  This paper addresses the distributed frequency control problem in a
multi-area power system taking into account of unknown time-varying power
imbalance. Particularly, fast controllable loads are utilized to restore system
frequency under changing power imbalance in an optimal manner. The imbalanced
power causing frequency deviation is decomposed into three parts: a known
constant part, an unknown low-frequency variation and a high-frequency
residual. The known steady part is usually the prediction of power imbalance.
The variation may result from the fluctuation of renewable resources, electric
vehicle charging, etc., which is usually unknown to operators. The
high-frequency residual is usually unknown and treated as an external
disturbance. Correspondingly, in this paper, we resolve the following three
problems in different timescales: 1) allocate the steady part of power
imbalance economically; 2) mitigate the effect of unknown low-frequency power
variation locally; 3) attenuate unknown high-frequency disturbances. To this
end, a distributed controller combining consensus method with adaptive internal
model control is proposed. We first prove that the closed-loop system is
asymptotically stable and converges to the optimal solution of an optimization
problem if the external disturbance is not included. We then prove that the
power variation can be mitigated accurately. Furthermore, we show that the
closed-loop system is robust against both parameter uncertainty and external
disturbances. The New England system is used to verify the efficacy of our
design.
