  We investigate the sensitivity of the transient performance of power systems
controlled by Distributed Power-Imbalance Allocation Control (DPIAC) on the
parameters of the control law. We model the disturbances at power loads as
Gaussian white noises and measure the transient performance of the frequency
deviation and control cost by the H_2 norm. For a power system with a
communication network of the same topology as the power network, analysis shows
that the transient performance of the frequency can be greatly improved by
accelerating the convergence of the frequencies to the nominal value through a
singe control gain coefficient. However, the control cost increases linearly as
this control gain coefficient increases. Hence, in the feedback control law,
DPIAC, there is a trade-off between the frequency deviation and control cost
which is determined by this control gain coefficient. By increasing another
control gain coefficient, the control cost can be decreased with an accelerated
consensus of the marginal costs during the transient phase. Furthermore, the
behavior of the state approaches that of a centralized control law when the
consensus of the marginal costs is accelerated.
