*4.2. Location of Installation and Economic Aspects*

The installation location represents an interesting point of analysis in terms of production capability, government incentives and payments to private citizens for the production of the energy. Moreover, also the lifestyle of people plays an important role and therefore the average consumption per capita of the electric energy. In order to extend the economic analysis Italy, Germany, France, Spain, Bulgaria, Romania, Greece and Croatia have been considered as reference countries. As well known, these countries have different PV plant performances, different policies to improve the use of electricity generated from renewable sources and different people's lifestyle. In detail, the common strategy is based on a feed-in tariff (FIT) system with different values and timing of the incentives.

The economic data for each country (average consumption per capita, production facility, energy cost and incentives) have been referred of a PV plant installed in the capital of each countries. Moreover, has been considered a family composed by four people that lives in the capital of each countries. In Table 15 the considered economic data are reported.


**Table 15.** Economic data of the reference countries reproduced from [20], reproduced from proceedings of the 2018 International Conference on Smart Grid, IEEE: 2018.

These data are based on the following consideration:


It should be noted that France has the highest value of average consumption per capita. This data is very high with respect to the production facility of the PV plant, so the analysis for the use of DRS is particularly difficult. The higher value of the energy production is in Greece, whereas, Romania and Croatia only offer incentives for 15 and 12 years. It should be noted that these considerations have influenced the economic results.

## *4.3. Inverter*

The inverter represents the heart of the production from the solar energy. In particular, as well known, this system allows the electric energy conversion from DC to AC in order to inject the power surplus into the grid. Therefore, in the case of inverter fault it is not possible to use the energy with a consequence economic loss. From different studies, it is known that the inverter is the component more sensitive to failure. In [2], the authors considered an inverter life equal to 10 years. Nevertheless, it is not possible to estimate with accuracy the lifetime of an electronic component. For this reason, by considering a possible worst case, in this study it was assumed that the average lifetime of the inverter is equal to seven years. As far as the cost is concerned, according to [36] for a residential PV plant with 6 kWp of power the average cost is equal to 1000 €.

#### *4.4. Increase of Production by DRS*

The purpose of a DRS system is to increase the power of a PV plant in the case of a reduction of the total power production. The increment of the power production is a parameter that depends on the DRS topology and therefore hard to estimate. Indeed, the increment of power depends on the type of DRS and therefore of the number of possible available configuration. Thus, the number of possible reconfiguration available play an important role. By considering that a DRS with high number of switches allows many reconfigurations with respect to a DRS with a low number of switches, it is supposed to provide a higher increment of power. Nevertheless, this consideration is not enough to estimate the increment of power provided by a DRS with a defined number of switches, because it is possible that a DRS with high number of switches has redundant configurations. For this reason, in this work the same value of power increment has been considered for each DRS and fixed equal to 10% for the sake of simplicity. This obviously represents an unfavourable condition for DRS with high number of switches and higher costs. Nevertheless, this choice allows to emphasize the effect on the economic analysis of the costs and lifetime for each DRS.

## *4.5. Aging and Maintenance of PV Plant*

After the installation, a natural phenomenon is the aging of the PV components. This phenomenon causes a reduction of the power and it increases over the time. Thus, in the economic analysis has been considered a reduction of power after the first year of the installation equal to 3% and a reduction for each year equal to 0.5%. Moreover, also a periodic maintenance has been considered with a cost equal to 100 €/year.

#### **5. Economic Results and Discussion**

As described above, the economic analysis of this study is focused on the evaluation of the economic benefits by using a DRS system four years after the installation of the PV plant with a power reduction equal to 35%. In particular, four cases of DRS have been analysed in different EU countries in order to extend the economic results. Figure 12 shows the NPV trend over the time of four cases of DRS1-4 and without DRS for each country.

The best result has been obtained in Spain with the highest value of the NPV after 20 years due to the incentives per year. Positive NPV values have been obtained in Italy, Bulgaria and Greece thanks to the high values of the production facility. Romania and Croatia have been penalized for a lower duration of the incentives, whereas, France and Germany have been penalized for the lower values of the production facility. The values of the NPV for each country and for each DRS are summarized in Table 16.

**Figure 12.** NPV trend over the time of four cases of DRS1-4 and without DRS, in (**a**) Italy, (**b**) Germany, (**c**) France, (**d**) Spain, (**e**) Bulgaria, (**f**) Romania, (**g**) Greece and (**h**) Croatia.

By analysing the NPV values of Table 16, it is interesting to note that DRS4 allows one to obtain the best results also in the cases in which there the negative values of NPV. Moreover, this result is interesting because the DRS4 present the second highest cost equal to 1148 € also by considering the worst case for the DRS with higher costs. Other interesting consideration can be done by changing the increment power. By considering an increment of the power equal to 20%, the NPV values obtained are reported in Table 17.


**Table 16.** NPV values after 20 years (increment power 10%).

**Table 17.** NPV values after 20 years (increment power 20%).


In respect to the previous case, the DRS4 with an increment of power equal to 20% allows to obtain positive values of the NPV also for Romania and Croatia. This result is realistic because the DRS4, thanks to the high number of switches and thus the high number of the possible configurations, may generate an increment of power equal to 20%. Another interesting point of analysis is the payback time. In Table 18, the payback times for each country and for each DRS in two power increment cases are reported.


**Table 18.** Payback time for increment of power equal to 10% and 20%. In some cases the payback time exceeds the reasonable time for the return on the investment, and it is not evaluated (n.e.).

Spain and Italy present the best results and it is interesting to note that the same values in the two cases of the increment of power have been obtained. In other countries (Germany, France and Romania), it was necessary to extend the duration of the investment in order to find the payback time but in all cases the best results have been obtained with DRS4 and an increment of power equal to 20%. Only in Bulgaria and Greece a reduction of the payback time has been obtained, an increment power equal to 20%, 13 years to 12 years and from 15 years to 12 years, respectively.
