  Potential of electrical loads in providing grid ancillary services is often
limited due to the uncertainties associated with the load behavior. A knowledge
of the expected uncertainties with a load control program would invariably
yield to better informed control policies, opening up the possibility of
extracting the maximal load control potential without affecting grid
operations. In the context of frequency responsive load control, a
probabilistic uncertainty analysis framework is presented to quantify the
expected error between the target and actual load response, under uncertainties
in the load dynamics. A closed-form expression of an optimal demand
flexibility, minimizing the expected error in actual and committed flexibility,
is provided. Analytical results are validated through Monte Carlo simulations
of ensembles of electric water heaters.
