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Abstract

Ambient Forcing is a novel method to sample random states from manifolds of differential-algebraic equations
(DAE). These states can represent local perturbations of nodes in power systems with loads, which introduces
constraints into the system. These states must be valid initial conditions to the DAE, meaning that they fulfill
the algebraic equations. Additionally, these states should represent perturbations of individual variables in
the power grid, such as a perturbation of the voltage at a load. These initial states enable the calculation of
probabilistic stability measures of power systems with loads, which was not yet possible, but is important as
these measures have become a crucial tool in studying power systems. To verify that these perturbations are
network local, i.e. that the initial perturbation only targets a single node in the power grid, a new measure,
the spreadability, related to the closeness centrality [1], is presented. The spreadability is evaluated for an
ensemble of typical power grids. The ensemble depicts a set of future power grids where consumers, as well
as producers, are connected to the grid via inverters. For this power grid ensemble, we additionally calculate
the basin stability [2] as well as the survivability [3], two probabilistic measures which provide statements
about asymptotic and transient stability. We also revisit the topological classes, introduced in [4], that have
been shown to predict the basin stability of grids and explore if they still hold for grids with constraints and
voltage dynamics. We find that the degree of the nodes is a better predictor than the topological classes for
our ensemble. Finally, ambient forcing is applied to calculate probabilistic stability measures of the IEEE
96 test case [5].