Ambient forcing: sampling local perturbations in constrained phase spaces

Abstract Ambient forcing is a novel method to sample random states from manifolds of differential-algebraic equations (DAE). These can represent local perturbations nodes in power systems with loads, which introduces constraints into the system. must be valid initial conditions DAE, meaning that they fulfill algebraic equations. Additionally, these should individual variables grid, such as perturbation voltage at load. enable calculation probabilistic stability measures was not yet possible, but important have become crucial tool studying systems. To verify are network local, i.e. only targets single node new measure, spreadability, related closeness centrality (Freeman 1978 Soc. Netw. 1 215–39), presented. The spreadability evaluated for an ensemble typical grids. depicts set future grids where consumers, well producers, connected grid via inverters. For this ensemble, we additionally calculate basin (Menck et al 2013 Nat. Phys. 9 89–92) survivability (Hellmann 2016 Sci. Rep. 6 29654), two provide statements about asymptotic and transient stability. We also revisit topological classes, introduced (Nitzbon 2017 New. J. 19 033029), been shown predict explore if still hold dynamics. find degree better predictor than classes our ensemble. Finally, ambient applied IEEE 96 test case (Grigg 1999 Trans. Power Syst. 14 1010–20).