Power grids and uncertaintyThe rapid advance of renewable generation leads to a host of mathematical challenges, leading to exciting problems in both discrete and continuous mathematics and related fields, covering probability, analysis and optimization. Specifically, on shorter timescales there are increasing problems of control and optimization, while new questions of physical and economic design are emerging on the longer investment timescales. Network flows must be managed reliably under uncertain demands, uncertain supply, emerging network technologies and possible failures and, further, prices in related markets can be highly volatile.
In his talk Bert will focus on rare events in power grids. In a well-designed network, events that affect the security of the system, such as line failures or blackouts, should be rare. The goal of this research is to develop computationally feasible chance constraints for such events that could be used for planning, taking into account the uncertainty of, for example, wind energy. The results are also intended as a first step towards a qualitative understanding of the propagation of multiple failures, which can lead to large blackouts. Our mathematical model provides an explanation why such failures propagate in a non-nearest neighbor fashion, as one would expect from epidemics models.