Principal flow patterns across renewable electricity networks

¹ Frankfurt Institute for Advanced Studies - Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany
² Department of Engineering, Aarhus University - Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark
³ Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology 76344 Eggenstein-Leopoldshafen, Germany
⁴ Department of Sustainable Systems Engineering (INATECH), University of Freiburg Emmy-Noether-Strasse 2, 79110 Freiburg, Germany

Received: 13 June 2018
Accepted: 4 October 2018

Abstract

Using Principal Component Analysis (PCA), the nodal injection and line flow patterns in a network model of a future highly renewable European electricity system are investigated. It is shown that the number of principal components needed to describe 95% of the nodal power injection variance first increases with the spatial resolution of the system representation. The number of relevant components then saturates at around 76 components for network sizes larger than 512 nodes, which can be related to the correlation length of wind patterns over Europe. Remarkably, the application of PCA to the transmission line power flow statistics shows that irrespectively of the spatial scale of the system representation a very low number of only 8 principal flow patterns is sufficient to capture 95% of the corresponding spatio-temporal variance. This result can be theoretically explained by a particular alignment of some principal injection patterns with topological patterns inherent to the network structure of the European transmission system.