  Set-theoretic control is a useful technique for dealing with the uncertainty
introduced into power systems by renewable energy resources. Although set
operations are computationally expensive in large systems, distributed
approaches serve as a remedy. In this paper, we propose a novel consensus-based
approach for set-theoretic frequency control in power systems. A robust
controlled-invariant set (RCI) for the system is generated by composing RCIs
for each bus in the network. The process of generating these sets uses a
consensus-based approach in order to facilitate discovery of mutually
compatible subsystem RCIs. Each bus seeks to maximize the size of its own RCI
while treating the effects of coupling as an unknown-but-bounded disturbance.
The consensus routine, which demonstrates linear convergence, is embedded into
a backwards reachability analysis of initial safe sets. Results for a 9-bus
test case show that simple model predictive controllers associated with the
resulting RCIs maintain safe operation when the system is subjected to worst
case (adversarial) fluctuations in net demand, where conventional controllers
are shown to fail.
