  Primary Frequency Control (PFC) is a fast acting mechanism used to ensure
high-quality power for the grid that is becoming an increasingly attractive
option for load participation. Due to speed requirement and other
considerations, it is often desirable to have distributed control laws. Current
distributed PFC designs assume that the costs at each geographic location are
independent. However, many networked systems, such as those for cloud
computing, have interdependent costs across locations and therefore need
geographic coordination. In this paper, distributed control laws are designed
for interdependent, geo-distributed loads in PFC based on the optimality
conditions of the global system. The controlled frequencies are provably
stable, and the final equilibrium point is proven to strike an optimal balance
between load participation and the frequency's deviation from its nominal set
point. The case with a significant communication delay for control is also
analyzed. We evaluate the proposed control laws with realistic numerical
simulations. Under current technology, the proposed control laws achieve a
convergence time that is smaller than droop control alone and is comparable to
that of distributed control without interdependent costs. Results also
highlight significant cost savings over existing approaches under a variety of
settings.
