## 5 Simulation Results
### Comparative Assessment of Different Power Control Schemes
case (i) and the diesel units reaching their maximum load (up to 105% of their rated power), as shown in diagrams Figure 8b,c. This is not the case with the other three methods, that provide a similar response following the contingency. ROCOF, calculated with a 500 ms sliding window, is contained at around \(-\)1 Hz/s in cases (ii)-(iv), avoiding risks of further loss of generation, unlike case (i), where a value of \(-\)1.5 Hz/s is reached. Typical ROCOF withstand capabilities are 1-2 Hz/s for a time window of 500 ms [71]. According to system codes for islands (e.g., [58,72] for Greek islands and Cyprus), generating units are not obligated to remain connected when ROCOF exceeds \(-\)1 Hz/s. With the filter-based AGC method (case (i)), the BESS retains a small charging power after G4 trips, slowly increasing to >300 kW in about 1 min after the disturbance (Figure 8b). This is the result of the AGC operating principle in this case, described in Section 2.2.1, which dictates that batteries take up solely the fast-varying component of secondary regulation, thus leaving the main regulation burden exclusively on the thermal units, without exploiting all available resources (e.g., BESS reserves) even when the system is under stress. As a result, the remaining 3 \(\times\) 1 MW diesel units are overloaded up to 105% of their rated power, as shown in Figure 8c, until G5 is started 12.5 min after the disturbance. Sustained overloading of generating units (which may last much longer than 12.5 min in real-life systems) poses unnecessary risks to system operation; same is true as regards the depletion of upward regulating reserves until standby generation is brought on-line, that would leave the system exposed in case of a RES output drop in the meantime. Similar drawbacks would characterize any regulation method relying on frequency deviations to initiate SOC restoration, as the frequency is quickly restored to near 50 Hz values (\(-\)15 s after the disturbance in the simulations). In cases (ii)-(iv) (BAU, no AGC feedback, proposed method), battery participation to secondary regulation results in sustaining a high output power after the loss of G4, as shown in Figure 8b, which depletes its energy reserves. In cases (iii)-(iv), this activates the local SOC controller \(\sim\)3 min following the trip of G4, when the SOC enters its lower variation zone (SOC \(<\) 25%). This happens because the initial SOC is low (30%) and therefore BESS does not have the required energy reserves for sustained secondary regulation at a high participation factor (\(pf_{b,ED,up}\) = 67%). Battery operation at a low SOC can easily happen, e.g., due to RES forecasting errors leading to the deployment of aFRR, or possibly in the case of cascaded contingencies. In cases (iii) and (iv), in the interval 6-15 min, BESS operates in the lower SOC activation zone (20-25%), resulting in a gradual \(P_{b,soc}^{*}\) decrease, diminishing the active power of the battery unit, as shown in Figure 8b. Eventually, the BESS ends up operating at near zero output, with its SOC above the minimum level, with a sufficient safety margin, as described in the tuning process of \(K_{Ni}\) in Section 2.1. In this state, the BESS is unable to continue providing aFRR. During this process, the battery does not discharge, but recharging is not initiated in the same dispatch interval as the G4 loss, to avoid further depletion of reserves provided by the remaining three diesel units (see Figure 8c). This response clearly showcases the proper coordination between SOC restoration and maintenance of system reserves with the proposed method. In the BAU SOC control method (case (ii)), the BESS participates in aFRR provision for around 6 min after the disturbance, but when SOC drops below 22.5%, the local SOC controller of Figure 5 drives the battery to idling in 10 s (at a rate of \(-\)0.1 pu/s, Table A2 in Appendix A).