PV and Demand Models for a Markov Decision Process Formulation of the Home Energy Management Problem

This paper proposes a hierarchical approach for estimating residential PV and electrical demand models using historical data. In brief, the method involves first clustering historical data into different day types, and then estimating PV and demand models using kernel regression. Clustering is done to capture intraday variations in the PV and demand profiles, with the aim of capturing much of these intertemporal correlations in the day-type labels. This allows the draws from the kernel estimates within a day type to be done independently. This approach conforms with a Markov decision process construction of the smart home energy management system (SHEMS) problem, which is the ultimate target of the modeling procedure. Moreover, in practical applications, the SHEMS will need the type of a coming day in order to select a daily demand model, which can be done seamlessly using state identification methods. In comparison, forecasting a day's demand profile using time series forecasting methods produces a prediction method that does not provide a probability structure that is directly incorporated into a Markov decision process scheduling model.