Optimal power consumption for demand response of thermostatically controlled loads

Abstract

Summary We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads such as air conditioners. This is motivated by the need to synthesize the demand response for a load serving entity (LSE) catering a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day‐ahead price, load forecast, and ambient temperature forecast, while respecting each individual load's comfort range constraints. The resulting synthesis problem is intractable when posed as a direct optimization problem after Euler discretization of the dynamics, since it results in a mixed‐integer linear programming problem with number of variables typically of the order of millions. In contrast, in this paper, we show that the problem is amenable to continuous‐time optimal control techniques. Numerical simulations elucidate how the LSE can use the optimal aggregate power consumption trajectory thus computed, for the purpose of demand response.

Optimal Control of Thermostatic Loads for Planning Aggregate Consumption: Characterization of Solution and Explicit Strategies

“…These results motivate a decomposition strategy (Section V) allowing us to solve simpler subproblems over monotone price segments. This paper extends our earlier results [10] to apply Pontryagin's Maximum Principle (PMP) for the planning problem accounting switching constraints. Section VI concludes the paper.…”

Demand Response Analogues for Residential Loads in Natural Gas Networks

“…The objective functions consider economic factors like cost savings [20], [21], operation profits [18], [22]- [24], engineering, reliability [25], risk minimization [18], greenhouse gas emission reductions [19], [26], social welfare [17], [22] and user comfort [27]. Other lines of work include optimal control of ensembles of Thermostatically Controlled Loads (TCLs) [28]- [30] which are very closely related to the models and DR formulations that are presented in this paper. Ensemble-based optimal control problems reduce electricity consumption from TCLs (typically air-conditioners) during the summer months by utilizing thermal inertia.…”

“…Ensemble-based optimal control problems reduce electricity consumption from TCLs (typically air-conditioners) during the summer months by utilizing thermal inertia. In this line of work [28], a simple Newtonian thermal model (an RC circuit model) for heat exchange between the surroundings and a house is utilized. We use similar thermal models in this article to develop a DR program in a natural-gas setting to cater to the heating needs of households in winter months.…”

“…Whereas electric power based DR is well developed, natural gas DR is relatively new and these governing equations have yet to be fully established. In this article, we utilize thermodynamic models of heat flow developed for electric power TCLs [28], [30] and contribute a natural gas DR formulation for these dynamic models.…”

“…Eqs. (1a) is a Newtonian equation that captures the dynamics of heat flow within the house h. A similar equation is used to model TCLs in the electric power DR literature [28]. In Eq.…”