Short-Term Electricity Load Forecasting Using a New Intelligence-Based Application

Abstract

Electrical load forecasting plays a crucial role in planning and operating power plants for utility factories, as well as for policymakers seeking to devise reliable and efficient energy infrastructure. Load forecasting can be categorized into three types: long-term, mid-term, and short-term. Various models, including artificial intelligence and conventional and mixed models, can be used for short-term load forecasting. Electricity load forecasting is particularly important in countries with restructured electricity markets. The accuracy of short-term load forecasting is crucial for the efficient management of electric systems. Precise forecasting offers advantages for future projects and economic activities of power system operators. In this study, a novel integrated model for short-term load forecasting has been developed, which combines the wavelet transform decomposition (WTD) model, a radial basis function network, and the Thermal Exchange Optimization (TEO) algorithm. The performance of this model was evaluated in two diverse deregulated power markets: the Pennsylvania-New Jersey-Maryland electricity market and the Spanish electricity market. The obtained results are compared with various acceptable standard forecasting models.

1. Introduction

Over the past decade, the demand for electricity has been experiencing rapid growth, primarily driven by the processes of urbanization and industrialization [1]. However, due to the diverse requirements of customers and their varied energy usage models, electricity demand does not follow a uniform trajectory, making accurate predictions challenging with a random model [2,3,4]. This unpredictability can lead to several issues, including the operation of nonessential generating units, increased fuel consumption, and higher operational costs. Consequently, the need for precise load forecasting has become crucial in effectively managing these challenges.

Load forecasting plays a pivotal role in grid-connected systems by providing policymakers with critical information for efficient capacity planning [5]. By accurately predicting electricity demand, load forecasting helps to ensure that sufficient resources and infrastructure are available to meet the requirements of consumers. Additionally, it assists in achieving optimal scheduling through the process of economic dispatch and unit commitment, ensuring that electricity generation is efficiently coordinated with the demand profile.

To address these complexities, load forecasting leverages historical load data and incorporates relevant information such as weather conditions. This integration of data and other factors brings forth essential insights that enable policymakers to make informed decisions regarding resource allocation, energy procurement, and system operation. Using load forecasting techniques within grid-connected systems, policymakers can better plan and manage electricity generation and distribution, leading to improved reliability, reduced operational costs, and a more sustainable energy system.

In recent years, the field of load forecasting has witnessed significant advancements, primarily driven by the integration of intelligent techniques and data-driven models. One such approach that has gained traction is the use of intelligence-based applications, which leverage artificial intelligence, machine learning, and optimization algorithms to improve the accuracy and efficiency of load forecasting models. Intelligence-based applications offer several advantages over traditional statistical and econometric methods in short-term electricity load forecasting. These approaches have the capability to capture complex nonlinear relationships and temporal dependencies present in load data, thereby providing more accurate predictions. By analyzing historical load patterns and their corresponding predictors, intelligence-based models can identify hidden patterns, trends, and seasonality in the data. This allows for a better understanding of the underlying factors influencing electricity demand and enables more accurate load predictions. Moreover, intelligence-based models have the ability to incorporate various exogenous factors that impact electricity demand, such as weather conditions, holidays, and special events. By considering these external influences, load forecasting models can adapt to changes in the environment and provide more reliable predictions. For example, weather conditions play a significant role in electricity demand, as heating and cooling needs are influenced by temperature fluctuations. By integrating weather data into the forecasting process, intelligence-based models can account for these factors and produce more accurate load forecasts. The integration of intelligent techniques in load forecasting has not only improved forecast accuracy but also revolutionized decision making in the energy sector. By leveraging advanced algorithms and data-driven methodologies, intelligence-based applications empower policymakers and energy providers to optimize resource allocation, enhance energy efficiency, and make informed decisions that align with the changing demands of electricity markets. These models enable stakeholders to anticipate peak demand periods, identify potential energy imbalances, and plan the deployment of generation resources more effectively. Furthermore, intelligence-based load forecasting allows for the identification of demand response opportunities, where consumers can modify their electricity usage in response to market signals, leading to more efficient and sustainable energy consumption.

In general, load forecasting has three classes, namely, short-, mid-, and long-term. Short-term forecasting has gained great attention owing to its facilitating utility companies and dispatchers to conduct secure and economic activities on the optimum daily operation of the power system [6,7].

Accurate load forecasting becomes more challenging on account of the ongoing development of power grids and increasing grid management complexity [8,9]. Numerous countries have launched electricity markets and made the participation of multiple agents easier, providing a competitive environment and decreasing costs for consumers. Load forecasting in the electricity market has turned out to be one of the essential tasks for electricity market units [10].

In general, load forecasting is conducted by the employment of models based on conventional or artificial intelligence. Different conventional models, such as the multiple linear regression model [11], the autoregressive integrated moving-average (ARIMA) model [12], and exponential smoothing [13], can forecast applications. These conventional models can be easily used and have elevated calculation speeds. Nevertheless, the precision efficiency of the aforementioned models has failed due to the nonlinear characteristics of electrical load data. Time series methods are very efficient for very short-term forecasting (usually within timespans shorter than 24 h). Time series methods depend on ARIMA models [14] or functional methods [15,16], utilizing daily and weekly patterns in the electricity load data. Machine-learning (ML) approaches have been stronger at the incorporation of external data for short-term and mid-term forecasting (timespans of longer than one day). These learning models use calendar features (e.g., the day of the week and time of the year) and meteorological impacts (e.g., wind speed and temperature) or tariff choices, because inputs are subsequently trained on several points of historical data (commonly 3–5 years). The Global Energy Forecasting Competition provides a good review of load forecasting procedures [17].

Common algorithms include black box machine-learning (ML) models, like gradient boosting machines [18] and neural networks [19,20], or statistical approaches, like Generalized Additive Models (GAM) [21]. Black box approaches are appealing because of their good forecasting implementations; however, in general, they are affected by a lack of interpretability. GAMs are attractive for electric utilities because they incorporate the flexibility of a completely nonparametric model and the simplicity of a multiple regression model, and they are computationally effective for a scale using a large piece of data [22]. The authors in reference [23] propose utilizing extreme gradient boosting (XGBoost) for forecasting the weekly hourly power plant load, incorporating weather factors and historical load data. The study also addresses the complexity of the XGBoost hyperparameter tuning phase. A novel short-term forecasting model was developed by Li et al. on the basis of a modified long short-term memory (LSTM) network and an autoregressive feature selection model to predict household electricity load [24]. Fekri et al. provided an online adaptive recurrent neural network (RNN), which is a method for load forecasting with the potential for constant learning from recently arrived data and adaptation to novel patterns [25]. A helpful method for the issue of electricity load forecasting was suggested by Jalali et al. through a deep neuroevolution algorithm for the automatic design of a convolutional neural network (CNN) structure using an enhanced grey wolf optimizer (EGWO) as a new changed evolutionary algorithm [26]. A powerful short-term electrical load forecasting structure was put forward by Chitalia et al. with the potential to show differences in building operation, irrespective of building type and location [27].

This study focuses on proposing an artificial intelligence-based application for short-term electricity load forecasting, aiming to achieve more precise and powerful predictions. The key contribution of this research lies in the development of a combined strategy model that can provide accurate forecasts over extended time periods. The study offers several contributions, which are summarized as follows:

• The research introduces the wavelet transform method as a signal decomposition technique for the analysis of original electricity load data. By decomposing the data into different frequencies, the wavelet transform allows for a more comprehensive understanding of the underlying patterns and variations within the load profile.
• The study proposes a novel combined intelligent-based application that integrates the radial basis function (RBF) network and the Thermal Exchange Optimization (TEO) algorithm for short-term electrical load prediction. This combination of techniques aims to enhance the accuracy and robustness of load forecasting models.
• The developed model is applied and validated in two valid electricity markets, namely, the Pennsylvania-New Jersey-Maryland (PJM) market and the Spanish electricity market. By conducting experiments in different market contexts, the study assesses the generalizability and effectiveness of the proposed application across diverse settings.

To evaluate the performance of the proposed application, it is compared against various well-known benchmark models that are commonly used in short-term load forecasting. This comparative analysis provides insights into the superiority and effectiveness of the developed intelligent-based approach.

2. Wavelet Transform Decomposition Model

WTs are classified under discrete wavelet transform (DWT) and continuous wavelet transform (CWT). The CWT (W_(a,b)) related to signal $f_{\left(x\right)}$ for wavelet ${\phi }_{\left(x\right)}$ is as follows [28,29]:

$$W_{(f,a,b)}=\frac{1}{\sqrt{a}}{\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}{f}_{(x)}{\phi }_{\left(\frac{x-b}{a}\right)}dx}$$

(1)

where parameter $a$ and $b$ are responsible for the wavelet spread and central position, respectively. Moreover, the $W_{(f,a,b)}$ coefficient is the matching of the original signal $f_{\left(x\right)}$ with the scaled or translated mother wavelet, and ${\phi }_{\left(x\right)}$ is the mother wavelet. Consequently, the set of $W_{(f,a,b)}$, associated with a specified signal, presents the signal wavelet of the mother wavelet.

DWT is more effective than CWT and similar to CWT regarding accuracy [29]:

$$W_{(m,n)}=2^{-(m/2)}{\displaystyle \sum _{t=0}^{T-1}{f}_{(t)}{\varphi }_{\left(\frac{t-n{.2}^m}{2^m}\right)}}$$

(2)

$T$ is the signal $f_{\left(t\right)}$ length. The scaling and translation factors are functions of $n$ and $m$$\left(\alpha =2^m,b=n{.2}^m\right)$; additionally, $t$ shows the discrete time index.

According to the above-mentioned sections, the main challenge of load forecasting regarding the present dataset can be the load large volatility in individual apartments. As a result, to choose the best model, the performance of the models regarding the prediction of apartment-level load data was considered further.

3. TEO Algorithm

The TEO algorithm is a new optimization method that is based on Newton’s law of cooling. This law states that the rate of heat loss for an object is directly proportional to the difference in temperature between the object and its surrounding environment at a given time [30]. In the TEO algorithm, several search agents are considered as cooling objects (recognized or reference nodes), and other nodes that are not recognized or NLOS nodes are considered as the environment. The exchange of heat between the cooling objects and the environment (reference nodes and NLOS nodes) is mathematically expressed using Equations (3) and (4):

$$T_i^{c-env}=\left(1-\left({cv}_1+{cv}_2\ast \left(1-N_{CI}\right)\ast rnd\right)\right)\ast T_i^{p-env}$$

(3)

$$N_{CI}=\frac{C_{IN}}{{Max}_{Iter}}$$

(4)

where $T_i^{p-env}$ and $T_i^{x-env}$ denote the preceding and adjusted temperatures of the environment’s objects (the place of reference nodes and NLOS nodes in the network), with ${cv}_1$ and ${cv}_2$ regarded as the variables utilized to control the localization or detection operation. Moreover, C_IN and MaxIter stand for the present iteration number and the maximum number of iterations. Additionally, Equation (8) and the earlier steps of the TEO optimization algorithm are used to update the temperature of the object and its surrounding environment. Equation (5) is used to update the temperature of the object, and Equation (6) is used to update the temperature of the environment:

$$T_i^{new-env}=T_i^{x-env}+\left(T_i^{old-env}-T_i^{x-env}\right)\ast e^{-\beta N_{CI}}$$

(5)

$$\beta =\frac{{CosineN}_{CI}\left(Obj\right)}{{CosineN}_{CI}\left(Worst\_Obj\right)}$$

(6)

A comparison of the rnd value to a predefined prevention threshold was performed at this juncture for the random selection of a single dimension of the ith search agent to regenerate its value according to Equation (7):

$$T_{i,j}=T_{i,Min}+rnd\ast \left(T_{j,Max}-T_{j,Min}\right)$$

(7)

where T_i,j is regarded as the jth variable of the ith search agent, with T_j,Min and T_j,Max as the lower and upper thresholds of the jth variable, respectively.

4. RBF Neural Network

The basic structure of the radial basis function (RBF) network consists of three distinct layers [31]. The first layer is responsible for taking in input patterns and establishing connections between the network and its environment. The second layer, which is the only hidden layer in the network, applies the Radial Basis Function. The third layer, which is linear, uses the activation pattern responses of the network. The relationship between the inputs and outputs of the network is described by a multivariate equation:

$$y_{ij}\left(x\right)={\sum }_{j=1}^K{\sum }_{i=1}^N{W}_{mj}G\left(‖x_i-c_m‖\right)+b+e_{ij}$$

(8)

where $y_{ij}$ denotes the i, j-th element of the output matrix Y_N,K; N indicates the number of observations (data); K denotes the number of outputs in the RBFNN (or responses). If M is indicated as the number of hidden neurons (or the RBF centers), w mj stands for the m, j-th element of the weight matrix W_M+1,K, m = 1, 2, …, M, M + 1 indicates the number of hidden neurons’ add bias (b), x_N,K indicates the input patterns, c_m denotes the square centroids matrix M × M, and E_N,K indicates the matrix of residuals of e_ij; subsequently, Y_N,K(x) = d_ij is considered the process output. A matrix form is written as follows:

$$d_{ij}=GW$$

(9)

An unbiased estimator for the weights, denoted as W, is presented for the well-established outcome of multivariate ordinary least squares:

$$W={\left(\acute{G}G\right)}^{-1}\acute{G}Y$$

(10)

where G is obtained through the distance $‖x_i-c_m‖$ using the radial basis function in Gaussian form:

$$G\left(‖x_i-c_m‖\right)=exp\left(-{‖x_i-c_m‖}^2\right)$$

(11)

Such a Euclidean distance $‖x_{NM}-c_{MM}‖$ can be substituted with the Mahalanobis distance obtained through Equation (12) as follows:

$$r=\sqrt{{\left(x_i-c_m\right)}^{}}{\sum }_{}^{-1}\left(x_i-c_m\right)$$

(12)

where ∑ denotes the global covariance matrix for the input patterns and is exactly similar for all centers. G is defined by the following form:

$$G=\left[\begin{array}{c}G\left(x_1-c_1\right)\\ G\left(x_2-c_1\right)\\ ⋮\\ G\left(x_N-c_1\right)\end{array}\begin{array}{c}G\left(x_1-c_2\right)\\ G\left(x_2-c_2\right)\\ ⋮\\ G\left(x_N-c_2\right)\end{array}\begin{array}{c}\cdots \\ \cdots \\ \ddots \\ \cdots \end{array}\begin{array}{c}G\left(x_1-c_m\right)\\ G\left(x_2-c_m\right)\\ ⋮\\ G\left(x_N-c_m\right)\end{array}\right]$$

(13)

Equation (5) uses the distance between x_i and c_i, and the radial basis function is a function that has the ability to monotonically increase or decrease its response based on the distance from a fixed point known as the center or centroid. The radial basis function is applied to this distance, with the most common form being the Gaussian function, represented by Equation (14):

$$\phi \left(r\right)=exp\left({-r}^2\right)$$

(14)

5. The Developed AI-Forecasting Model

The current study conducted an in-depth investigation into a three-step forecasting model specifically designed for load forecasting in electricity markets. In this study, different lagged hours were regarded as the duration of the load signal, resulting in a suitable precise load forecast and computation burden. To provide a visual representation of the entire forecasting application (WT-RBF-TWO), Figure 1 illustrates the overall framework. Furthermore, a summary of the suggested load forecast plan is outlined in the following steps:

Step 1:

Decomposing the original load signal using the wavelet transform decomposition (WTD) technique into four distinct components: D1, D2, D3, and A4. This decomposition enables the separation of various frequency bands within the load data, allowing for a more detailed analysis of load patterns and variations.

Step 2:

Developing a series of candidate input variables for load prediction, which includes the four components obtained from the WTD, as well as lagged values of the load signal. Additionally, normalizing both the candidate inputs and outputs is crucial to ensure that the data are on a consistent scale, facilitating the subsequent modeling process.

Step 3:

Predicting the output variable using the WT-RBF-TWO model. In this step, the radial basis function (RBF) parameters are optimized by the temporal weighted optimization (TEO) technique. The TEO serves to enhance the precision of the RBF model during the learning stage of the prediction process by assigning appropriate weights to the historical load data. This temporal optimization accounts for the significance of different historical data points and their relevance to the current forecasted period. The RBF parameters were considered to be decision variables, and the RMSE error indicator was considered to be the objective function.

By following this three-step approach, the WT-RBF-TWO model aims to provide accurate load forecasts in electricity markets. The initial step involves decomposing the load signal into distinct components, and the second step focuses on generating suitable candidate input variables. Finally, the third step employs the WT-RBF-TWO model, with the TEO optimizing the RBF parameters to enhance the precision of load predictions. This comprehensive load forecast plan integrates advanced techniques, such as wavelet transform decomposition, radial basis function modeling, and temporal weighted optimization, to improve the accuracy and reliability of load forecasts in electricity markets.

6. Error Indices

To assess and compare the models, three measures are used: the mean absolute error (MAE), the root mean square error (RMSE), and the mean absolute percentage error (MAPE). These measures are used to evaluate the accuracy of the models, with lower values indicating better performance.

$$RMSE=\sqrt{\frac{1}{m}{{\displaystyle \sum _{i=1}^m\left(x_{ac{t}_i}-x_{fo{r}_i}\right)}}^2}$$

(15)

$$MAE=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|x_{ac{t}_i}-x_{fo{r}_i}\right|}$$

(16)

$$MAPE=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|\frac{x_{ac{t}_i}-x_{fo{r}_i}}{x_{ac{t}_i}}\right|}\times 100$$

(17)

where x_acti is the actual value, x_fori denotes the predicted value for a similar duration, and N denotes the number of time series.

7. Results and Discussion

7.1. Case Study

Case I:

The PJM electricity market in the USA is one of the biggest electricity markets worldwide [32]. In the current study, electricity load data obtained from this market in 2006 (see Figure 2) were utilized to indicate the suggested model’s capability. As previously stated, the last 4 weeks of each year’s season are chosen as the test data to simulate STLF at hand once a week in the PJM market for the winter, spring, summer, and fall within February, May, August, and November, respectively.

Case II:

The Spanish electricity market in Europe is the second case study. In the present study, the data on electricity load obtained from this market in 2002 (see Figure 2) were employed to demonstrate the suggested model’s capability. The fourth weeks of February, May, August, and November are chosen as the test data for winter, spring, summer, and fall, respectively.

7.2. Load Forecasting Results

In this section, we evaluate the performance of the proposed forecasting model using data from two valid electricity markets: the Pennsylvania-New Jersey-Maryland (PJM) market and the Spanish electricity market. We also compare the proposed model with two other metaheuristic algorithms, namely, the Genetic Algorithm (GA) and the Imperialist Competitive Algorithm (ICA). The evaluation focuses on predicting load based on data fluctuations in different seasons.

Table 1. The comparison results of the combined forecasting models for Case I and II.

Time	Models	Case I			Case II
		WT-RBF-GA	WT-RBF-ICA	WT-RBF-TEO	WT-RBF-GA	WT-RBF-ICA	WT-RBF-TEO
Spring	RMSE	0.044	0.033	0.020	0.121	0.069	0.017
	MAE	0.028	0.022	0.007	0.100	0.055	0.016
	MAPE (%)	8.415	5.466	4.979	7.034	4.810	3.899
Summer	RMSE	0.074	0.055	0.020	0.055	0.044	0.017
	MAE	0.061	0.045	0.010	0.043	0.033	0.007
	MAPE (%)	6.348	4.952	4.226	7.292	5.162	4.717
Fall	RMSE	0.027	0.020	0.006	0.097	0.071	0.014
	MAE	0.023	0.017	0.004	0.080	0.052	0.020
	MAPE (%)	7.156	6.657	4.255	7.844	5.618	4.212
Winter	RMSE	0.073	0.070	0.037	0.046	0.035	0.006
	MAE	0.056	0.049	0.023	0.038	0.028	0.004
	MAPE (%)	8.994	5.127	4.087	9.584	4.821	3.492

presents the comparison results of the combined forecasting models for Case I and II. The suggested WT-RBF-TEO model outperforms the other forecasting models in terms of a lower root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) in both cases. Among the compared models, the mixed models achieved competitive results compared to state-of-the-art algorithms. The closest competitor to the suggested method is the state-of-the-art version of ICA hybridized with WT-RBF-ICA, which achieved a performance close to that of the WT-RBF-TEO model. In addition, the measured and forecasted values of the electrical load in the PJM and Spanish electrical markets are indicated in Figure 3 and Figure 4, respectively.

To further analyze the accuracy of the proposed forecasting model, we compared the results with different forecasting models, namely, Multilayer Perceptron-Bayesian Regularization (MLP-BR) [33], a neural network (NN) [34], and Cascaded Neural Network-Evolutionary Algorithms (CNN-EA) [35]. The comparison results are presented in

Table 2. The comparison results of load forecasting models based on MAPE error index.

Seasons	MLP-BR	NN	CNN-EA	Proposed Model
Winter	13.22	9.82	4.44	3.49
Spring	12.92	8.87	4.31	3.90
Summer	11.98	10.43	4.78	4.71
Fall	12.24	9.54	4.75	4.21
Average	12.24	9.54	4.75	4.21

, which focuses on the MAPE error index.

Additionally, Figure 5 and Figure 6 provide visual representations of the MAPE and RMSE results, respectively, for the seasonal data. Figure 5 shows the MAPE results in different seasons, and Figure 6 displays the RMSE results in different seasons.

The obtained results of this study can be considered as a starting point for developing a potential data screening technique for time series electricity load datasets. This technique would allow users of load forecasting models to initially evaluate the nature of a load profile dataset, offering two benefits: reducing modeling complexity for certain applications and providing confidence levels for predicted electricity usage.

8. Conclusions

Machine-learning approaches, particularly deep-learning architectures, have gained significant popularity in the field of sensor-based electricity load prediction. However, many existing models rely on offline learning, whereby the model is trained once and used for future load inference without incorporating new data. This limitation hampers the ability of these models to leverage the benefits of updated information. To address this issue, this paper introduces a hybrid forecasting method designed to predict electricity load. The proposed method combines discrete wavelet transform (DWT) decomposition with a combination of radial basis function (RBF) and time series empirical orthogonal functions (TEO) as the main forecaster engine. To evaluate the effectiveness of the proposed method, two reliable electricity markets, namely, the Pennsylvania-New Jersey-Maryland market and the Spanish electricity market, were chosen as test cases. A comprehensive comparison analysis was conducted, revealing that the suggested method outperformed other forecasting methods in terms of error reduction and reliability. Furthermore, to assess the validity of the proposed model, three error measures were considered: the root mean square error (RMSE), the mean absolute error (MAE), and the mean absolute percentage error (MAPE). The results obtained from these measures consistently demonstrated that the proposed WT-RBF-TEO model exhibited superior accuracy, reliability, and prediction capability compared to alternative models such as WT-RBF-GA and WT-RBF-ICA.

Overall, this study highlights the advantages of the hybrid forecasting method in electricity load prediction. By incorporating DWT decomposition and a combination of RBF and TEO, the proposed model effectively utilizes historical data, resulting in improved forecasting performance. The findings of this research contribute to the advancement of electricity load prediction techniques and have practical implications for the efficient management of electricity markets.