Short-term load forecasting (STLF) is part and parcel of the efficient working of power grid stations. Accurate forecasts help to detect the fault and enhance grid reliability for organizing sufficient energy transactions. STLF ranges from an hour ahead prediction to a day ahead prediction. Various electric load forecasting methods have been used in literature for electricity generation planning to meet future load demand. A perfect balance regarding generation and utilization is still lacking to avoid extra generation and misusage of electric load. Therefore, this paper utilizes Levenberg–Marquardt (LM) based Artificial Neural Network (ANN) technique to forecast the short-term electricity load for smart grids in a much better, more precise, and more accurate manner. For proper load forecasting, we take the most critical weather parameters along with historical load data in the form of time series grouped into seasons, i.e., winter and summer. Further, the presented model deals with each season’s load data by splitting it into weekdays and weekends. The historical load data of three years have been used to forecast week-ahead and day-ahead load demand after every thirty minutes making load forecast for a very short period. The proposed model is optimized using the Levenberg-Marquardt backpropagation algorithm to achieve results with comparable statistics. Mean Absolute Percent Error (MAPE), Root Mean Squared Error (RMSE), ^{2}^{2}

Electric power load forecasting is essential for the planning and decision-making of power system management. Electric load generation, transmission, and distribution utilities heavily depend on load forecast. Therefore, these utilities need accurate methods to forecast electrical load to use their infrastructure effectively, safely, and economically [

Past research efforts focused on classical and computational intelligence techniques for load forecasting [

Besides the above, making accurate electrical load forecasting while considering seasons as well as the variations of weekdays and weekends is a challenging task. The load can act differently on different weekdays, such as Mondays and Fridays may have substantially distinct demands than Tuesdays and Thursdays due to the proximity of weekends. Furthermore, various parameters, i.e., time factors (hours, days, months, years), weather data, customer class, past required load, region expansion, increased load, etc., also affect load demands significantly [

This paper aims to develop a generalized deep learning-based model for STLF to address the challenges described above. The objective is to deal with weather parameters and load demand variations due to seasons, weekdays, and weekends in a better, more precise, and more accurate manner. In this regard, an artificial neural network (ANN) is proposed that contemplates historical load data grouped into winter and summer seasons. Each season is further sorted into weekends and weekdays independently, with each weekday sliced into 48 slabs while considering the variation within a single day. As the load profile is dynamic with temporal, seasonal, and day-to-day variations, thus, the proposed model forecasts the week-ahead electric load demand by predicting each weekday’s load after every thirty minutes. The prediction for a very short period attempts to make the load forecast more interactive for the reliable working of power systems. We use one of the best optimization techniques, i.e., the Levenberg-Marquardt (LM) backpropagation algorithm, to train the proposed model and optimize its performance. The performance of the proposed model is tested on the USA power industry’s historical hourly load data that is available publicly. Regression analysis is carried out through training, testing, and validation against the target vector to demonstrate correlation among them. The proposed LM-based ANN model intends to perform highly accurate STLF with significant convergence speed for improved power grid management and operations.

The main contributions of the paper are as follows.

We developed a model that deals with historical load data by separating it into different seasons (i.e., winter and summer). Further, each season is split into weekdays and weekends, with each day sliced into 48 slabs.

The LM backpropagation technique is adapted for optimized training of our proposed model, which is empowered via training to predict the day-ahead and week-ahead load demand after every thirty minutes.

We verify the proposed LM-based ANN model on past load data. The empirical results of RMSE and MAPE values indicate that the proposed model achieves better load forecast accuracy and convergence rate.

Regression analysis is performed after training to validate the model’s performance in terms of R^{2} (coefficient of determination) and R (correlation) between actual and forecasted load demand.

The rest of the paper is arranged as follows: Section 2 reviews the related work. The proposed LM-based ANN technique is elaborated in Section 3. Section 4 presents results and discussions. Finally, the paper is concluded in Section 5.

Generally, STLF includes the load forecast for hours to a week and is essential in the planning and management process of the power grid operations. Previous literature indicates that statistical methods and machine learning models are standard techniques for forecasting electric load of short-term nature.

Since the last decade, STLF has been performed using several machine learning techniques that provide realistic prediction accuracy [

ANN is also widely used for predicting different types of load forecasting, proving itself a valuable, general-purpose method for identifying patterned classification [

Researchers have also combined various classical models and deep learning techniques to develop a hybrid model and found significant improvement in forecast accuracy for power system applications, especially for predicting time series data. For example, Eapen et al. [

Different researchers have done much work to predict STLF; however, standardized accurate forecasting models are still lacking that can be used for all types of purposes and conditions. STLF is challenging as many other influencing parameters affect electricity load besides historical load demand, such as time of day, weekdays or weekends, climate factors, social variables, different seasons, etc. To resolve these problems and improve forecasting accuracy, in this paper, we have proposed a novel hybrid STLF model that organizes load data into different seasons (i.e., winter and summer). Further, the proposed model considers weekdays and weekends separately for every month of each season. Additionally, the time within each day is sliced into 48 slabs to forecast the load demand of the next day more accurately.

This work proposes an LM-based ANN model for STLF that simultaneously works on linear and nonlinear time series load data.

For accurate load forecasting, data is first fed to the preprocessing phase for cleaning purposes. The preprocessed data is inputted into the data classification phase to separate the load data into winter and summer seasons. Further, it is divided into weekends and weekdays, with each day’s data sliced into 48 splits. Next, the output of the data classification phase is passed to the proposed LM-based ANN model for training. We use an adaptive learning algorithm to train the model and use past load data for training to find the best possible weights. Afterward, the trained model is verified, and the next day’s load demand is forecasted for a very short period, i.e., thirty minutes. Following is the detail of each of these phases.

We have used the USA power industry’s publicly available electrical hourly load dataset^{1}

The load profile for weekdays and weekends differs significantly; therefore, a separate analysis is conducted for weekdays and weekends. Data is processed on a daily, 5-days, and week-by-week basis. Since the load demand for any given hour of the day is like previous days’ loads, thus, the LM-based ANN model is trained on the historical load data. The data is preprocessed to obtain accurate forecasts after training. There is a strong association between data appropriateness and convergence of the model, i.e., the more the data is finetuned, the early the model will converge. Therefore, data is first fed to the cleaning phase, replacing the faulty and missing fields with the average values of the previous days’ load data. As electric load data always contain outliers, thus, normalization follows the cleaning phase to limit the weighted sum within the bounds of the activation function.

For best prediction results, dataset organization is carried out according to the following criteria.

Load data is first organized based on seasons, i.e., grouping into summer and winter. The winter season is spread over three months, i.e., December, January, and February, whereas the summer comprises May, June, and July. The remaining months have the usual load demands.

Each month’s load data is further separated into weekdays (5 working days) and weekends (Saturday and Sunday). Working days and weekends are worked separately as the load demand for weekends is less than for working days. Thus, weekend load data is not used to forecast load demand for working days and vice versa. We worked on weekly five days load data to predict next week’s working days load forecast.

Considering the fluctuating criticality of the load demand, each hourly load sample is divided into two equal halves, with each half containing the load data for half-hour. It helps predict STLF more precisely and accurately for a short period.

The proposed model uses multilayer perceptron (MLP) architecture with two layers, i.e., a hidden layer and an output layer, as described in _{n}

Parameters | Values |
---|---|

No of layers | 3 (Input layer, hidden layer, output layer) |

Hidden layer neurons | 100 |

Input layer neurons | 5 |

Output layer neurons | 1 |

Number of hidden layers | 1 |

Activation function | Sigmoid function |

Training algorithm | Levenberg Marquardt backpropagation |

Number of epochs | 1000 (default) |

An activation function is used to achieve the desired outputs from the hidden layer. The activation function is required to be nondecreasing and differentiable for accurate training of ANNs. Thus, the log-sigmoid function

The Purelin transfer function is used as an activation function at the output layer, which is a linear transfer function that calculates a layer’s output from its net input.

The proposed model uses the Levenberg-Marquardt (LM) backpropagation algorithm, one of the best optimization functions with a better learning rate than the other functions available for forecasting. The LM algorithm was designed by Hagan et al. [

Initially, the model uses default values for the number of epochs and learning rate, which are adjusted later for model convergence during training. Moreover, the predicted load output is compared to the actual load data for performance evaluation, and different performance metrics have been applied. First, we calculated the mean absolute percentage error (MAPE) to check the accuracy of the proposed approach, which is defined as follows.

In

The second performance metric is the root mean squared error (RMSE), a performance assessment indicator that estimates the errors of the predicted load forecast. It is defined as follows.

The third performance metric is regression analysis, where we calculated the values of R^{2} and R. R^{2}, also called goodness of fit, which measures the extent that variability in the actual load is explained by variability in the forecasted load values. At the same time, R measures the correlation between actual and forecasted load demand. The formulae for R^{2} and R are as follows:
^{2}

In the model’s training process, we used the predictor and target datasets for training. The actual load values for a specific predictor dataset make up the target dataset. The training algorithm tries to minimize the difference between the expected output and actual output (loss function) and settles the weights and biases accordingly. The training goal is set at 0 to ensure zero tolerance for loss function. The training progresses to minimize the loss and enable the model to forecast the electric load accurately. The weights and biases are updated using backpropagation to reduce loss function.

Further, the movement of the error signal back to the input layer through the hidden layer can be generalized through the delta rule. The loss minimization procedure is repeated on an epoch-by-epoch basis until the model converges to a minimum or some stopping criteria meets, e.g., the total number of epochs. Initially, the number of epochs is 1000 (default value), which is later reduced to a maximum of 7 due to the early convergence of the model. An epoch is a comprehensive depiction of the ideal training regimen. The training procedure permits the LM-based ANN model to learn the relationship between inputs and outputs. It keeps learned information in the parametric form so that model can perform subsequent operations without retraining.

The model is trained to provide desired outputs using historical data as input signals. Typically, every input after some processing generates an output signal in a system. The ultimate goal of the model is optimization, i.e., to minimize the loss function. Thus, the Levenberg Marquardt (LM) backpropagation algorithm is employed to get the desired output by iteratively modifying the internal weight and bias parameters of the ANN hidden layer. Initially, these parameters are given random values, and the sum of square error _{n}

In the above equation, ^{th}^{th}

In the above equation,

Finally, validation and testing followed the training. After the network has been trained, it is put to the test by feeding it test load forecast data. The anticipated load output is compared to the actual load output to calculate the inaccuracy.

The proposed LM-based ANN model is empowered with training to forecast future load demands with acceptable accuracy. The results for the winter and summer seasons are obtained separately, with the summer season consisting of May, June, and July, while the winter season comprises December, January, and February. Moreover, the load demand within a month is forecasted separately for weekdays and weekends. Further, each day is sliced into 48 slabs to predict STLF for a very short period. Afterward, the following performance metrics are calculated to evaluate the model’s performance.

The regression analysis determines the values of ^{2}

All these plots estimate the accuracy with which the trained model forecasts the future load. These plots also depict the model’s capacity to learn the complex relationship between historical load demand, weather, and time data for accurate load forecasts. In each plot of ^{2}^{2}^{2}

Another way to represent the model’s performance on training and testing datasets is to measure the error rate across varying epochs. The model training is poor when there is high variance and bias. It indicates that the model is storing training dataset information instead of learning. High bias signifies a high rate of error during training and testing, whereas high variance indicates the noticeable gap between the prediction accuracy of training and testing of the model. In either case, the model performs poorly and results in vague generalization. Another problem is overfitting, which occurs when a model performs well in training but does not show good performance on testing. Such a model memorizes the dataset parameters instead of learning from them, leading to a lousy generalization.

Layers | Month | Hidden neurons | Learning function | Training function | RMSE | MAPE% | Epoch |
---|---|---|---|---|---|---|---|

2 | Dec | 100 | LEARNGDM | TRAINLM | 121.4 | 1.88 | 7 |

2 | Dec | 200 | LEARNGDM | TRAINLM | 116.5 | 1.72 | 4 |

2 | Dec | 300 | LEARNGDM | TRAINLM | 112.02 | 1.65 | 7 |

2 | Jan | 100 | LEARNGDM | TRAINLM | 213.3 | 3.04 | 6 |

2 | Jan | 200 | LEARNGDM | TRAINLM | 120.15 | 1.84 | 7 |

2 | Jan | 300 | LEARNGDM | TRAINLM | 105.4 | 1.74 | 5 |

2 | Feb | 100 | LEARNGDM | TRAINLM | 186.6 | 2.7 | 7 |

2 | Feb | 200 | LEARNGDM | TRAINLM | 110.8 | 1.62 | 5 |

2 | Feb | 300 | LEARNGDM | TRAINLM | 97.9 | 1.3 | 6 |

2 | May | 100 | LEARNGDM | TRAINLM | 154.3 | 1.9 | 7 |

2 | May | 200 | LEARNGDM | TRAINLM | 107.73 | 1.5 | 5 |

2 | May | 300 | LEARNGDM | TRAINLM | 73.56 | 1.08 | 6 |

2 | June | 100 | LEARNGDM | TRAINLM | 254.6 | 3.89 | 6 |

2 | June | 200 | LEARNGDM | TRAINLM | 205.83 | 2.71 | 7 |

2 | June | 300 | LEARNGDM | TRAINLM | 117.34 | 1.8 | 6 |

2 | July | 100 | LEARNGDM | TRAINLM | 297.5 | 3.7 | 7 |

2 | July | 200 | LEARNGDM | TRAINLM | 105.3 | 1.42 | 5 |

2 | July | 300 | LEARNGDM | TRAINLM | 98.45 | 1.4 | 6 |

Similarly, the log-sigmoid transfer function turns out to be good, giving better RMSE and MAPE values than the tan-sigmoid function used at the hidden layer neurons of the LM-based ANN model. It is also observed that the size of the dataset also contributes to the model’s performance, i.e., the larger the size of the dataset, the better the model’s performance. The table shows that the model gets the best results at very early epochs. Thus, our proposed LM-based ANN model resolved the problem of overfitting. Moreover, from the empirical results, it can be concluded that the network is trained to forecast with high accuracy.

The ultimate goal of this paper is to forecast the next day’s load with maximum accuracy. For which the LM-based ANN model is trained using the best hyperparameter values and optimized weights that give the best prediction results for the target load data. Finally, the best hyperparameter values of the model training are documented, and the model is tested with test data to check its prediction performance on unseen data.

^{st} five weekdays, with each day sliced into 48 slabs (total of 240 slabs) during different months of the summer season. Similarly, ^{st} five weekdays during different months of the winter season. The plots of both figures depict that the forecasted load is very close to the actual load demand. Thus, our proposed LM-based ANN model is robust enough to predict STLF for the next week.

We forecasted the load for the next day, with each day sliced into 48 slabs bearing maximum accuracy. Compared with other state-of-the-art machine learning techniques [

Power load prediction is essential for an effective energy system operation and scheduling. This paper proposed an LM-based ANN model to forecast short-term electricity load. We collected the USA Power Industry’s electric load dataset for model training from 2019 to 2021. Weekdays and weekends are separated for the winter and summer seasons, considering the significant variation of load demands for different seasons as well as for weekends and weekdays. Owing to the dynamic and temporal nature of the load profile, each day’s load is further divided into 48 slabs, each consisting of 30 min. We take time and weather data with historical load demand simultaneously as input to the LM-based ANN model due to the great impact of meteorological parameters on the next day’s load demand. The Levenberg-Marquardt optimization technique is used as a backpropagation algorithm in the LM-based ANN model to optimize its performance. The model’s performance is evaluated using statistical measures, i.e., RMSE, MAPE, R, R^{2}. The RMSE and MAPE give lower error rates, whereas R^{2} and R produce optimal values that prove the robustness of the LM-based ANN model. The empirical results show that the proposed electric load forecasting model outperforms in terms of forecast accuracy with the lowest error rates.

Although the LM-based ANN model is robust in processing time series data, its parameters still have some room for optimization (i.e., finetuning of significant parameters) to improve the computing efficiency. Moreover, forecasting accuracy can be further enhanced by considering other important factors, such as locations, social variables, etc. Our future work will investigate other deep learning-based forecasting mechanisms like convolutional neural networks and recurrent neural networks to deal with more complex and larger datasets.

The authors acknowledge the financial support provided in part by the

The authors declare that they have no conflicts of interest.