Mathematical Optimization for Analyzing and Forecasting Nonlinear Network Time Series

Abstract

This work presents an innovative short to mid-term forecasting model that analyzes nonlinear complex spatial and temporal dynamics in energy networks under demand and supply balance constraints using Network Nonlinear Time Series (TS) and Mathematical Programming (MP) approach. We address three challenges simultaneously, namely, the adjacency matrix is unknown; the total amount in the network has to be balanced; dependence is unnecessarily linear. We use a nonparametric approach to handle the nonlinearity and estimate the adjacency matrix under the sparsity assumption. The estimation is conducted with the Mathematical Optimisation method. We illustrate the accuracy and effectiveness of the model on the example of the natural gas transmission network of one of the largest transmission system operators (TSOs) in Germany, Open Grid Europe. The obtained results show that, especially for shorter forecasting horizons, proposed method outperforms all considered benchmark models, improving the average nMAPE for 5.1% and average RMSE for 79.6% compared to the second-best model. The model is capable to capture the nonlinear dependencies in the complex spatial-temporal network dynamics and benefits from both sparsity assumption and the demand and supply balance constraint.