Optimal demand response for thermal inertial loads employing stochastic renewables: A privacy respecting architecture and its continuum scaling limit

We consider the problem of optimally utilizing intermittently available renewable energy sources for inertial thermal loads. The particular focus of this paper is to reduce the need for dispatchable fossil fuel generation backup reserves, while satisfying thermal constraints of the loads, and to do so within an architecture where the individual loads control their own demands in a distributed manner so that privacy of every load's thermal state is respected. In this distributed architecture, no information about load states is communicated to the load aggregator. We model th e system as a distributed stochastic control problem with a control law parametrized by the individual set points of the loads, where the stochastic uncertainty is induced both by renewable energy availability as well as user temperature constraints. We design, optimize and analyze the parametrized policy, which has the key properties that it is privacy-respecting, employs distributed control via individual set-points, has low communication requirements, and is architecturally simple. While the optimal policy for a finite number of loads is intractable, and increasingly so as the number of loads increases, we show that the infinite population scaling limit as the number of loads increases is tractable. We employ Pontryagin's Minimum Principle to evaluate this, and show that it provides a near-optimal solution for the finite case.