## 5 Analysis of Behavior and Results
### Multi-Season Simulations  
The above simulated scenarios demonstrated the average daily operation of the BESS at the four seasons of the year. In all four simulated scenarios the capacity loss set points were calculated by utilizing the battery manufacturer's hard limits (DOD = 80% and Crate = 0.33). By running multi-season simulations, the BESS's capacity fade is estimated. In addition, the total economic profit for the consumer and the economic profit per season is calculated. Over and above, further multi-season simulations were implemented by using different ageing trajectories for the BESS. The main purpose of this task, was to explore the BESS's behavior when stricter restrictions are applied regarding the ageing prevention and how the economic profit is affected. Figure 16: BESS operation schedule: (**a**) Energy distribution; (**b**) Charging and discharging currents. Figure 17: BESS parameters. The simulated scenarios were implemented for five different capacity loss trajectories. The trajectories were defined for the following DODs: (a) DOD = 80%, (b) DOD = 70%, (c) DOD = 60%, (d) DOD = 50% and (e) DOD = 40%. At all five trajectories the Crate was set at its maximum permitted value (0.33). The duration of all simulated scenarios is 1 year. Considering that during autumn/winter the BESS is forced to operate two full charge/discharge cycles per day and during spring/summer one cycle per day the overall number of cycles through one year is 547. The estimated capacity loss for each scenario and the corresponding capacity loss set points are depicted in Figure 18.  
Figure 18: BESS estimated capacity loss and capacity loss trajectory: (**a**) for DOD = 80%; (**b**) for DOD = 70%; (**c**) for DOD = 60%; (**d**) for DOD = 50%; (**e**) for DOD = 40%. Excluding the first scenario where the ageing trajectory is determined for DOD = 80%, at all the other scenarios the estimated capacity loss at the end of the year is slightly higher than the corresponding set point. This is an outcome of applying dynamic optimization only at the discharging zones. The non-constrained operation during charging zones, increases the average operating current of the BESS and hence the estimated capacity loss. Nevertheless, applying charging without considering ageing constraints is inevitable in order to store the maximum possible energy at the BESS and hence achieve higher economic profit. During the one-year simulation for the 80% DOD ageing trajectory the economic profit was found to be 63.42 \(\upepsilon\) and the estimated capacity loss 10.12 Ah. Considering that the end of lifetime of a battery is when the capacity has been reduced to 80% of the nominal capacity, the BESS has surpassed half of the expected lifetime after just one year of operation. By replacing the ageing trajectory with the trajectory for DOD = 70%, the profit is reduced to 57.41 \(\upepsilon\) and the capacity loss to 8.84 Ah. This implies that the profit has been reduced by 9.5% while the capacity loss has been decreased by 12.6%. Therefore, by applying a slightly stricter ageing constraint to the dynamic optimization, it is observed that the premature ageing prevention rate is greater than the rate of the decreased economic profit. By applying a stricter capacity loss constraint (ageing trajectory DOD = 60%), it is noted that the economic profit after 1-year operation is reduced 48.57 \(\upepsilon\) and the battery stack's capacity fade to 7.05 Ah. Compared to the corresponding values of the first simulated scenario (trajectory for DOD = 80%) the economic profit is decreased by 23.4% while the BESS's capacity loss is reduced by 30.3%. Over and above, by applying the ageing trajectory for DOD = 50% the profit is furtherly decreased to 40.79 \(\upepsilon\) (35.7% decrement compared to scenario DOD = 80%) and the capacity loss to 5.26 Ah (48% decrement compared to scenario DOD = 80%).