## 5 Outcomes and Valuation  
The optimization algorithms (WOA, CS, FA, and SHO) are programmed in MATLAB2020a and MATLAB2022a (PSO) software, and the system is modeled in Simulink using the FOMCON toolbox. The spotted hyena optimizer algorithm is used to optimize the controller gain parameters.  
Valuation of Potent Outcomes for the Choice of Superlative Controller (Including Biodiesel and Geothermal Energy)  
The scheme inspected here for valuation embraces T-T-Bd in arena-1, T-T-GPP in arena-2, and T-H in arena-3 (Structure-1). This structure is adapted with PIDN/TIDN/TIDN-FOID subordinate controllers of discrete origin. Valuation is accomplished by including 1% step load tolerances in arena-1. The superlative accessible values of the respective controller's attributes are attained via SHO, with \(Pi_{\text{{SE}}}\). The structure is first and foremost adapted with the PIDN subordinate controller to acquire its attributes as well as the attributes of GPPt via SHO. The governor and turbine time constants gained is 0.1 s. The standards of \(G_{\text{{GPPt}}}\) and \(T_{\text{{GPPt}}}\) are similar in the rest of the paper. After that, TIDN and TIDN-FOID subordinate controllers are applied autonomously. The premium probable values are manifested in Table 1, and with these, potential outcomes are acquired, as shown in Figure 4. Extensive analysis of respective outcomes articulates the distinction of TIDN-FOID over added controllers concerning the narrowed level of crowning_overshoot (C_O), degree-of-fluctuations, and crowning_undershoot (C_U) in addition to the extent of settling duration (S_D). In Table 2, the equivalent figures C_O, C_U, and S_D values are displayed, showing the enhanced presentation of TIDN-FOID over PIDN and TIDN.  
Figure 3: Flowchart of the SHO algorithm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name of Controller** &
\begin{tabular}{c} **Corresponding Gains and** \\ **Parameters** \\ \end{tabular} & **Area-1** & **Area-2** & **Area-3** \\ \hline \multirow{4}{*}{PIDN} & \(K_{pi}\) * & 0.0016 & 0.0025 & 0.0027 \\  & \(K_{li}\) * & 0.3784 & 0.4651 & 0.5068 \\  & \(K_{Di}\) * & 0.4882 & 0.3788 & 0.3569 \\  & \(N_{l}\) * & 12.11 & 13.01 & 15.00 \\ \hline \multirow{4}{*}{TIDN} & \(K_{Di}\) * & 0.1532 & 0.4706 & 0.3715 \\  & \(K_{li}\) * & 0.4888 & 0.4426 & 0.5827 \\  & \(K_{Di}\) * & 0.8056 & 0.6795 & 0.5687 \\  & \(N_{l}\) * & 45.01 & 56.11 & 38.21 \\  & \(n_{i}\) * & 1.4091 & 2.5088 & 2.1078 \\ \hline \multirow{4}{*}{TIDN-FOID} & \(K_{pi}\) * & 0.5470 & 0.7826 & 0.8511 \\  & \(K_{Il}\) * & 0.6584 & 0.7650 & 0.8756 \\  & \(K_{Di}\) * & 0.8033 & 0.8862 & 0.9617 \\  & \(N_{i}\) * & 92.08 & 85.82 & 82.68 \\  & \(n_{i}\) * & 3.9977 & 2.8985 & 1.1748 \\  & \(K_{Pi}\) * & 0.4707 & 0.3868 & 0.4477 \\  & \(\lambda_{i}\) * & 0.0020 & 0.0082 & 0.0021 \\  & \(K_{FDi}\) * & 0.7356 & 0.4747 & 0.5937 \\  & \(\mu_{i}\) * & 0.0722 & 0.0259 & 0.0473 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Premium values of attributes of PIDN, TIDN, and TIDN-FOID subordinate controllers for the scheme including biodiesel and GPPt.  
Figure 4: Valuation of consequences of subsidiary controllers PIDN, TIDN, and TIDN-FOID for structure-1 (including biodiesel and GPPt) for 1% step load tolerances disparity time: (**a**) arena-1 frequency anomaly, (**b**) arena-2 frequency anomaly, (**c**) anomaly in power interrelating arena-2 and -3, and (**d**) anomaly in power interrelating arena-1 and -3.