  In this paper we focus on the parameter estimation of dynamic load models
with stochastic terms, in particular, load models where protection settings are
uncertain, such as in aggregated air conditioning units. We show how the
uncertainty in the aggregated protection characteristics can be formulated as a
stochastic differential equation with process noise. We cast the parameter
inversion within a Bayesian parameter estimation framework, and we present
methods to include process noise. We demonstrate the benefits of considering
stochasticity in the parameter estimation and the risks of ignoring it.
