###### Abstract
The methodology can and should interact with other tools such as Non-Intrusive Load Monitoring (NIALM), load segmentation, and Customer Baseline Loads (CBL) methodologies to face main DR problems and improve DER characteristics to participate in complex products and services in the coming years. The main contributions of this paper can be summarized as follows. The paper presents a model to improve the knowledge of Heat Pump Water Heaters (HPWH) dynamics (in the short and very short terms, relevant to use in Ancillary Services and Markets) through the consideration of Physical-Based Load Models (PBLM) methodologies. PBLM can also be used by aggregators to evaluate the potential and response of other main end-uses at residential and commercial levels: electric heaters (EH), electric thermal storage (ETS), heat pumps (HP), and water heaters (WH). This approach outperforms practical models, especially when new response policies, weather, or use changes appear. Basically, this is due to a lack of previous experience and available data arising from the use of other models. The proposed model gives feedback about the different temperatures of the water near the indoor sensors that return information to thermostats that drive the switching of compressors and ancillary resistors. This is important because the location of sensors is not always the same, and other models in the literature consider only one or two temperatures, which can cause errors in demand patterns, especially when DR is applied. Obviously, the model reports the temperature of hot water draws to check an appropriate customer service level during DR.  
Also, the model can provide end-use baselines (improving the definition of the overall baseline CBL) according to weather and water use habits and can evaluate demand despite the lack of measurements in specific DR conditions. This is a consequence of its grey-box structure. The methodology can take advantage of feedback and synergies from other potential tools used by aggregators or utilities (e.g., load clustering, NIALM, short-term load forecasting, and renewable forecasting). The rest of the paper is organized as follows. Section 2 depicts the characteristics of WH in different countries and the possibilities that arise for residential Electric Water Heater (EWH) loads in DR programs. Section 3 deals with the literature review of EWH load models and DR programs, focusing on residential DR programs. In Section 4, the methodology to define the elemental PBLM and the different tests used for the model definition and validation are stated. This includes practical considerations to achieve greater flexibility of the proposed PBLM model in new and complex products (e.g., in ancillary services). Section 5 outlines the segmentation and aggregation procedures to define groups of loads suitable to get an ensemble of loads that can participate in DR policies with accurate surveillance of customer comfort, according to the characteristics of the elemental model (and real loads) defined in Section 5. Section 6 presents some simulation results of the model in two scenarios: peak shaving and the change of storage pattern to follow renewable generation. Some advantages and practical limitations of models and loads are discussed. Finally, the main findings and recommendations of the study are presented in Section 7.