# Novel Data-Driven Models Applied to Short-Term Electric Load Forecasting
## 5 Conclusions  
This work provides a comprehensive analysis of a significant number of novel forecasting models from different fields and areas of research, exploring reduced-order dynamical systems techniques (DMD), classic ML models (linear regression, random forest, gradient boosting, k-nearest neighbors, support vector regression, and AdaBoost), DL models (convolutional and recurrent architectures and their combination), DL sequence to sequence models (Seq2 seq with and without attention), and specific DL ensemble models (gaNet). All techniques were applied to a unique dataset obtained from real data from a Spanish utility, which implies having a homogeneous set of results that allows a systematic comparison between models. Figure 17: Principal eigenvectors (\(\Phi\)) of the DMD algorithm (best linear mapping) for the temporal evolution of the load values. The eigenvectors are in order of importance (according to their corresponding eigenvalues) and represent the main modes of temporal evolution of the time-series. They clearly show the strong daily/weekly periodicity of the load values. The values shown correspond to a rolling window of 720 h (1 month). In this case, 16 eigenvectors were needed to capture 99% of the total signal energy. Some of the models analyzed have been widely applied to STLF (e.g., classical machine learning models), while others have rarely been applied (e.g., sequence to sequence, attention, DMD), and some of them have been applied for the first time to STLF, as far as we know (e.g., deep learning ensemble models specifically suitable for time-series forecasting, and specific configurations combining convolutional and recurring layers). The main conclusions obtained from this work are the following: (a) A rolling window of 1 week appears to be the best value for most models, and longer and shorter values do not, on average, provide better results. (b) Another interesting result is that including additional features (date/time, weather) could provide an improvement in the results in some scenarios, but not in general, the models that obtain better results simply using the past values of load being more numerous. (c) For very-short term forecasts, it is important to note that simple linear models and Seq2 seq architectures provide better results than more complex models. (d) For longer-term forecasts, deep learning models consisting of convolutional layers followed by recurrent layers provide the best results, better than pure convolutional or recurrent networks and similar, in forecasting performance in DL ensemble models (gaNet). (e) When the focus is to have good average forecasts, considering both very short-term and medium-term forecasts, the best models are DL ensemble models (gaNet), followed by CNN/RNN network combinations. This work also validates the importance of deep ensemble models and how they provide better performance results for predictions with increasing degrees of uncertainty. It corroborates other studies that try to understand the foundations of this behavior, considering different points of view. This work presents a specific deep ensemble model that originated by combining ideas from gradient boosting and residual networks [11] and demonstrates the results from other ensemble architectures [27; 61] where emphasis is placed on the random initialization of the different ensemble entities. As already mentioned, the electrical sector is a critical infrastructure and therefore one of the main industries exposed to security and fraud attacks, i.e., DDoS (distributed denial of service) cybersecurity threats. It could also be vulnerable to so-called ransomware cybersecurity attacks, where the attacker hijacks (typically through encryption) customer data that can only be recovered after payment to the attacker. One specific threat scenario is related to charging and billing. In smart grids, the central billing system receives customer consumptions from so-called smart meters through communication technologies.