  The dynamic response of power grids to small events or persistent stochastic
disturbances influences their stable operation. Low-frequency inter-area
oscillations are of particular concern due to insufficient damping. This paper
studies the effect of the operating point on the linear time-invariant dynamics
of power networks. A pertinent metric based on the frequency response of grid
dynamics is proposed to quantify power system's stability against inter-area
oscillations. We further put forth an optimal power flow formulation to yield a
grid dispatch that optimizes this novel stability metric. A semidefinite
program (SDP) relaxation is employed to yield a computationally tractable
convex problem. Numerical tests on the IEEE-39 bus system demonstrate that the
SDP relaxation is exact yielding a rank-1 solution. The relative trade-off of
the proposed small-signal stability metric versus the generation cost is also
studied.
