## Appendix A Nominal and Adjusted Values for Battery and PV Energy  
### Energy Cost Calculations  
In this section, the calculations to compute the nominal and adjusted costs of the energy coming from the battery and the PV panels are presented.  
The nominal cost for the use of the battery is computed using Equation (11).  
\[C_{batt}^{nom}=\frac{CAPEX_{batt}}{TOE_{min}} \tag{12}\]  
where \(CAPEX_{batt}\) stands for the capital expenditure (the cost) of the battery, while the \(TOE_{min}\) stands for the minimum through output energy of the battery or the minimum energy that the manufacturer guarantees that the battery will deliver during its lifetime (see Table 12). The \(TOE_{min}\) is computed for specific test conditions set by the manufacturer of the battery.  
In our case, we assume that \(TOE_{min}\) is computed for the nominal battery cycling life \(CL_{max}\). Therefore, when CL decreases, that causes \(TOE\) to decrease accordingly, increasing the cost of the energy delivered by the battery in the same proportion. The correction factor for the reduction in the battery cycling life \(B_{LR}\), is presented in Equation (13).  
The nominal cost of the energy delivered by the battery \(C_{batt}^{h}\), computed in Equation (12), is adjusted the equivalent cycling life (CL) of the battery [36], as presented in Equation (13).  
\[B_{LR}=\frac{CL}{CL_{max}} \tag{13}\]where \(CL\) is the equivalent battery cycling life while \(CL_{max}\) is the maximum (theoretical) battery cycling life according to the model proposed by [PERSON] et al. [36].  
Then, the factor \(B_{LR}\) is used to adjust the nominal cost of the battery presented in Equation (A1) to obtain the corrected battery cost. This is expressed in Equation (A3).  
\[C_{batt}^{corr}=\frac{C_{batt}^{nom}}{B_{LR}}\] (A3)  
Then, for a given EMS strategy, the equivalent \(B_{LR}\) can be computed in order to obtain the corrected battery cost \(C_{batt}^{corr}\). This cost is considered constant for the entire test period. For the sake of simplicity, we consider that these average use conditions of the battery are kept throughout all its lifetime, so that the reduction of its cycling life is consistent with the calculations.  
An analogous approach as the one presented in Equations (A1)-(A3) can be followed to obtain the average cost of PV energy, \(C_{pv}\).  
The nominal cost of the energy delivered by the PV panels \(C_{pv}^{nom}\), can be obtained with the Equation (A4).  
\[C_{pv}^{nom}=\frac{CAPEX_{pv}}{TOE_{exp}}\] (A4)  
where \(CAPEX_{pv}\) stands for the capital expenditure (the cost) of the PV array (without taking into account the balance-of-system costs), while \(TOE_{exp}\) represents the expected through-output-energy, which is computed based on the historical PV output power measurements of the study-case site and the warranted life and output-power of the PV panels given by the manufacturer (see Table A1).  
In the meantime, an equivalent to the \(B_{LR}\) can be found for the PV power production, that is related to the reduction in the through output energy due to curtailment. This is called PV curtailment factor (\(PV_{CF}\)) and is expressed in Equation (A5).  
\[PV_{CF}=\frac{E_{pv}^{potential}-E_{pv}^{curtail}}{E_{pv}^{potential}}=\frac{E_{ pv}^{real}}{E_{pv}^{potential}}\] (A5)  
where \(E_{pv}^{potential}\) is the potential output energy of the PV installation during the test period for the given GHI conditions, while the \(E_{pv}^{curtailed}\) represent the total curtailed energy during the test period.  
In this case, for a particular EMS strategy, the results of Equation (A5) are extrapolated as if the curtailment policy were to repeat for the entire life of the PV installation. Under this assumption, Equation (A3) can be rewritten to compute the corrected cost of the energy delivered by the PV panels, as in Equation (A6).  
\[C_{pv}^{corr}=\frac{C_{pv}^{nom}}{PV_{CF}}\] (A6)