## 5 Outcomes and Valuation
### Valuation of the Influence of Time Delay on the Potency of the Scheme including Biodiesel and GPPt  
In the above subsection, it is observed that the presence of biodiesel and GPPt in the system has a noteworthy influence on the system dynamics. Now, the system with biodiesel and GPPt is included with non-linearity time delay (\(\tau_{d}\)) in all the areas. Here, \(\tau_{d}\) is considered varied in different areas, i.e., \(\tau_{d1}\) = 0.3 s in area-1, \(\tau_{d2}\) = 0.2 s in area-2, and \(\tau_{d3}\) = 0.1 s in area-3. The superlative values of attributes of TIDN-FOID controller via SHO is provided in Table 6. Through these standards, the outcomes are distinguished in Figure 8 for the system with and without time delay. As per our current understanding of each outcome, the incorporation of time delay degrades the system. However, in order to make the system reflect real-world conditions, the association of time delay is needed; hence, the rest of the assessments are performed in the presence of time delay. Only four responses are provided here.  
Figure 7: Estimation of combined effect of biodiesel and GPPt on scheme potency via SHO-augmented TIDN-FOID subordinate controller using 1% step load tolerances: (**a**) arena-2 frequency anomalies, (**b**) arena-3 frequency anomalies, (**c**) anomaly in power interrelating arena-1 and -2, and (**d**) anomaly in power interrelating arena-1 and -3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name of Controller** & \multicolumn{2}{c}{**Corresponding Gains and Parameters**} & \multicolumn{1}{c}{**Area-1**} & \multicolumn{1}{c}{**Area-2**} & \multicolumn{1}{c}{**Area-3**} \\ \hline  & \(K_{\text{F}i}\) * & 0.7849 & 0.8416 & 0.9610 \\  & \(K_{\text{I}i}\) * & 0.2748 & 0.6100 & 0.2748 \\  & \(K_{\text{D}i}\) * & 0.8866 & 0.6639 & 0.6137 \\  & \(N_{i}\) * & 64.66 & 45.11 & 70.88 \\ TIDN-FOID & \(n_{i}\) * & 4.5528 & 5.4326 & 6.5170 \\  & \(K_{\text{F}i}\) * & 0.8555 & 0.4074 & 0.8386 \\  & \(\lambda_{i}\) * & 0.9755 & 0.7028 & 0.2556 \\  & \(K_{\text{F}Di}\) * & 0.5163 & 0.3872 & 0.5575 \\  & \(n_{i}\) * & 0.9689 & 0.6345 & 0.6229 \\ \hline \hline \end{tabular}  
* Signify the optimum values.  
\end{table}
Table 6: Best values of attributes of TIDN-FOID subordinate controllers for structure-3 (i.e., including biodiesel, GPPt, and time delay (\(\tau_{d}\))).  
Figure 8: Estimation of the impact of time delay on scheme potency via SHO-augmented TIDN-FOID subordinate controller using 1% step load turbulences for scheme-3 (\(\tau_{d1}\) = 0.3 s in area-1, \(\tau_{d2}\) = 0.2 s in area-2, and \(\tau_{d3}\) = 0.1 s in area-3): (**a**) arena-1 frequency anomalies, (**b**) arena-2 frequency anomalies, (**c**) anomaly in power interrelating arena-1 and 2, (**d**) anomaly in power interrelating arena-1 and 3.  
Valuation of the Influence of RFB on the Potency of the Scheme, including Biodiesel and GPP, with Time Delay  
In this subsection, the influence of redox flow battery (RFB) is inspected by associating its outcomes with the outcomes of scheme-3 (i.e., a system with T-T-Bd in arena-1, T-T-GPPt in arena-2, and T-H in arena-3, with time delay). TIDN-FOID is considered a subordinate controller. The premium values of attributes of the TIDN-FOID subordinate controller for the scheme in the existence of RFB are shown in Table 7. For these values, the outcomes for the scheme with and without RFB are distinguished in Figure 9. Intensive clarification of each outcome demonstrates the excellence of the scheme potency with the existence of RFB, concerning the diminished level of C_O, C_U, and S_D via the TIDN-FOID controller with 1% step load disturbance in the presence of time delay. Only four responses are provided here.  
Figure 9: Estimation of impact of RFB on scheme potency involving the SHO-augmented TIDN-FOID subordinate controller using 1% step load turbulences for structure-4: (**a**) arena-1 frequency anomaly, (**b**) arena-2 frequency anomalies, (**c**) anomaly in power interrelating arena-1 and -2, and (**d**) anomaly in power interrelating arena-1 and -3.