4.1 Spectral Effect
Based on qualitative information and quantitative data found in the literature, a hourly relation between the spectral factor and AM for CIGS and high-eff c-Si was developed. The AM is calculated from the solar angle, which is already present in the Model, then, the relative spectral factor is included in the total harvest equation as a percentage variation of the energy coming from the global horizontal radiation. The equation were validated by comparing the average monthly values of the spectral factor obtained with the one in the literature. A linear trend was found to well fit the behaviour of high-eff c-Si whereas a polynomial trend was chosen for the CIGS.
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For the CIGS, the spectral effect stays very low at the beginning, then it grows quickly, reaching its maximum value of 8 % when the AM is 10. On the other hand, for the hif-eff c-Si, the spectral effect grows linearly, reaching the maximum value of 10 when the AM is 20. This was chosen because, in Figure 34, it can be noticed that the points when the highest value of MM are reached for high-eff c-Si, are all concentrated at the lowest irradiance level and do not tend to happen again for higher radiation power. On the other hand, for the CIGS case, high values of MM are present at several level of irradiance and happen more often. An AM of 10 is more likely to happen during the whole year than 20, as can be deduced from Table 8.
Despite some imperfections in the case of the CIGS, it could be of interest to implement the method discussed in the methodology chapter, Error! Reference source not found.in the Excel Tool and examine how it affects the results in terms of backup needed. The same seven cities of the angular effect study were taken under examination and for each of them, a comparison between the performance of the same energy system with and without the consideration of the spectral impact was made, both for the case of high-eff c-Si and CIGS. In
Figure 46 is shown the result for the former technology, the blue graph represents the variation in total annual production, a positive variation reflects an improvement. The red graph is the variation in hours of backup needed, therefore a negative variation means that the system is more self-sufficient. As expected, locations at low latitude shown a loss of yearly production and self-sufficiency, due to the high solar angle throughout the whole year, which lead to a blue-shifted spectral distribution. Whereas, in mid-high latitudes the production becomes slightly bigger and there are less hours of backup needed, because the AM in these locations has higher values and the shorter wavelengths are filtered, especially in the mornings and in the evenings. However, the overall
Variation in total yearly production [kWh] and hours of backup needed [h] vs latitude for high-eff c-Si
Yearly production variation
backup variation
51 needed was witnessed for the city of Frankfurt at 50 degrees North, with very similar weather conditions as Freiburg, and it accounted for 172 hours less than the 2900 hours needed in the case without considering the spectral impact, an yearly improvement of 6 %, followed by Milan, registering 109 hours less of backup needed.
Improvements which are not repeated in Nordic cities like Copenhagen and Stockholm, which show no more than 22 hours less than the 3500 hours of the base case, an yearly improvement less than 0,6% and that, according to the logic, should have shown the largest effect.
Figure 46 - Variation in the total annual production of solar energy and hours of backup needed when implementing the spectral impact for 7 locations at different latitude in the case of high-eff c-Si
A similar analysis was performed for the CIGS technology. The relation between the spectral impact and the AM illustrated in Figure 35 was added in the Excel sheet, multiplying those values times the incoming radiation. For the same seven cities, the output in terms of annual PV production and hour of backup needed were compared
and plotted in
Variation in total yearly production [kWh] and hours of backup needed [h] vs latitude for high-eff c-Si
Yearly production variation
backup variation
52 Figure 47. In this case, the city of New Delhi presents the best gains in terms of backup requirements, increasing the system self-sufficiency by 201 hours compared to the 2600 needed in the reference case, an yearly improvement of 7.7 %, followed by Milan (131 h and 7.5 %) and Frankfurt (162 h and 5.6 %).
Figure 47 - Variation in the total annual production of solar energy and hours of backup needed when implementing the spectral impact for 7 locations at different latitude in the case of CIGS technology
4.2 Optimal Tilt Angle
In the Excel Tool the optimal tilt angles, both to maximize PV production and self-sufficiency, were searched for several locations and different cases. Moreover, the number of panels and batteries were varied to see if that affected the output. The results are shown in Table 13. For each location, the latitude, the best tilt angle in terms of production and self-sufficiency are listed in the first three columns highlighted in red. The column “comments”
explains what variation was made to the system, such as an increase in number of PV panels, an addition in storage capacity or a variation in the load. Then, during this process, it was noticed that these variations were not affecting the tilt angle for the PV production optimization, but only the one related to the maximum self-sufficiency.
Variation in total yearly production [kWh] and hours of backup needed vs latitude for CIGS
Variation in total yearly production [kWh] and hours of backup needed vs latitude for CIGS
Variation in production
backup variation
53 Furthermore, it became clear that an addition in number of panels and/or batteries can be well described by one parameter, the hours of backup needed. As the PV array power rating and the storage capacity rise, the hours of backup needed decreases. Therefore, the hours of backup needed was considered when searching for the best tilt angles for the following cases.
Table 13 - Optimal Tilg Angles to maximize the PV production and to maximize the self-sufficiency over a year, for several lcoations and different system set-ups
It was found that many cases present an optimal tilt angle that maximizes the PV production whose value is similar to the latitude angle. Whereas, the optimal tilt angle that maximizes the self-sufficiency often increases with the number of panels and batteries that are available, or the self-sufficiency itself, reaching values equal to 20 degrees more than the latitude angle. In the columns “latitude”, “max PV production” and “max self-sufficiency”, the cases that followed this logic are highlighted in yellow. All the cities whose results differ from the main trend are located below the 30th parallel, in the tropical region. In those cases, the optimal tilt angle that maximizes the production is from 10 to 20 degrees more than the latitude angle, while the one that maximizes the self-sufficiency does not follow any consistent trend. The results are shown graphically in Figure 48. Two linear trends were drawn through the Excel function “LINEST”, to find an equation that could describes them.
54 Figure 48 - Optimal Tilg Angles to maximize the PV production and to maximize the self-sufficiency over a year, at different
latitudes
From the results above, it was decided to include in the Excel tool a suggestion for the tilt angle with a margin of error of about 10 degrees, which the customer may or may not choose to observe, as follow:
If the system is grid-connected, meaning that the power in excess can be sold:
𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑇𝑖𝑙𝑡 𝐴𝑛𝑔𝑙𝑒 = 0,39 ∗ 𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒 + 31° ± 5°
If the system is off-grid, the excess power is lost and the self-sufficiency is the main objective:
𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑇𝑖𝑙𝑡 𝐴𝑛𝑔𝑙𝑒 = 0,76 ∗ 𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒 + 24° ± 10°
4.3 Dittenheim site
The results were taken from the model for the case study in Dittenheim, Germany and the KPIs analysed are presented in this chapter. Several cases were taken under examination and are illustrated in more details in the Appendix.
Overall, the KPIs for 4 main scenarios will be analysed. The scenarios are:
1: 6 PV panels and no batteries
2: 12 PV panels and 3 batteries
3: 18 PV panels and 3 batteries
4: 24 PV panels and 4 batteries
In Figure 49 the fraction of solar energy of the total energy consumed by the site in the four different scenarios is shown. The higher the number of PV panels, the larger is the share of the renewable source.
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55 Figure 49 - Fraction of Solar Energy in the total energy consumption for 4 scenarios
Then, Figure 50 illustrates the Discounted Cumulative cash flow value achieved in the 25th year of operation, in red, and the payback period of all the expenses in blue. The third scenario, with 18 PV panels and 3 batteries is the most economically feasible.
Figure 50 - Discounted Cumulative Cash Flow achieved in the 25th year of operation and the payback period of the investment for the 4 different scenarios
Finally, Figure 51 shows the grid-related annual CO2 emission in each case. The case “zero” refers the case when the system is fully reliable on the grid only. In green is the emission reduction compared to the “zero” case.
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Discounted Cumulative Cash Flow in 25th year [k€] and Payback (years)
Cash Flow Payback
56 Figure 51 - CO2 emissions for each scenario, in grey, and the emission reduction compared with the grid-only case, in green
4.4 Mexico Site
The results for the mexican site are presented in this chapter. Three system will be compared among each other, one fully reliant on the GenSet, a battery + DG case and a hybrid case with PV – BESS – DG. In the Appendix B the hourly profiles and detailled results are illustrated.
Figure 52 shows the capital investment needed, the produced yearly savings, the payback period and the ton of CO2 emitted in the three cases studied: Only DG, batteries + DG and Hybrid PV/DG/BESS system. The much higher Capex in the third case compared to the second, is due to the cost of solar array structure, civil works for foundations and the panels themself, which are not required in the case with only the battery. Despite the different investment, the payback periods are the same, since in the third case the presence of solar energy allows to save about a double amount of money every year.
Figure 52 - Capital investment, payback period and ton of CO2 emitted in the three cases. Only DG, BESS+ DG and Hybrid
9.1
57 The opportunity of integrating a pure solar system, without genset nor grid, was analysed in the tool. The main challenge of having a power system with only solar panels and batteries is to provide site autonomy throughout all year. Figure 53 plots the capital cost of a purely renewable power system as a function of the site availability provided. Covering all the hours of the year becomes extremely more expensive due to the much higher amount of panels and batteries needed to increase the marginal autonomy. Moreover, some Telecom site do not have enough space for such a large solar array. Therefore, unless a telecom site can accept some pre-planned shut down of the service during the year, it is prefered to maintain the presence of the genset, although utilizing it as little as possible, enough to cover those 10 to 20 % of the hours of the year when batteries and solar PV are not available.
Figure 53 - Capital cost of a pure renewable system as a function of the Telecom site availability provided