  As the penetration of intermittent energy sources grows substantially, loads
will be required to play an increasingly important role in compensating the
fast time-scale fluctuations in generated power. Recent numerical modeling of
thermostatically controlled loads (TCLs) has demonstrated that such load
following is feasible, but analytical models that satisfactorily quantify the
aggregate power consumption of a group of TCLs are desired to enable controller
design. We develop such a model for the aggregate power response of a
homogeneous population of TCLs to uniform variation of all TCL setpoints. A
linearized model of the response is derived, and a linear quadratic regulator
(LQR) has been designed. Using the TCL setpoint as the control input, the LQR
enables aggregate power to track reference signals that exhibit step, ramp and
sinusoidal variations. Although much of the work assumes a homogeneous
population of TCLs with deterministic dynamics, we also propose a method for
probing the dynamics of systems where load characteristics are not well known.
