  Frequency control rebalances supply and demand while maintaining the network
state within operational margins. It is implemented using fast ramping reserves
that are expensive and wasteful, and which are expected to grow with the
increasing penetration of renewables. The most promising solution to this
problem is the use of demand response, i.e. load participation in frequency
control. Yet it is still unclear how to efficiently integrate load
participation without introducing instabilities and violating operational
constraints.
  In this paper we present a comprehensive load-side frequency control
mechanism that can maintain the grid within operational constraints. In
particular, our controllers can rebalance supply and demand after disturbances,
restore the frequency to its nominal value and preserve inter-area power flows.
Furthermore, our controllers are distributed (unlike the currently implemented
frequency control), can allocate load updates optimally, and can maintain line
flows within thermal limits. We prove that such a distributed load-side control
is globally asymptotically stable and robust to unknown load parameters. We
illustrate its effectiveness through simulations.
