## The first numerical test that will be shown

Fig. 4. α that maximizes the annual income vs. the penalty cost [€/kWh].Figure optionsDownload full-size imageDownload as PowerPoint slide

Fig. 5 is very similar to Fig. 4: it shows the PV plant yearly profit [€/year] vs. the value of the penalties [€/kWh]. Again, this quantity decreases when the cost of the penalties increases because there is the convenience to limit economic losses.

Fig. 5. Maximum annual income of the PV plant [€/year] vs. the penalty cost [€/kWh].Figure optionsDownload full-size imageDownload as PowerPoint slide

Fig. 6 shows the amount of IPI-145 that can be considered “lost”, since it can be produced but it cannot be sold to the ESMO. This is the case when pr(t) is strictly greater than pc(t) (i.e. when red line is higher than green line). This is not really “lost” energy, since it can be produced and it can be used by the owner of the Ph plant, if this is allowed by the contract with the ESMO. Rather obviously, this quantity increases when the cost of the penalties increases; in fact, the parameter chosen for the supply of electric energy decreases and therefore the amount of energy sold to the ESMO decreases; but the technical capability of the PV plant remains unchanged, and therefore the energy that “remains” in the hands of the PV plant owner increases.b)PV system integrated with batteries