  We consider the problem of smart and flexible loads providing contingency
reserves to the electric grid and provide a Distributed Gradient Projection
(DGP) algorithm to minimize loads' disutility while providing contingency
services. Each load uses locally obtained grid-frequency measurements and
inter-load communication to coordinate their actions, and the privacy of each
load is preserved: only gradient information is exchanged---not disutility or
consumption information. We provide a proof of convergence of the proposed DGP
algorithm, and we compare its performance through simulations to that of a
"dual algorithm" previously proposed in the literature that solved the dual
optimization problem. The DGP algorithm solves the primal problem. Its main
advantage over the dual algorithm is that it is applicable to convex---but not
necessarily strictly convex---consumer disutility functions, such as a model of
consumer behavior that is insensitive to small changes in consumption, while
the dual algorithm is not. Simulations show the DGP algorithm aids in arresting
grid-frequency deviations in response to contingency events and performs better
or similarly to the dual algorithm in cases where the two can be compared.
