title: Voltage collapse in complex power grids.
abstract: A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow. Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling. However, methods to test for voltage collapse are dominantly simulation-based, offering little theoretical insight into how grid structure influences stability margins. For a simplified power flow model, here we derive a closed-form condition under which a power network is safe from voltage collapse. The condition combines the complex structure of the network with the reactive power demands of loads to produce a node-by-node measure of grid stress, a prediction of the largest nodal voltage deviation, and an estimate of the distance to collapse. We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.
authors.affiliation: Department of Electrical and Computer Engineering, Engineering Building 5, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
authors.forename: John W
authors.initials: JW
authors.lastname: Simpson-Porco
authors.affiliation: Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH), Physikstrasse 3, CH-8092 Zürich, Switzerland.
authors.forename: Florian
authors.initials: F
authors.lastname: Dörfler
authors.affiliation: Department of Mechanical Engineering, Center for Control, Dynamical Systems and Computation, Engineering Building II, University of California at Santa Barbara, Santa Barbara, 93106-9560 California, USA.
authors.forename: Francesco
authors.initials: F
authors.lastname: Bullo