## 4 Results and Discussion
### Determination of the Optimal Operative Profiles  
The previous sections presented the influence of different algorithm parameters on the solution. In order to proceed further with the simulations, meaningful values should be chosen. For the following analysis, a battery of 2 kWh and a thermal storage of 1200 L were selected. The simulations can investigate 15 climate zones, 10 typical days, and different building types and sizes. Moreover, for every scenario, two operating modes are investigated: full-load and partial-load. For the sake of brevity, only a part of these solutions is presented in this paper. A subset of five climate zones was selected: Z-15, Z-13, Z-4, Z-12, and Z-5. These zones are representative of the coldest and hottest climate zones in Germany and include a vast majority of its population.Furthermore, a subset of five typical days will be presented, covering all the seasons, days of the week, and weather: UWB, USB, SWX, WWB, WSB. Finally, the results of six building sizes are presented: SFH and MFH, with one, two, or three living units each. In Figure 11, the results for the typical day UWB are presented. Similarly, the results for the other four typical days are reported in Figures 12-15. The horizontal axes represent the climate zone and the building size. For every scenario, the darker column (purple and green) represents the operation at full-load, while the lighter column (blue and yellow)  
Figure 10: Influence of water tank size on daily cost, for different initial water levels. Climate Zone 5, typical day WSB, battery 2 kWh, operation full-load. represents the operation at partial-load. The height of the column represents the daily operating cost of each scenario, in EUR, accounting for fuel consumed and electricity bought and sold from the grid (see Equation (8)). Some costs are shown with a label, in order to allow a comparison between climate zones, building size, and operating mode. It can be seen that, for the intermediate seasons (Figures 11 and 12), the operation at full-load is always more convenient of about 10-20%. Obviously, cost increases with building size and varies between 2.12 (SFH1) and 8.81 (MFH3). A small but consistent difference in cost is seen within climate zones: Z-15 generally requires the lowest costs, while Z-5 the highest. Furthermore, little difference can be seen between a working day and a weekend day, with no clear pattern: the operating cost difference for the same scenario between Figures 11 and 12 lays within a few EUR cents. In a typical summer day (Figure 13), the operating cost is significantly lower than in the intermediate seasons, because the thermal and electrical power demands are lower. Partial-load operation is, again, more expensive than the full-load operation of about 10-20%. Finally, the results for typical winter days show, as expected, the highest operating costs. Zones 12 and 5 are characterized by the highest values, while Zone 5 by the lowest. It can be seen that, during winter working days (Figure 14), multiple climate zones for SFH1  
Figure 11: Cost comparison between full-load (left column, purple, and green) and partial-load operation (right column, blue, and yellow) for different climate zones and building types, for a UWB typical day (intermediate season, working day, cloudy). Figure 12: Cost comparison between full-load (left column, purple and green) and partial-load operation (right column, blue and yellow) for different climate zones and building types, for a USB typical day (intermediate season, weekend day, cloudy). and SFH2 and all the zones for MFH are characterized by a more convenient operation in partial-load. Similarly, during winter weekend days (Figure 15), all zones for SFH1 and some zones for MFH1 exhibit a more convenient partial-load operation. This behavior indicates that partial-load operation has potential to be more convenient for small buildings (SFH1, SHF2, and MFH1) in the winter season, hence in those situations in which frequent, small consumption are needed.