  We present a framework based on spectral graph theory that captures the
interplay among network topology, system inertia, and generator and load
damping in determining the overall grid behavior and performance. Specifically,
we show that the impact of network topology on a power system can be quantified
through the network Laplacian eigenvalues, and such eigenvalues determine the
grid robustness against low frequency disturbances. Moreover, we can explicitly
decompose the frequency signal along scaled Laplacian eigenvectors when
damping-inertia ratios are uniform across buses. The insight revealed by this
framework partially explains why load-side participation in frequency
regulation not only makes the system respond faster, but also helps lower the
system nadir after a disturbance. Finally, by presenting a new controller
specifically tailored to suppress high frequency disturbances, we demonstrate
that our results can provide useful guidelines in the controller design for
load-side primary frequency regulation. This improved controller is simulated
on the IEEE 39-bus New England interconnection system to illustrate its
robustness against high frequency oscillations compared to both the
conventional droop control and a recent controller design.
