## 4 Case Example
### Step 4. Calculate BESS Ageing  
BESS ageing is closely related to its C rate and temperature (among other factors), as previously explained in Section 3. The higher the C rate, the higher the temperature augmentation in the battery. Hence, the BESS configuration has a huge influence on the BESS ageing, since batteries with a higher number of cells in parallel work with lower C  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & \(P_{LIMIT}\) & \(P_{BESS-req}\) & \(E_{BESS-req}\) & **Min. BESS Config.** & \(E_{BESS}\) \\ - & [kW] & [kW] & [kWh] & - & [kWh] \\ \hline SB & 70 & - & - & - & \\ S6 & 60 & 7.13 & 0.015 & 13s1p & 2.64 \\ S5 & 50 & 17.13 & 0.12 & 13s1p & 2.64 \\ S4 & 40 & 27.13 &  
rates, i.e., with less stress. This implies that \"bigger\" BESSs may last longer than \"smaller\" BESSs, which may be beneficial from a cost-benefit point of view.  
Four configurations have been tested for each BESS: the minimum number of cells so that the energy requirements are satisfied, and three more configurations increasing one extra branch each time, so that the C rate is decreased.  
Commonly, a BESS is considered as aged when it loses 20% of its capacity retention.  
As seen in Figure 11, Scenario S4 presents a very different behaviour from the minimum configuration to the minimum plus one. This happens because the C rate is diminished to a half when the branches in parallel are increased by one (from 1 to 2), which is a big difference according to the ageing model. A higher number of branches in parallel do not improve that much the behaviour, although the ageing is further reduced, as expected.  
Scenario S3, which is the summer scenario with more energetic demand from the BESS, does not present a high ageing. This happens because the highest C rates are close to 1C, and there are few moments where those C rates are reached, even though the BESS is dispatching power during longer periods along a day. However, ageing for Scenario S3 is higher than Scenario S6, the BESS is working with a less intermittent profile, implying that temperature is higher during a cycle. Scenario S5 presents a higher ageing that Scenario S3 for the minimum BESS configuration, given that the C rate is higher (close to 3C), although it works for shorter times with that C rate. In any case, a low ageing is expected for every scenario except for Scenario S4.  
For winter scenarios, as seen in Figure 12, Scenarios W8 and W7 present a low ageing due to the few periods of time under which the BESS is dispatching power, even though the C rate for W7 and the minimum BESS configuration reaches 5C. Besides, a low ageing is expected for Scenarios W3 and W4 which, being the most energetic form the point of view of the BESS, are hugely over-dimensioned in terms of power (very low C rates).  
Scenario W6 presents a similar behaviour as S4, where increasing the number of branches in parallel from 1 to 2 prevents from an excessive ageing, which is produced as a consequence of working with C rates higher than 8C for a few moments along a day. Scenario W5 steadily improves its ageing as the branches in parallel increase, although it suffers from the highest ageing except for the minimum BESS configuration.  
Figure 11: Days until \(\
abla Q=20\%\) as a function of the BESS configuration in summer.