## 5 Simulation Results
### Comparative Assessment of Different Power Control Schemes
With the proposed method (case (iv)), the SOC control activation and the resulting reduction in BESS output and \(c_{b,up}\) are both communicated back to the AGC system, reducing \(pf_{b,up}\) and increasing \(pf_{g,up}^{*}\), thus substituting the diminishing BESS contribution by other load-following units, as shown in Figure 8e,f. Step-changes noted in the aFRR participation factors when G4 is lost and G5 comes on-line (Figure 8e,f) are due to the normalization of \(pf\) values to a unity sum. In case (iii), the AGC is not informed of changes in BESS output, thus small frequency deviations are observed when the SOC enters its minimum zone (at \(\sim\)6 min, see Figure 8a zoomed-in view). The BAU SOC control scheme results in more pronounced frequency deviations. Frequency disturbances are also noted in the filter-based AGC method when the BESS output power is saturated at the rated value (\(-\)500 kW), partly losing its capability to track the fast-varying component of the AGC signal. Improved frequency regulation performance of the proposed control scheme is also confirmed by the frequency quality metrics in Figure 9, due to smooth SOC control coordination with the AGC of the system. For example, the standard deviation of the frequency in the proposed method (case (iv)) is reduced by 49%, 38% and 28% in comparison to cases (i), (ii) and (iii), respectively. G5 is brought on-line at 900 s, allowing restoration of the system back to its normal operating condition. As shown in Figure 10a, the battery system is not participating in the ED process in the filter-based AGC scheme, since its SOC is regulated by the p-controller of Figure 4. Thus, although the BESS has a zero ED base point (shown in Figure 10a), its real-time power absorption is around 300-400 kW for most of the first 15 min of the simulation. The comparison of Figure 8b,c and Figure 10a showcases this mismatch between ED and real-time operation, as the occurring overloading of the three remaining diesel units in the first 15 min is not reflected in the ED results. Since the same ED process is used in cases (ii)-(iv), and the SOC is similar in all cases, no major difference is evident in the economic dispatch results illustrated in Figure 10b-d. In all three cases (ii)-(iv), the SOC reaches its minimum value at around 10 min (Figure 8d) and the ED problem, solved for two the consecutive intervals, 15-30 and 30-45 min, issues a charging command (\(P^{*}_{b,ED}=-400\) kW) to restore SOC; the full BESS rated power (500 kW) is not used for recharging, due to the downward aFFR of 100 kW allocated to the batteries in this time interval (see Table 1). This shows that the proposed method manages SOC regulation whilst respecting committed reserves of all units, unlike the filter-based AGC method where the ED results do not reflect real-time operation. Economic dispatch orders to all units are implemented using a 5 min ramp, to minimize interference with secondary frequency regulation [46]. This is the reason for the small deviation of SOC from its reference by the end of the simulated 1 h interval, evident in Figure 8d. As shown in Figure 8e,f, with the proposed method, participation factors are smoothly restored back to their ED values (\(pf=pf_{ED}\)), as soon as the SOC leaves its control activation zone. As noted in Section 4, the equivalent battery cycles are used as a simple degradation metric. Case (i) results in 0.27 cycles in the 1 h simulation timeframe, case (ii) in 0.45, while cases (iii)-(iv) both lead to 0.43 cycles. The increased cycling in cases (ii)-(iv) is associated with the BESS discharging down to 22-23%, to support secondary frequency regulation following the disturbance (Figure 8d), while improved cycling in case (i) comes at the detriment of regulating performance. No major differences are noted in terms of battery degradation in cases (ii)-(iv). Overall, the simulation results provided in this section demonstrate the effectiveness of the proposed method and its advantages compared to other approaches.