Application of smoothing techniques to solve the cooling and heating residential load aggregation problem

The main objective of this paper is to obtain the duty‐cycle probability forecast functions of cooling and heating aggregated residential loads. The method consists of three steps: first, the single loads are modelled using systems of stochastic differential equations based on perturbed physical models; second, intensive numerical simulation of the stochastic system solutions is performed, allowing several parameters to vary randomly; and third, smoothing techniques based on kernel estimates are applied to the results to derive non‐parametric estimators, comparing several kernel functions. The use of these dynamical models also allows us to forecast the indoor temperature evolution under any performance conditions. Thus, the same smoothing techniques provide the indoor temperature probability forecast function for a load group. These techniques have been used with homogeneous and non‐homogeneous device groups. Its main application is focused on assessing Direct Load Control programs, by means of comparing natural and forced duty‐cycles of aggregated appliances, as well as knowing the modifications in customer comfort levels, which can be directly deduced from the probability profiles. Finally, simulation results which illustrate the model suitability for demand side – bidding – aggregators in new deregulated markets are presented.