  We consider frequency control of synchronous generator networks and study
transient performance under both primary and secondary frequency control. We
model random step changes in power loads and evaluate performance in terms of
expected deviations from a synchronous frequency over the synchronization
transient; what can be thought of as lack of frequency coherence. We compare a
standard droop control strategy to two secondary proportional integral (PI)
controllers: centralized averaging PI control (CAPI) and dis- tributed
averaging PI control (DAPI). We show that the performance of a power system
with DAPI control is always superior to that of a CAPI controlled system, which
in turn has the same transient performance as standard droop control.
Furthermore, for a large class of network graphs, performance scales
unfavorably with network size with CAPI and droop control, which is not the
case with DAPI control. We discuss optimal tuning of the DAPI controller and
describe how inter- nodal alignment of the integral states affects performance.
Our results are demonstrated through simulations of the Nordic power grid.
