Optimal power flow schedules with reduced low-frequency oscillations

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.