A Multivariate Time Series Analysis of Electrical Load Forecasting Based on a Hybrid Feature Selection Approach and Explainable Deep Learning  
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smart grids. Accurate and reliable forecasting of electrical energy generation and load consumption is necessary in this context. In the past decade, short-term forecasting studies, which aim to minimize energy supply interruptions, typically lasted one hour to seven days, while long-term forecasting studies, which estimate energy capacity planning investments, spanned one to twenty years. Within the sphere of operations and planning studies in power systems, medium-term load forecasting (MTLF) is indispensable for various purposes, including fuel purchasing and fuel reserve planning, power system maintenance planning, hydro-thermal coordination, and electricity price regulations. MTLF methods can be categorized into two main groups: classical methods, which involve statistical and econometric modeling, primarily time series analysis methods based on variations of autoregressive integrated moving average (ARIMA), exponential smoothing (ETS), and linear regression (LR), and data-driven methods, including artificial intelligence (AI) and machine learning (ML) modeling [1]. Classical approaches are adaptable up to a certain level, but they are not capable of modeling non-linear relationships effectively. As a result, additional procedures such as decomposition and local approaches are required. Due to these limitations, researchers have become increasingly interested in using ML and computational intelligence models to overcome these challenges. Neural networks (NN) are extensively utilized in prediction studies, with multilayer perceptrons (MLPs), weighted evolving fuzzy NNs, and NNs combined with linear regression and AdaBoost commonly used structures in MTLF. The widespread usage of deep learning (DL) methods in AI technologies, particularly in recent decades, presents an opportunity to enhance ML techniques for power system forecasting problems. DL techniques are found to be more advantageous and superior to classical approaches in terms of achieving success in complex models and modeling non-linear relationships, as well as the ability to cross-learn on extensive time series data. DL techniques are also valued for their accuracy and flexibility in time series forecasting [2; 3; 4]. Basic structures, such as multi-layer perceptrons (MLPs), recurrent neural networks (RNNs), and convolutional neural networks (CNNs), along with their combinations, are contemporary deep learning architectures. For time series tasks, RNN offers several advantages, such as non-linear learning capabilities, effectiveness in obtaining information about the time series, and the ability to discern the impact of other parameters on the load data simultaneously [5]. The LSTM architecture was proposed to address the issue of vanishing gradient when processing long sequences in RNNs [6]. It is important to note that LSTM's effectiveness is demonstrated by its victory in the M4 forecasting competition of 2018, which employed 100,000 real-world time series [7]. Thus, the LSTM model and its variations [8; 9; 10; 11; 12; 13; 14; 15], as well as their combinations with other forecasting models [16; 17; 18; 19; 20; 21; 22; 23], are typically utilized for forecasting medium-term loads, as with other load forecasting timeframes. ELF can be performed using solely historical load data or using historical load data and external factors that impact electricity consumption as input variables to extract a pattern. Multivariate input configurations, which include additional electrical load-related features, often improve the forecast results [24].