  Effective utilization of flexible loads for grid services, while satisfying
end-user preferences and constraints, requires an accurate estimation of the
aggregated predictive flexibility offered by the electrical loads. Virtual
battery (VB) models are often used to quantify the predictive flexibility in
thermostatic loads (e.g. residential air-conditioners, electric water-heaters),
which model the temporal evolution of a (virtual) energy state via a first
order dynamics including self-dissipation rate, and power and energy capacities
as parameters. Uncertainties and lack of information regarding end-usage and
equipment models render deterministic VB models impractical. In this paper, we
introduce the notion of stochastic VB models, and propose a \textit{variational
autoencoder}-based deep learning algorithm to identify the probability
distribution of the VB model parameters. Using available sensors and meters
data, the proposed algorithm generates not only point estimates of the VB
parameters, but also confidence intervals around those values. Effectiveness of
the proposed frameworks is demonstrated on a collection of electric
water-heater loads, whose operation is driven by uncertain water usage
profiles.
