  The increased integration of intermittent and decentralised forms of power
production has eroded the stability margins of power grids and made it more
challenging to ensure reliable and secure power transmission. Reliable grid
operation requires system-scale stability in response to perturbations in
supply or load; previous studies have shown that this can be achieved by tuning
the effective damping parameters of the generators in the grid. In this paper,
we present and analyse the problem of tuning damping parameters when there is
some uncertainty in the underlying system. We show that sophisticated methods
that assume no uncertainty can yield results that are less robust than those
produced by simpler methods. We define a quantile-based metric of stability
that ensures that power grids remain stable even as worst-case scenarios are
approached, and we develop optimisation methods for tuning damping parameters
to achieve this stability. By comparing optimisation methods that rely on
different assumptions, we suggest efficient heuristics for finding parameters
that achieve highly stable and robust grids.
