## 6 Results and Discussion
### Evaluating the Flexibility of HPWH: Prosumers  
New PV generation in residential segments, driven by economic incentives, has increased the number of consumers becoming prosumers (consumers involved in energy generation activities through small renewables; in the proposed scenario basically PV generation and small consumer segments). However, sometimes, these prosumers cannot take full advantage of the energy they generate, as the consumption and generation periods do not match adequately. Moreover, net-demand evaluation (e.g., short-term load forecasting to define bids in energy markets) is less accurate because PV generation is more unpredictable than \"conventional\" demand, and this makes it more difficult to evaluate net demand (i.e., loads demand minus PV generation) requirements. Consequently, aggregators and balance responsible parties can foresee more problems in energy balance concerns due to the increasing load forecasting errors in power systems areas with a higher penetration of these prosumers. For this reason, the use of Demand Response strategies applied to thermostatically controlled loads, such as HPWH loads, can improve the performance of these systems, but HPWH should be flexible enough to increase and decrease demand to follow changes in renewable generation (or short-term generation forecasts). An alternative is the use of energy storage (batteries), but this alternative involves additional capital costs, which becomes an additional barrier for these customer segments. The main objective of this simulation is to delay the consumption period of the HPWH to the hours in which more PV generation is available. In this paragraph, the flexibility of HPWH loads to follow the curve of PV generation has been tested. At the same time, PBLM software surveys the behavior of temperatures (state variables) inside the tank to guarantee the customers' comfort during and after DR. The PV system studied is a real 45 kWp PV plant installed in the south-east of Spain. The PV panels are fixed facing south and tilted 30 \({}^{\circ}\). The PV generation profiles (average) for every month are depicted in Figure 13.  
The control strategy applied to the aggregated HPWH is to limit consumption in the morning and compensate for this reduction during the hours that PV generation is  
Figure 12: Aggregation of 100 HPWH loads (granularity of simulation one minute): (**a**) Demand profile; (**b**) Average temperatures inside the tank (notice the stratification of water inside the tank). Figure 13: Monthly average PV generation for a year: (**a**) January–June. (**b**) July–December. performed. The temperature of the mixed water (X\({}_{2}\)) inside each tank remains between 50 \({}^{\circ}\)C and 62 \({}^{\circ}\)C. Figure 14a depicts the simulation results for a day in which there is a reduction of the PV generation at 13:00 (i.e., the generation pattern changes with respect to monthly average due to weather changes; see Figure 13). Figure 13 shows the baseline profile for the HPWH consumption in red. The green curve represents the target profile for DR to improve the energy use from the PV system. Finally, the final profile for the HPWH demand after applying the DR strategies and the comfort conditions are shown in blue. Figure 14b shows the average temperatures inside the tanks of the HPWH loads for the simulated day. Simulation results show a delay in WH demand from 7:00 to 12:00. Solar production is used to supply the HPWH requirements. However, at 15:00, some of the HPWHs have reached their maximum temperature to guarantee efficiency in energy conversion (62 \({}^{\circ}\)C; [32]). In this case, the modified HPWH demand profile cannot meet the target. This drawback can be overcome using the ancillary resistor (to reach higher temperatures; i.e., 65 \({}^{\circ}\)C), but this policy involves some risk: the possibility of customer burns. The use of a water mixing valve avoids this health risk, but its use is not very common in Spain.