Abstract
In this paper, the authors pursue probabilistic aggregate dynamical models for n identical induction machines connected to a bus, capturing the effect of different mechanical inputs to the individual machines. They explore model averaging and review in detail four procedures for linear models. They describe linear systems depending upon stochastic parameters, and develop a theoretical justification for a very simple and reasonably accurate averaging method. They then extend this to the nonlinear model. Finally, they use a recently introduced notion of the stochastic norm to describe a cluster of induction machines undergoing multiple simultaneous parametric variations, and obtain useful and very mildly conservative bounds on eigenstructure perturbations under multiple simultaneous parametric variations.
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