## Appendix A Nominal and Adjusted Values for Battery and PV Energy
### Energy CO\({}_{2}\) Content Calculations  
Following a similar method as the one presented in Section A.1, in this section the nominal values for the CO\({}_{2}\) content of the energy delivered by the battery and PV, based on their embedded carbon emissions (see Table A1) are computed.  
The nominal values for the CO\({}_{2}\) content of the battery and PV panels are computed as follow:  
\[\text{CO}_{2 batt}^{nom}=\frac{E_{\text{CO}_{2 batt}}}{TOE_{min}}\] (A7)  
\[\text{CO}_{2 pv}^{nom}=\frac{E_{\text{CO}_{2 pv}}}{TOE_{exp}}\] (A8)  
where \(E_{\text{CO}_{2X}}\) stands for the embedded CO\({}_{2}\) emissions expelled to the atmosphere during the manufacturing process of the DER \(X\) (see Table A1).  
The corresponding corrected values for the CO\({}_{2}\) content of battery CO\({}_{2}^{h}\)_hatt_ and PV energy CO\({}_{2}^{h}\)_pv_, are computed by changing the capital cost \(CAPEX_{x}\) in Equations (A3) and (A6), and replacing it with the embedded CO\({}_{2}\) emissions during manufacturing. In these way, we obtain the relations to compute the corrected values for the CO\({}_{2}\) content of battery and PV energy, as presented in Equations (A9) and (A10).  
\[\text{CO}_{2}_{batt}^{corr}=\frac{E_{\text{CO}_{2}_{batt}}}{TOE_{min}\cdot\frac {CL}{CL_{max}}}=\frac{\text{CO}_{2}_{batt}^{nom}}{B_{LR}}\] (A9)  
\[\text{CO}_{2}_{pv}^{corr}=\frac{E_{\text{CO}_{2 pv}}}{TOE_{exp}\cdot\frac{E_{pv} ^{potential}-E_{PS}^{curtailed}}{E_{pv}^{potential}}}=\frac{\text{CO}_{2}_{pv}^{nom }}{PV_{CF}}\] (A10)  
The coefficients \(B_{LR}\) and \(PV_{CF}\) are the same as for the calculations of EC (see Equations (A2) and (A5)), as well as the \(TOE_{min}\) and \(TOE_{exp}\) (see Table 11).  
A summary of the \(CAPEX\) and embedded CO\({}_{2}\) emissions of the battery and PV panels, as well as their nominal energy cost, is presented in Table 11. The costs do not include balance-of-system expenses.  
In order to compute the through-Output-Energy (\(TOE\)), the expected annual PV production is obtained for the study-case site. This calculation is based upon historical GHI measurements during the test period (\(\approx\)1 year). This annual energy output is then extrapolated for the number of years that PV panels are expected to last, according to the manufacturer (30 years with a 0.26% annual degradation). In this way, the -average- total energy that the PV array is expected to deliver throughout its lifetime (\(TOE\)) is obtained.  
Regarding the \(TOE\) value for the battery, it is the minimum--warranted--energy that the battery will deliver during its lifetime, regardless of its profile of use, according to the manufacturer.  
The CAPEX costs are based on--average--market prices in Europe for PV panels and Lithium-ion batteries, for the capacity requirements of the Drahi-X MG.  
Regarding the embedded CO\({}_{2}\) emissions (greenhouse gases emitted through the manufacturing process, including extraction of raw materials), several studies were consulted and the values were taken from the ones that seemed more adapted to the European case, and to the manufacturing sites of the type of PV panels and batteries expected to be used in the Drahi-X MG. The references used to obtain the \(TOE\), CAPEX and embedded CO\({}_{2}\) emissions (\(E_{CO_{2}}\)) are presented in Table 11.  
With the aforementioned values, Table 11 is completed using Equations (A7) and (A8) to obtain the nominal values of CO\({}_{2}\) content per kWh of energy delivered by the battery and PV panels, respectively. In a similar manner, Equations (A1) and (A4) are used to obtain the nominal cost per kWh delivered by the battery and PV panels, respectively.