## 5 Results and Discussion
### Simulation Results
#### 5.2.1 Results under Different Controller Configurations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**No Controllers**} & \multicolumn{2}{c}{**PSSs**} & \multicolumn{2}{c}{**BESS Controllers**} & \multicolumn{2}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}  & \(P(\boldsymbol{\kappa}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\zeta}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\kappa}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\zeta}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\kappa}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\zeta}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\kappa}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\zeta}<\boldsymbol{0.1})\) \\  & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} \\ \hline
1 & 100 & 100 & 0 & 95.9100 & 0 & 0 & 0 & 0 \\
2 & 96.5000 & 100 & 90.6403 & 100 & 0 & 0 & 0 & 0 \\
3 & 92.0600 & 100 & 95.4195 & 100 & 0 & 0 & 0 & 0 \\
4 & 94.4200 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\
5 & 0 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\ \cline{1-1}
5 & - & - & - & - & - & - & - & - \\
15 & 0 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of stability indices under different controller conditions using proposed method. Figure 12: Damping constant of most critical eigenvalue. the case with only-PSS connection compared with the base case. Specifically to improve Modes 1 to 3, we performed further investigations. They were found to be interarea modes that are generally difficult to improve by only using PSSs. Thus, BESS controllers were sought to improve them, which is discussed below. The results under the BESS controller category of Table 2 were computed by assuming all three BESS controllers of the test system were connected, and all PSSs were disabled. It was first necessary to find the best feedback signal for each BESS controller before tuning them. This paper uses residue analysis for this purpose, as discussed in Section 4.1.2.2. The signal that provides the highest residue for BESS1, BESS2, and BESS3 was found to be an active power flow between Lines 45 to 51, active power flow between Lines 41 to 42, and real power flow between Lines 43 to 44, respectively. The proposed method was then used to tune the BESS controllers. The previously risked Modes 1 to 3 in the case with only PSSs, which have a high likelihood of being small-signal unstable, have a low likelihood of being low-frequency unstable, as can be seen from Table 2 for the case with BESS controllers. However, the probability of the damping constant being greater than the critical margin, and the probability of the damping factor being lower than the critical margin for other modes (4-15) increases drastically for this controller configuration. This is largely because they are mainly local modes that cannot be effectively damped by only using BESS controllers as they use remote signals from the PMU. The final controller configuration case considers the test system with a connection of both BESS controllers and generators (1-12) with PSS. The objective function given by Equation (16) is first solved to obtain the optimized parameters for all PSSs and POD controllers. The convergence of the objective function is shown in Figure 13, and the minimum value of 5123 was achieved in 44 iterations. As can be seen from Table 2 under the PSS and BESS controller heading, all modes have a low probability of being small-signal unstable with respect to their margin values, showing the effectiveness of the proposed coordinating approach of utilizing PSS and BESS controllers. In addition, we used the optimization-based tuning method (OBTM) proposed by Reference [42] to compare the effectiveness of our proposed method. The probabilistic indices related to small-signal instability are always lower with the controllers tuned using the proposed method than the compared method, as can be seen from Table 4.