Data driven day-ahead electrical load forecasting through repeated wavelet transform assisted SVM model

Highlights

• A new Repeated WT based SVM (RWT-SVM) model is proposed for the forecasting of the day-ahead electrical load.

• The mean absolute error for each decomposition level is different and is the reference for selection of the decomposition level for RWT.

• RWT of the selected decomposition level leads to reduced MAE for that particular level and thus overall forecasting error is reduced.

Abstract

Electrical load forecasting is an integral tool used by the grid operator to operate the smart power network. The information related to the electrical load is a prerequisite towards the effective and optimal operation of the power network with renewable and conventional generation resources. Economical bidding in the energy markets is directing research towards a superior forecasting model. Statistical and machine learning models have been used for electrical load forecasting while considering the electrical load as a time-series signal. This paper proposes a hybrid model that combines the Wavelet Transform (WT) and Support Vector Machine (SVM) features in estimating a regression model for electrical load forecasting utilizing the historical time-series information of electrical load. The WT decomposes the electrical load time-series data into various sub-series. The error contribution in forecasting due to the individual sub-series is estimated using Mean Absolute Error (MAE) in forecasting for each sub-series. The proposed Repeated WT-based SVM model (RWT-SVM) selects the sub-series with the highest MAE for further decomposition through WT. This results in a better forecasting model for the sub-series with the highest MAE, thereby improving the overall forecasting ability of the RWT-SVM model. The superiority of the proposed Repeated WT-based SVM model (RWT-SVM) for electrical load forecasting is justified using various data sets and comparing with some of the existing forecasting models.

Introduction

Electrical load requirement is an increasing function and is a reflection of a nation’s development index. Load forecasting is an essential part of the operation, maintenance, and expansion of the modern smart power network. Electrical load forecasting is an important study for the effective utilization of generation resources and their economic dispatch. The forecasted load data decide the unit commitment of generating resources. Besides these, electrical load forecasting finds its importance in electricity market transactions, optimal control of the attached energy storage, operation and maintenance scheduling of generating units, and in the expansion planning of the existing power network [1]. The horizon of electrical load forecasting depends on its end application. This leads to various categories of load forecasting horizons that differ in time-scale as [2]:

• Very short-term or ultra short-term (minutes to hours ahead)

• Short-term ($1$ day to weeks ahead)

• Medium-term (months to $1$ year ahead)

• Long-term (years ahead)

Modeling is an intrinsic part of any system/phenomena identification, and estimation [3]. Different models for electrical load forecasting are proposed in the literature [1]. Some models are more accurate for specific horizons, while other models can be used for different horizons. The different load forecasting models available in the literature can be grouped under different heads based on specific criteria. For example, if the number of variables is considered while forecasting the electrical load, the models can be categorized under the univariant model and multivariant model [4]. In a univariant model, only the historical load data is necessary for electrical load forecasting. Time-series models come under the group of the univariant model. Load forecasting model that includes more than one variable such as temperature, humidity, and historical electrical load data belongs to the multivariant model. The artificial Neural Network (ANN) model belongs to the class of multivariant model if the inputs to ANN are more than one. Load forecasting models can also be differentiated based on the dependency on the initial conditions. If the initial conditions are varied and the electrical load forecasting model changes, such models are probabilistic models while the models, that are robust against initial conditions are deterministic [4]. The time-series model and regression model are deterministic models, while the ANN model is a probabilistic model. Depending upon the approach of electrical load forecasting model, the models can also be classified as statistical, or machine learning-based models [2]. Time-series and regression models are statistical models, while ANN and Support Vector Machine (SVM) based models are Machine Learning (ML) based models. Some load forecasting models cannot be categorized as they have a complimentary feature from different groups, and such models are hybrid models [2]. These models tend to condescend to others due to superior forecasting results, as they amalgamate advantages of the groups they are derived from.

Initially, time-series model-based approach [5], [6] was used for electrical load forecasting modeling. It uses the standard Box–Jenkin approach for the estimation of the load forecast model. Some of the hybrid models partially utilize time-series approaches [7], [8]. However, lately, these approaches are rarely used, and researchers are drifting towards machine learning-based models and their hybridization with other statistical or machine learning models [4].

In general, the machine learning-based model uses ANN [9], [10], SVM [11], and the associated hybrids. ANN models available in literature differ in the number of inputs to ANN and the associated training approaches. In [12], Particle Swarm Optimization (PSO) based training is used to develop an ANN-based model, where the input to ANN comprises information related to historical load data, temperature, humidity, holidays, and week-offs. BOOsted Neural Network (BooNN) based approach is used in [13]. BooNN has a set of ANN that are trained iteratively, where at each iteration, the error between the estimated output from previously trained ANN and the actual output is minimized. Feedforward neural network-based approach is used in [14] and a comparison with echo state network is made. The inputs to the ANN are the historical electrical load information with timestamps, temperature, humidity, and solar irradiance. The electrical load data is clustered using the K-means approach and clusters are based on load values and information related to weekdays. A generalized regression neural network for estimation of electrical load forecast is proposed in [15], where fruit fly optimization algorithm is used for training of the neural network. An SVM-based approach is presented in [16], where sub-sampling is used to reduce the computational complexity of SVM. Another variant of SVM modeling with ambient temperature and electrical load data as input is proposed in [17]. SVM with parameters tuned by PSO is proposed in [18]. Thus, these machine learning-based models differ in terms of the input parameters and training approaches, besides different machine models used.

One of the approaches of hybrid model estimation of electrical load forecast is to decompose the historical load data and use any of the statistical/ML-based models. Generally, decomposition of load data time-series helps better estimate the electrical load forecast model compared to the non-decomposed time-series load data. Apart from better estimation, decomposition of load data also help in denoising the historical load data. Decomposition of electrical load data is carried out using any available Multi-Resolution Analysis (MRA) techniques. The decomposed sub-series is then modeled through the statistical/ML method. The estimated sub-series model is used to forecast the electrical load for the corresponding sub-series. These forecasted sub-series are reconstructed using the inverse of the MRA technique. A hybrid model using Empirical Mode Decomposition (EMD) followed by SVM is proposed in [19], [20]. EMD is used to decompose and denoise the input data, and the decomposed sub-series is modeled through SVM. A similar approach is also taken in [21], however, the decomposed sub-series obtained after EMD is modeled through Least Square Support Vector Machine (LS-SVM). Variational Mode Decomposition (VMD), which is superior in denoising the input data as compared to EMD, is used in [22] followed by sub-series model estimation by Long Short Term Memory (LSTM) neural network. A combination of EMD and Deep Belief Network (DBM) is used in [23] for time-series modeling of electrical load data.

WT is another MRA technique used in decomposing the input data of any type and is widely used in various fields [24]. In [25], the input electrical load data is decomposed using Wavelet Transform (WT), and three different models are used to estimate the decomposed load data. A radial basis function-based neural network, time-series model, fuzzy inference neural network based models are used, and a comparison among them is shown in [25]. A second-order gray neural network-based model is used in [26] for the estimation of decomposed load data using WT. The decomposed load data time series are also estimated using SVM in [27], [28]. In [29], a hybrid model is proposed where WT is used to decompose the input data, and the sub-series is modeled using Triple Exponential Smoothing (TES) and Weighted Nearest Neighbor (WNN) models. The proposed hybrid model is superior to its building block models, which are TES and WNN. In [30], ANN is used to model the sub-series after input series decomposition through WT. However, the proposed model is not compared with any existing model. A similar study is also carried out in [31], where the parameter of ANN is optimized using Bat Algorithm (BA). Deep Neural Network (DNN) along with WT is used in [32] and its superiority over SVM is verified.

A general approach observed in all these decomposition-based hybrid models is the decomposition of input load data time-series using any of the available MRA techniques followed by estimating the decomposed sub-series using either statistical/ML models. Fig. 1 shows the generalized approach for these types of hybrid electrical load forecasting models. The first stage is the decomposition stage which can be carried out by MRA techniques such as WT/EMD/VMD. The second stage is the model estimation and forecasting of decomposed sub-series. The third stage is the reconstruction of the forecasted sub-series through the inverse of the decomposition. To the best of the author’s knowledge, none of the decomposition-based hybrid electrical load forecasting models have explored the contribution of forecasting error due to individual sub-series towards total forecasting error. In this work, WT-SVM hybrid model [27] is used as a reference model, and the effect of forecasting error due to individual sub-series is estimated. The sub-series with the highest forecasting error contribution is selected and a superior hybrid forecasting model is proposed.

The major contributions, in this paper, towards day-ahead electrical load forecasting are:

• A varying error contribution of decomposed sub-series towards total error in forecasted value is estimated and used.

• Utilizing the varying error contribution, a repeated wavelet-based SVM (RWT-SVM) model is proposed that gives a better day-ahead electrical load forecasting model as compared to wavelet transform-based SVM (WT-SVM) model [27].

The organization of the paper is as follows. A brief discussion of the basics of WT, SVM, and WT-SVM is done in Section 2. The proposed day-ahead electrical load forecasting model is given in Section 3. The proposed model is tested for real electrical load data for three different places, and the result with discussion is shown in Section 4. The conclusion of the paper is drawn in Section 5.