Quantifying maximum controllable energy demand in ensembles of air conditioning loads

Flexible loads such as residential air-conditioners (ACs) can be directly controlled to provide demand-side regulation and balancing services to the grid. In aggregation, an ensemble of ACs may be seen as a distributed energy storage resource with a capacity modulated by ambient temperature and the AC temperature set-points. Existing research has predominantly focused on modelling and controlling the aggregate demand response of such ensembles, but relatively little work has been devoted to quantifying controllable energy resource as a function of ensemble diversity. This paper investigates analytic bounds on the aggregate energy demand transients induced by step changes in temperature set-points for ensembles of ACs. An analytic characterisation of the transient demand response of homogeneous ensembles is used to bound the controllable energy demand of heterogeneous ensembles constructed by aggregation of clusters of identical loads. The analysis shows that the transient energy demand of a heterogeneous ensemble can be bounded by that of an associated mean homogeneous ensemble as a function of the set-point step size relative to the ACs hysteresis regulation band width. The proposed analytic bounds are numerically evaluated for the simulated demand responses of AC ensembles with various degrees of heterogeneity