High dimensional dependence in power systems: A review

Weather-driven renewable generation is characterized by being uncertain and geographically dependent. In this regard, the recent deployment of wind and solar power has had a significant impact on the operation and planning of modern electricity grids; justifying the need to model high dimensional dependence. It is a relevant topic which is starting to have a significant importance in power systems. This paper presents a general overview on different multivariate dependence modeling techniques, namely parametric, non-parametric and copula functions. In addition, approximated methods based on limited information e.g. some statistical measures or a predefined dependence structure are presented. Autoregressive moving average (ARMA) and Markov models are discussed as general frameworks to reproduce spatio-temporal processes. Moreover, different applications in power systems are discussed in detail, along with a case study exemplifying the importance of a correct dependence modeling of wind generation.