## 5 Simulation Results
### Comparative Assessment of Different Power Control Schemes  
Time-domain simulation results in Figure 8 show the response of the system in the following cases:  
1. Filter-based AGC (Section 2.2.1)--red dash-dotted line. 2. BAU SOC control (Section 2.2.2)--orange dotted line. 3. SOC control with no AGC feedback (Section 2.2.3)--green dashed line. 4. Proposed method (Section 2.1)--blue continuous line. The system requirements for aFRR-up and -down reserves in the simulation interval are 300 kW and 550 kW, respectively; the latter are increased to compensate for the PV output rise (\(\sim\)200 kW/h). The reserves allocated to diesel units and the BESS are presented in Table 1. Following the loss of G4, dispatch scheduling is executed out-of-step, to redefine unit commitment and reserves allocation to controllable units. As a result, G5 is brought on-line and aFRR-down reserves provided by the BESS in cases (ii)-(iv) are reduced, as shown in Table 1, in order for the batteries to restore their depleted energy reserves, again reaching their reference SOC (\(SOC^{b*}\) = 55%). Figure 7: (a) Wind speed, (b) solar irradiation and (c) residual load (load-renewable energy source generation) during the 1 h simulation interval. The frequency, the diesel units' total output, the BESS active power, the battery SOC and the aFRR-up participation factors of the BESS and DUs are shown in Figure 8 for \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reserves** & \(\sum\limits_{gi\in G}\left(FCR_{sp,t}^{gi}\right)\) & \(FCR_{sp,t}^{b}\) & \(\sum\limits_{gi\in G}aFRR_{up,t}^{gi}\) & \(aFRR_{up,t}^{b}\) & \(\sum\limits_{gi\in G}aFRR_{dn,t}^{gi}\) & \(aFRR_{dn,t}^{b}\) \\ \hline Case (i) & 600 & 300 & 300 & 0 & 550 & 0 \\ \hline Cases (ii)–(iv) & 600 & 300 & 100 & 200 & 50 (0–15 min) & 500 (0–15 min) \\  & & & & & 450 (15–60 min) & 100 (15–60 min) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Allocation of system reserves (in kW) to DUs and BESS. Figure 8: Response following a diesel unit outage at 150 s and synchronization of another unit at 900 s, for the different regulation methods of cases (i)–(iv). (**a**) Frequency, (**b**) BESS active output power (positive: injection, negative: absorption), (**c**) diesel units’ (DUs) aggregate active power, (**d**) SOC, (**e**) DUs’ automatic frequency restoration reserve (aFRR)-up participation factor, (**f**) BESS aFR-up participation factor. the entire simulation interval. Figure 9 illustrates the main performance metrics for each method, namely, the frequency range (\(f_{range}\)), standard deviation (\(\sigma_{f}\)) and percentage of time outside the \(\pm 50\) mHz band (\(T_{out\pm 50\,\mathrm{mHz}}\)). The ED results for all cases are displayed in Figure 10.  
In the filter-based AGC method, the SOC deviation from its reference (55%) develops a charging term (\(P_{b,soc}^{*}\)) in its local controller that prevails over frequency regulation (term \(P_{b,b}^{*}\)), resulting in full-power recharging over most of the first 2.5 min of the simulation (pre-fault). Through this operation, SOC is restored to 34% when G4 trips. In the other three methods (cases (ii)-(iv)), the allocation of 500 kW downward aFRR reserves to the BESS leads to \(P_{b,ED}^{*}=0\) during the first 15 min (Figure 10b-d), given the prioritization of aFRR provision over SOC restoration (\(C_{dn}^{sl,r}>C^{sl,soc}\)). Thus, a near-zero battery output is observed in the pre-fault period. Tripping of G4 leads to a maximum frequency excursion down to 48.9 Hz in case (i), and 49.3 Hz in all other cases. The inferior performance of the filter-based AGC is the result of relatively reduced primary reserves provided by the batteries after the contingency in  
Figure 10: Economic dispatch results, for cases (i)–(iv). (a) Filter-based AGC, (b) BAU, (c) no AGC feedback, (d) proposed method. Figure 9: Frequency quality metrics, for cases (i)–(iv). (a) Frequency range, (b) frequency standard deviation, (c) time outside 49.95–50.05 Hz.