aforementioned models for successive days in March 2018. Finally, shows the finest performances procured from the fuzzy-RBFNN and fuzzy-RBF-CNN models, whereas the standard model shows analogous performance.Figure 3
Comparison of the proposed model with standard models in a two-day period of March 2018.


### 6.3. Cretan Power Network

Tables6 and 7 show the MAPE and RMSE for the week ahead horizon of the fuzzy-RBF-CNN and standard models. The working of the proposed model is closer to ML-SVM. In this case, when predicting one day ahead, the MAPE and RMSE of ML-SVM have lesser difference in comparison to the proposed model. In case of more than 2 days ahead horizon, this proposed model outperforms all the standard models. On comparison of the MAPEs of 24 h-SVM with the MAPEs of fuzzy-RBFNN and ML-SVM, the proposed fuzzy clustering approach is more successful for longer horizons, as it provides 39% and 34% mean improvements in ML-SVM and fuzzy-RBF-CNN, respectively, when compared with 24 h-SVM. The application of CNN to the output of the RBFNN hidden layer gives remarkable robustness to RBFNNs and performs better than SVM. It is shown that the unsatisfactory performance of 24 h-MLR proves more complexity in the previous case study. Furthermore, “persistence method” is better than 24 h-MLR and 24 h-SVM in the case of a longer horizon. Table 8 shows the MAPE values for the ML-SVM and proposed model that are obtained with a similar evaluation approach. Table 9 shows the performance results from training, testing, and validation of the fuzzy-RBFNN model in terms of RMSE, MSE, and MAE.Table 6
MAPEs for the proposed model and standard models.
Days aheadPersistence24 h-MLR24 h-SVMML-SVMLSTMFuzzy-RBFNNFuzzy-RBF-CNN16.153.953.582.852.203.281.9025.514.253.892.382.253.683.3536.876.955.854.663.753.893.5246.516.055.014.824.053.082.7057.086.455.254.954.374.183.8968.686.287.176.035.474.282.9078.787.457.696.185.984.384.01Table 7
RMSEs for the proposed model and standard models.
Days aheadPersistence24 h-MLR24 h-SVMML-SVMFuzzy-RBFNNFuzzy-RBF-CNN1102.6984.5560.3444.3564.1256.402125.1199.4865.5250.4867.9360.353126.30101.8878.7274.1170.9364.014134.28100.7299.5576.8573.0266.455140.56115.51132.4958.3874.3267.656144.20120.17178.4559.1175.0168.087119.02139.20222.5669.3175.9469.12Table 8
Performance evaluation of the presented model and ML-SVM in both working and nonworking days using MAPE values.
Days aheadML-SVMFuzzy-RBF-CNNWorking daysNonworking daysWorking daysNonworking days12.822.153.921.6322.392.752.402.1232.652.912.632.4242.802.952.812.4052.943.232.922.6265.014.384.952.6875.154.525.024.87Table 9
Results from training, testing, and validation of the fuzzy-RBFNN model.
Fuzzy-RBFNN modelPerformanceR2MSE (%)MAE (%)All data0.892.2010.28Training0.931.398.20Testing0.873.3814.0Validation0.861.228.30For nonworking days, the proposed model (Fuzzy-RBF-CNN) performs better than ML-SVM and results in a 14% improvement on average. While on working days, ML-SVM performs better than the proposed model in the case of current-day prediction while having similar performance for day-ahead forecasting. Figure4 illustrates prediction of both presented models for a nonworking day (15/08/2019) and a working day (16/12/2019). It shows a performance improvement of fuzzy-RBF-CNN when compared with the standard model for both days. Specifically, during morning hours, the standard model error outreach 9%, whereas using the proposed fuzzy-RBF-CNN model for the same morning hours, this error comes out to be lower than 1%. Figure 5 shows the convergence characteristics for four models (i.e., ML-SVM, LSTM, Fuzzy-RBFNN, and Fuzzy-RBF-CNN) and represents MSE values for each model. This graph shows that our proposed model shows harmony in both accuracy and convergence rate when compared with other models. Results for training, testing, and validation are presented in Figure 6.Figure 4
Comparison of the proposed model with standard models in a two-day period of August 2019.Figure 5
Convergence characteristics with MSE values.Figure 6
Results from training, testing, and validation.


## 6.1. Standards

To certify the work of the presented hybrid model, two advances and a traditional forecasting model are developed. The shape of the first two models consists of 24 regressors with similar structures. Each regressor is trained to obtain prediction data for one hour a day. For the first standard model, regressors are developed using the MLR approach [55], while for the second model, SVMs [66] are employed. This standard model is marked as 24 hr MLR and 24 h-SVM. For validating the performance of the proposed fuzzy-RBF-CNN, the RBF-CNN regressors are being replaced by SVMs. This method is marked as ML-SVM, having 3 layers. SVM is a supervised learning algorithm that does very well in the classification of data into different datasets. MLR offers generic and extendable configurations for clustering, classification, regression, etc. Fuzzy-RBFNN is eminent from other techniques in terms of universal approximation and higher learning speed. These three techniques are widely used to address other research problems. The membership functions corresponding to all variables of the fuzzy-RBF-CNN first layer are designed once and applied to all presented case studies without fine tuning. Fuzzification of the input variables leads to the creation of fuzzy rules using the linguistic representations of the corresponding membership functions. Each fuzzy rule defines a data cluster of the fuzzy-RBF-CNN first layer to which an RBF-CNN regressor will be connected. The fuzzy rules are constructed using an iterative training procedure.Using the same technique as discussed in this proposed work, the input data is clustered in the first layer. Different SVMs are trained for each cluster to develop different forecasts, and the mean of the developed ensemble predictions gives rise to the final prediction value. The forecast values applied to the proposed model obtained from RBFNN are determined.For every activated cluster, these values first produce the mean of three RBFNN outputs and then all activated cluster predictions. This model is marked as fuzzy-RBFNN. Furthermore, the execution of the persistence method is evaluated and then compared with the proposed model and the two aforesaid models [56].


## 6.2. Hellenic Interconnected Network

During forecasting, the MAPEs of fuzzy-RBF-CNN and fuzzy-RBFNN have identical values in comparison to other benchmarks, which indicate less robustness. In Tables3 and 4, the MAPE and RMSE of the proposed model are shown. Initially, load time series data of a nonlinear and complex nature are demonstrated and compared for the accuracy obtained from 24 h-MLR and 24 h-SVM. The performance of 24 h-SVM and ML-SVM indicates less improvement by the proposed model. The proposed method achieves improvements in the range of 5% to 20% [56]. However, in comparison to the least square method (generally used for RBFNN second layer) activations performed by CNN on RBF gives around a 9% improvement in outcome.Table 3
MAPEs for the proposed model and standard models.
Day aheadPersistence methodMLRSVMML-SVMLSTMFuzzy-RBFNNFuzzy-RBF-CNN15.903.453.001.931.801.851.5727.723.783.252.191.901.951.6336.333.813.302.291.851.951.6546.703.943.502.452.201.971.6356.704.083.612.502.192.001.6866.014.113.682.542.172.011.6977.854.143.702.602.202.051.72Table 4
RMSEs for the proposed model and standard models.
Day aheadPersistence methodMLRSVMML-SVMFuzzy-RBFNNFuzzy-RBF-CNN11308710593583490460217717806626275114703190280168966051247141978852750731515475519088857827825204796183990179878852548071770888802800534487In this case study, comparing the execution of ML-SVM with that of 24 h-SVM, the structure developed from the fuzzy clustering approach shows remarkable improvement for the short horizon, whereas for the longer horizon (more than 4 days ahead), both ML-SVM and 24 h-SVM show similar performance. For this study, higher forecast accuracy is attained by RBF-CNN regressors.Table5 shows the calculated MAPEs for fuzzy-RBF-CNN and ML-SVM structures obtained while calculating forecast values for working and nonworking days. For a complete prediction scope including both working and nonworking days, this proposed model shows better performance than the standard model. On nonworking days, the MAPE of Fuzzy-RBF-CNN is 2.11% in the case of three and four days-ahead horizon.Table 5
Performance evaluation of the presented model and ML-SVM in the case of both normal and special days using MAPE values.
Day aheadML-SVMFuzzy-RBF-CNNWorking daysNonworking daysWorking daysNonworking days12.822.202.482.1023.153.402.701.0533.253.512.711.1143.483.582.691.1153.583.602.741.1563.603.622.751.1373.653.702.781.15Figure3 illustrates the accuracy of the aforementioned models for successive days in March 2018. Finally, shows the finest performances procured from the fuzzy-RBFNN and fuzzy-RBF-CNN models, whereas the standard model shows analogous performance.Figure 3
Comparison of the proposed model with standard models in a two-day period of March 2018.


## 6.3. Cretan Power Network

Tables6 and 7 show the MAPE and RMSE for the week ahead horizon of the fuzzy-RBF-CNN and standard models. The working of the proposed model is closer to ML-SVM. In this case, when predicting one day ahead, the MAPE and RMSE of ML-SVM have lesser difference in comparison to the proposed model. In case of more than 2 days ahead horizon, this proposed model outperforms all the standard models. On comparison of the MAPEs of 24 h-SVM with the MAPEs of fuzzy-RBFNN and ML-SVM, the proposed fuzzy clustering approach is more successful for longer horizons, as it provides 39% and 34% mean improvements in ML-SVM and fuzzy-RBF-CNN, respectively, when compared with 24 h-SVM. The application of CNN to the output of the RBFNN hidden layer gives remarkable robustness to RBFNNs and performs better than SVM. It is shown that the unsatisfactory performance of 24 h-MLR proves more complexity in the previous case study. Furthermore, “persistence method” is better than 24 h-MLR and 24 h-SVM in the case of a longer horizon. Table 8 shows the MAPE values for the ML-SVM and proposed model that are obtained with a similar evaluation approach. Table 9 shows the performance results from training, testing, and validation of the fuzzy-RBFNN model in terms of RMSE, MSE, and MAE.Table 6
MAPEs for the proposed model and standard models.
Days aheadPersistence24 h-MLR24 h-SVMML-SVMLSTMFuzzy-RBFNNFuzzy-RBF-CNN16.153.953.582.852.203.281.9025.514.253.892.382.253.683.3536.876.955.854.663.753.893.5246.516.055.014.824.053.082.7057.086.455.254.954.374.183.8968.686.287.176.035.474.282.9078.787.457.696.185.984.384.01Table 7
RMSEs for the proposed model and standard models.
Days aheadPersistence24 h-MLR24 h-SVMML-SVMFuzzy-RBFNNFuzzy-RBF-CNN1102.6984.5560.3444.3564.1256.402125.1199.4865.5250.4867.9360.353126.30101.8878.7274.1170.9364.014134.28100.7299.5576.8573.0266.455140.56115.51132.4958.3874.3267.656144.20120.17178.4559.1175.0168.087119.02139.20222.5669.3175.9469.12Table 8
Performance evaluation of the presented model and ML-SVM in both working and nonworking days using MAPE values.
Days aheadML-SVMFuzzy-RBF-CNNWorking daysNonworking daysWorking daysNonworking days12.822.153.921.6322.392.752.402.1232.652.912.632.4242.802.952.812.4052.943.232.922.6265.014.384.952.6875.154.525.024.87Table 9
Results from training, testing, and validation of the fuzzy-RBFNN model.
Fuzzy-RBFNN modelPerformanceR2MSE (%)MAE (%)All data0.892.2010.28Training0.931.398.20Testing0.873.3814.0Validation0.861.228.30For nonworking days, the proposed model (Fuzzy-RBF-CNN) performs better than ML-SVM and results in a 14% improvement on average. While on working days, ML-SVM performs better than the proposed model in the case of current-day prediction while having similar performance for day-ahead forecasting. Figure4 illustrates prediction of both presented models for a nonworking day (15/08/2019) and a working day (16/12/2019). It shows a performance improvement of fuzzy-RBF-CNN when compared with the standard model for both days. Specifically, during morning hours, the standard model error outreach 9%, whereas using the proposed fuzzy-RBF-CNN model for the same morning hours, this error comes out to be lower than 1%. Figure 5 shows the convergence characteristics for four models (i.e., ML-SVM, LSTM, Fuzzy-RBFNN, and Fuzzy-RBF-CNN) and represents MSE values for each model. This graph shows that our proposed model shows harmony in both accuracy and convergence rate when compared with other models. Results for training, testing, and validation are presented in Figure 6.Figure 4
Comparison of the proposed model with standard models in a two-day period of August 2019.Figure 5
Convergence characteristics with MSE values.Figure 6
Results from training, testing, and validation.


## 7. Conclusion and Future Scope

Accurate LF is important for applications in different operations of the power grid and in decision-making. More accurate load forecasting mitigates the energy cost, enhances power system security, develops the optimal power plan, and therefore provides socioeconomic benefits for power grid management. The individual forecasting models fail to achieve desirable performance due to some limitations: (1) being unable to conduct forecasting with highly varying data like electric loads; (2) needing a large amount of historical data for forecasting; (3) having low accuracy due to the absence of a data preprocessing feature; and (4) overfitting and a low convergence rate. A hybrid model or combined model reduces the negative influences that are inherent in each individual model. It also takes the most advantages of individual models and is less sensitive to the certain factors that make individual model to give unsatisfactory performance. It is clear that for load forecasting, the hybrid model is highly fruitful than the individual model. So, this study develops the hybrid forecasting model and completely utilizes the benefits of individual models with enhanced performance. In this paper, a fuzzy-based prediction framework integrated with a deep learning network has been presented for STLF. This hybrid approach can capture hidden characteristics of load pattern and gain the accuracy in results of load forecasting. This complete framework is integrated with three processes: (i) hybrid architecture composed by RBF, convolution, and pooling in a fully connected two-layer network; (ii) fuzzy clustering algorithm that splits the input variables into orthogonal expansions after data preprocessing; and (iii) FLANN algorithm-based optimization technique. The main idea behind this study is to generate ensemble predictions from multiple local regressors, and this regression variable activates the forecast process using the data clustering method to assign the input to different clusters. This proposed model is designed to predict the one-week ahead load demand, and its performance is tested on two power networks, i.e., the Hellenic interconnected and Cretan power networks. This method is verified by comparing it with four benchmark models like 24 hr-MLR, 24 hr-SVM, ML-SVM, and Fuzzy-RBFNN, in terms of forecasting accuracy. On the basis of the obtained results and complete analysis, the following conclusions are being drawn: firstly, in comparison to the LSTM method (generally for RBFNN second layer), activations performed by CNN on RBF give around a 9% improvement in forecasting accuracy. It indicates that higher forecast accuracy is attained by RBF-CNN regressors. Secondly, the application of CNN on the RBFNN hidden layer gives high robustness. Third, the proposed model (Fuzzy-RBF-CNN) performs better than ML-SVM and results in a 14% improvement on average. Fourth, in comparison of the MAPEs of 24 h-SVM and fuzzy-RBFNN, the fuzzy clustering approach is more successful, as it provides 39% and 34% better performance with reference to 24 h-SVM. Thus, it shows the effectiveness of the fuzzy clustering method and the improvement in RBFNN response by CNN. This deep learning hybrid technique offers the limitation that it will not perform properly for complex hierarchical data structures. For future work, weather conditions can also be fed as an input to the hybrid model to improve the research findings. Also, researchers can forecast the power loads for weather insensitive customers by searching the choice of input frames to mitigate negative impact of weather characteristics.



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*Source: 8669796-2023-03-03.xml*