  Non-linear equations describing the time evolution of frequencies and
voltages in power grids exhibit fixed points of stable grid operation. The
dynamical behaviour after perturbations around these fixed points can be used
to characterise the stability of the grid. We investigate both probabilities of
return to a fixed point and times needed for this return after perturbation of
single nodes. Our analysis is based on an IEEE test grid and the second-order
swing equations for voltage phase angles $\theta_j$ at nodes $j$ in the
synchronous machine model. The perturbations cover all possible changes
$\Delta\theta$ of voltage angles and a wide range of frequency deviations in a
range $\Delta f=\pm1$~Hz around the common frequency $\omega=2\pi
f=\dot\theta_j$ in a synchronous fixed point state. Extensive numerical
calculations are carried out to determine, for all node pairs $(j,k)$, the
return times $t_{jk}(\Delta\theta,\Delta \omega)$ of node $k$ after a
perturbation of node $j$. We find that for strong perturbations of some nodes,
the grid does not return to its synchronous state. If returning to the fixed
point, the times needed for the return are strongly different for different
disturbed nodes and can reach values up to 20 seconds and more. When
homogenising transmission line and node properties, the grid always returns to
a synchronous state for the considered perturbations, and the longest return
times have a value of about 4 seconds for all nodes. The neglect of reactances
between points of power generation (internal nodes) and injection (terminal
nodes) leads to an underestimation of return probabilities.
