## 3 Results  
As previously introduced, simulations have been performed adopting network frequency data from CESA for the year 2016 [27], with 1 s sampling rate and a resolution of 0.1 MHz. The economic data used come from the market prices on the DAM and on the BM for Italy and Germany (for what concerns FCR capacity remuneration). These choices have been operated for offering results that can be generalized to the whole CESA. The adoption of CESA's frequency decreases the applicability of these results to systems with less inertia and with larger frequency deviations, such as UK [42]. The model adopted is an empirical multiparameter SoC evolution model. It is obtained via an experimental campaign on an industrial BESS. Therefore, if, on the one hand, the model is accurate in representing the whole operational efficiency (also including the effect of PCS and of auxiliary systems), on the other hand, this model is validated for that device only and it could feature its peculiar behaviors. Furthermore, the possibility of an outage of the plant during the year is neglected. The adopted workstation features an Intel(r) Core(tm) i7-10510U CPU @ 1.80 GHz, 2304 Mhz, 4 Cores, 8 Logical Processors. The approximate elapsed time is 1.5 h per simulated year. The results of the simulations are provided in the following. In Figure 9, the comparison of the strategies adopted can be seen. Each set-up can be evaluated in terms of the provided energy for FCR: obviously, as it can be seen, this energy is larger where the NP is lower. The dead-band case (DB, in red) shows a low NP (3.2%). Energy for SoC restoration widely varies among strategies. Base and over/under-regulation (O/U) case (in black and brown) present no energy flow for the sake of restoration, oppositely dead-band (DB) case (in red) features 7.8 GWh for restoring SoC against 18.2 GWh provided for FCR: energy flows for restoration are 43% of provided energy. In the No DoF case, the need of energy flows for restoration is lower (27%) since SoC restoration takes place (and service provision stops) only when SoC reaches the maximum or minimum thresholds; however, the NP is significant (7.3%) since service provision restarts only when SoC reaches its target value. In the other strategies, the portion of energy flown dedicated to SoC restoration varies between 27% and 32%. BESS lifetime (t\({}_{\text{EoL}}\)) estimated via the SoH model is generally very low: it ranges from 6.8 y for the Base case to 5.0 y for the DB case. As can be  
Figure 9: Summary of the results of the yearly simulations. Absolute value of energy for FCR (E\({}_{\text{-FCR}}\)), absolute value of energy for SoC restoration (E\({}_{\text{-rest}}\)), the BESS expected life (t\({}_{\text{-EoL}}\)), the ratio of NP with respect to total energy requested for FCR, the IRR at 5 y are shown for each of the Cases: base case, no DoF case, over/under-regulation case (O/U), dead-band case (DB), available energy case (AE) and double threshold case (DT). seen, \(\mathrm{t_{EOL}}\) is usually inversely proportional to the overall absolute value of energy flown: it is well known that limiting the equivalent cycles decreases the cycle of aging. Therefore, limiting the energy flows that do not imply a consistent revenue stream should be a target of the asset owner to preserve the BESS. As already described, in the electricity balancing two main parties are involved: the system operator (which procures services) and the BSP (the service supplier). The two clusters of columns on the right part of Figure 9. can be investigated to evaluate the perspective of these two actors. The system operator aims to increase the reliability of provision: this is measured by NP, which must be kept as low as possible. NP below 5% can be taken as a conventional threshold to define an acceptable provision of service [10]. From this standpoint, the best result is obtained via DB (3.1%), while the other acceptable cases are AE (4.8%) and DT (4.9%).