# A Game Theoretic Approach for Energy Sharing in the Italian Renewable Energy Communities
## 4 Case Study
### Sources Availability  
With respect to the generation side, two technologies have been investigated: photovoltaic and hydroelectric. More in detail, we consider the possibility to install a single hydro power plant and several PV power plants. The main data about the availability of these sources are reported in Table 2.  
Theoretically, each rooftop could host a PV plant, nevertheless it is trivial to exclude some of them due to their particular shape, orientation and shadows. For this reason, the number of considered rooftops in the optimization has been reduced to 20. This represents the number of surfaces for which the installation of a PV plant is supposed to be reasonable. The area and the orientation of the surfaces have been evaluated with GIS software, while the slopes have been defined with realistic values from 10\({}^{\circ}\) to 40\({}^{\circ}\). The installation cost for each plant is considered different, going from the lowest value equal to 1400 EUR/kWh to the highest value equal to 2000 EUR/kWh.  
The production profiles for each of these plants are automatically requested via API to the PVgis tool \"Performance of grid-connected PV\" [33], in order to properly take into account the shadows from high horizon. Since the location of all the surfaces is almost the same, this type of shadow does not introduce big differences among the plants, and each power profile is mainly characterised by the orientation and the slope of the single surface. The profile is requested to PVgis for a PV plant with a rated power of 1 kW based on crystalline silicon cells, and the sum of the system losses is set to 14%. In Figure 6, the profiles  
Figure 5: Estimated power consumption of LV users of Chiou.  
obtained for each of the 20 surfaces are reported for four days. From this zoom, it is possible to see the effect of the different orientation on the daily production profiles. The heatmap in Figure 7 reports the average profile with time divided into two axis: the day of the year and the hour of the day. In this way, it is easy to see the daily and seasonal trends. This specific profile is not used in the model, but it is useful to see the seasonal behaviour of this type of generators.  
The production profile of the hydroelectric power plant is a standard profile, built from the production profiles of similar power plants in the area. Since the maximum allowed size of a generator connected to the Italian LV network is 200 kW, only power plants with a nominal power lower than 200 kW are used to build the standard profile. In the area under evaluation, there are 6 monitored hydroelectric power plants with the following rated power: 40 kW, 6.4 kW, 72 kW, 45 kW, 45 kW. Looking to their production profiles, it is clear there is a common path defined by the seasonal water availability. In Figure 8, the standard production profile of the hydroelectric power plant is depicted compared with the five measured profiles of the real plants currently in place. They are all normalized by their maximum power and the reference profile is obtained as the median value for each hour of the year. It is also shown in Figure 9, where it is possible to see the seasonal trend and the absence of a daily trend. The number of the equivalent working hours per year for the profile obtained is equal to 4205.  
Figure 6: Daily differences among PV power profiles.  
Figure 7: Average photovoltaic power production.