Large fluctuations in locational marginal prices.

This paper investigates large fluctuations of locational marginal prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form [Formula: see text] where is the vector of LMPs at the power grid nodes, and , [Formula: see text] are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modelling uncontrollable renewable generation.

Emergence of Scale-Free Blackout Sizes in Power Grids.

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes, contrasting previous studies suggesting that this nature is governed by self-organized criticality. Our results are based on a new mathematical framework combining the physics of power flow with rare event analysis for heavy-tailed distributions, and are validated using various synthetic networks and the German transmission grid.

Emergent Failures and Cascades in Power Grids: A Statistical Physics Perspective.

We model power grids transporting electricity generated by intermittent renewable sources as complex networks, where line failures can emerge indirectly by noisy power input at the nodes. By combining concepts from statistical physics and the physics of power flows and taking weather correlations into account, we rank line failures according to their likelihood and establish the most likely way such failures occur and propagate. Our insights are mathematically rigorous in a small-noise limit and are validated with data from the German transmission grid.