  A consensus-control-based multi-level control law named Multi-Level
Power-Imbalance Allocation Control (MLPIAC) is presented for a large-scale
power system partitioned into two or more areas. Centralized control is
implemented in each area while distributed control is implemented at the
coordination level of the areas. Besides restoring nominal frequency with a
minimal control cost, MLPIAC can improve the transient performance of the
system through an accelerated convergence of the control inputs without
oscillations. At the coordination level of the control areas, because the
number of the areas is smaller than that of nodes, MLPIAC is more effective to
obtain the minimized control cost than the purely distributed control law. At
the level of the control in each area, because the number of nodes is much
smaller than the total number of nodes in the whole network, the overheads in
the communications and the computations are reduced compared to the pure
centralized control. The asymptotic stability of MLPIAC is proven using the
Lyapunov method and the performance is evaluated through simulations.
