###### Abstract  
Residential segments are of the greatest interest from the point of view of Demand-Side Resources and Decarbonization. Main end-uses such as water heaters, heating, and cooling have interesting opportunities: first, they can store energy, and this is relevant for the integration of renewables. Second, they are candidates for efficiency and electrification, increasing their demand share and the flexibility of demand. This paper aims to formulate an elemental Physical-Based Heat Pump Water Heater model that will enable the use of these energy-efficient appliances through aggregation in complex products, considering the advantages for demand and supply sides. Simulation results show that the individual performance is quite accurate and that the proposed model is flexible enough to be used to take more profit from energy markets or to easily respond to fast-occurring events. The model can be easily aggregated and used to obtain baselines, an important point for Demand Response evaluation. Results also demonstrate that demand-supply coordination and balance can be improved using these models to reduce or mitigate the risks and volatility of renewables without inducing a noticeable loss of service. Consequently, the contribution of this responsive load can be modelled through this methodology, making the engagement of more customer segments in Demand Response policies more credible and deploying new segments, such as prosumers. demand response; energy efficiency; heat pumps; physical-based load modelling; aggregation; energy balance; distributed energy resources +
Footnote †: journal: _sciences_  
Kyoto and Paris agreements have changed the energy policy of several countries during the last decades. For instance, decarbonizing our society in the next two decades will involve a dramatic change in energy conversion and demand [1]. This scenario requires the change from gas and fossil fuels to electricity and renewable sources (RES), but the increase in demand requires efficiency and, perhaps, the change of usage patterns to better align demand with renewable outputs (for example, Photovoltaics) and system requirements (e.g., increasing the hosting capacity at distribution levels) taking profit through synergies with other resources, such as battery storage. First, electricity should play a more important role in the future through electrification (especially in heating/cooling and water heating end-uses). Residential sectors should gain interest because they explain 30-35% of the overall demand and a similar share in emissions (up to 10-15% of GHG emissions in some countries [2]). Second, the energy mix will experience a revolution that benefits the penetration of renewables (RES) both at low (prosumers) and large scale, but renewable generation and residential demand are not synchronized most of the time. Third, due to this growth in RES, several states in the US, EU, and other countries have experienced frequent periods of overproduction in the Power System. This means that non-dispatchable base-load generation and RES have exceeded demand during some periods, resulting in the curtailment of RES or negative prices in energy markets. This can be observed in the European Power Exchange, EPEXSPOT market [3] since 2018; for instance, prices in the EPEX SPOT market (Belgium) reached \(-\)\(\xi\)115.31/MWh in April 2020. Escalating prices of gas, decommissioning of carbon power plants, and an increase in the cost of CO\({}_{2}\) emissions, as well as a lack of responsive resources in the system, can explain this scenario; consequently, a lack of elasticity of demand contributes to price volatility. This paper proposes a physical-based model for Water Heaters (WH) and a methodology that takes advantage of flexible loads to better integrate Distributed Energy Resources (DER) into residential segments.