Multivariate forecasting in energy systems with a large share of renewables

Forecasts of renewable power production and electricity demand for multiple time periods and/or spatial expanses are required to operate modern power systems. Furthermore, probabilistic forecasts are necessary to facilitate economic decision-making and risk management. This gives rise to the challenge of producing forecasts that capture dependency between variables, over time, and between multiple locations. The Gaussian Copula has been widely used for multivariate energy forecasting, including for wind power, and is readily scalable given that the entire dependency structure is described by a single covariance matrix; however, estimating this covariance matrix in high dimensional problems remains a research challenge. Furthermore, it has been found empirically that this covariance matrix is often non-stationary and evolves over time. Two methods are presented for parameterising covariance matrices to enable conditioning on explanatory variables and as a step towards more robust estimation.

We consider two approaches, one based on modelling the parameters of covariance functions using additive models, and the second modelling individual elements of the modified Cholesky decomposition, again using additive models. We show how this gives rise to a wide range of possible parametric structures and discuss model selection and estimation strategies. Finally, we demonstrate though two case studies the improvement in forecast quality that these methods yield, and the importance and value of capturing the dynamics of dependency structures in wind power forecasting and net-load forecasting in the presence of embedded renewables.