On the probability of current and temperature overloading in power grids

Abstract

The advent of renewable energy sources has huge implications for the design and control of power grids. On the engineering side, reliability is currently ensured by strict con- straints on current, voltage and temperature. However, with growing supply-side uncertainty induced by renewables, these will need to be replaced by probabilistic guarantees, allowing constraints on a given line to be violated with a low probability, e.g., several minutes per year. In the present note we illustrate, using large deviations techniques, how replacing (probabilistic) current constraints by temperature constraints can lead to capacity gains in power grids.