  New classes of performance measures have been recently introduced to quantify
the transient response to external disturbances of coupled dynamical systems on
complex networks. These performance measures are time-integrated quadratic
forms in the system's coordinates or their time derivative. So far,
investigations of these performance measures have been restricted to
Dirac-$\delta$ impulse disturbances, in which case they can be alternatively
interpreted as giving the long time output variances for stochastic white noise
power demand/generation fluctuations. Strictly speaking, the approach is
therefore restricted to power fluctuating on time scales shorter than the
shortest time scales in the swing equations. To account for power productions
from new renewable energy sources, we extend these earlier works to the
relevant case of colored noise power fluctuations, with a finite correlation
time $\tau > 0$. We calculate a closed-form expression for generic quadratic
performance measures. Applied to specific cases, this leads to a spectral
representation of performance measures as a sum over the non-zero modes of the
network Laplacian. Our results emphasize the competition between inertia,
damping and the Laplacian modes, whose balance is determined to a large extent
by the noise correlation time scale $\tau$.
