Structured Kernel Based Modeling: An Exploration in Short-Term Load Forecasting

This paper considers an exploratory modeling strategy applied to a large scale reallife problem of power load forecasting. Different model structures are considered, including Autoregressive models with eXogenous inputs (ARX), Nonlinear Autoregressive models with eXogenous inputs (NARX), both of which are also extended to incorporate residuals that follow an Autoregressive (AR) process (AR-(N)ARX). These models are parameterized either as a full black-box model or as partially linear structures. Starting from the Least Squares Support Vector Machines (LSSVMs) formulation for regression, relevant properties from the problem at hand can be imposed as additional constraints which can be incorporated in a straightforward way within the primal-dual optimization formulation and be solved through convex optimization. For the case study of short-term load forecasting, it is shown that a structured model can reach results comparable to the full black-box model, with the additional benefit of having interpretable coefficients. It obtains satisfactory results when the model structure and the hyperparameter selection procedure are tailored towards the application, taking into account prior knowledge or relevant properties of the problem.