## 3 Results
### Economic Optimum Systems of the Five Cases
#### 3.1.2 Energy Balance of the Economic Optimum Systems  
To interpret the different battery capacity reductions in each case, it may be useful to observe the changes in the internal energy balance of the system. Different internal energy flows correspond to the different size of components of the lead-acid or Li-ion battery optimal systems. This section pays attention to two relevant quantities in standalone systems with storage and renewable generation: the energy cycled in the battery and the excess energy. Due to the variability of the solar resource, in standalone PV systems, storage is necessary to satisfy the demand of the loads at times when there is not enough PV production. Thus, a part of the energy supplied to the loads comes from the battery, where it has been cycled. When the solar resource is practically zero, all the energy must be supplied from the battery. However, when the solar resource is present, the energy comes to a greater or lesser extent from the PV generator, and can be complemented by that from the battery. In addition, long-term storage in batteries is hardly feasible. Because of all this, standalone PV systems often have a high amount of excess energy. When sizing a standalone PV system, many different combinations of PV production and storage are possible, among which there is an economically optimal one. When changing the technical characteristics and/or the costs of the components of the system, as in this comparison with the battery, the economic optimum varies. Consequently, the amounts of cycled energy and excess energy are also affected. Organized in a similar way to the previous tables, Tables 8 and 9 show these significant parameters of the internal energy balance in the optimal PV systems and hybrid systems for the five case studies. Figure 7 shows the percentage differences in battery capacity and energy cycled in the battery in the system, between the economic optimum systems with Li-ion and lead-acid batteries. As shown in Figure 7a, in PV systems, relatively big variations in battery capacity corresponded to proportionally small variations in cycled energy. Even with capacity reductions, two of the cases showed slight increases in cycled energy. In four of the five cases of hybrid systems, as shown in Figure 7b, the variations in energy cycled were also relatively small, in comparison with the variations in the battery size. However, in the case of irrigation pumping, the cycled energy was strongly reduced (\(-84\%\)) but also to a lesser extent than the battery capacity (\(-92\%\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Battery Type** & **Energy Cycled (kWh)** & **Excess Energy (kWh)** \\ \hline \multirow{2}{*}{Winery} & Lead-acid & 26,862 & 368,503 \\  & Li-ion & 26,727 & 405,595 \\ \hline \multirow{2}{*}{Irrigation pumping} & Lead-acid & 15,163 & 242,476 \\  & Li-ion & 12,033 & 511,890 \\ \hline \multirow{2}{*}{Pig farm} & Lead-acid & 107,863 & 576,442 \\  & Li-ion & 105,798 & 871,075 \\ \hline \multirow{2}{*}{Single-family home} & Lead-acid & 3290 & 23,881 \\  & Li-ion & 3353 & 15,667 \\ \hline \multirow{2}{*}{Second home} & Lead-acid & 892 & 6318 \\  & Li-ion & 886 & 8044 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Energy cycled and excess energy in economic optimum PV systems. Figure 8 shows the percentage differences in energy cycled in the battery and in excess energy in the system, between the economic optimum systems with Li-ion and lead-acid batteries. As shown in Figure 8a, in PV systems, small variations in cycled energy corresponded to proportionally large variations in excess energy. On the contrary, in hybrid systems there were no large variations in excess energy, as shown in Figure 8b. This was because when reducing the battery capacity, there were periods when stored energy was not available and had to be compensated with more power generation.