## 4 Controller Tuning Methodology
### Base Case: FR Provided by Diesel Governor  
We consider a base case without the control loops proposed in Section 5 to highlight the main contribution of VSWTs for FR. However, during the absence of the proposed control loops, all FR will be provided by the diesel governor. To validate the base case of the VSWT hybrid wind-diesel power system, we used a step response of 0.5 pu (starts from 1.1 to 1.6 p.u) as \(\mathrm{P_{load}}\). This step response depicts the loss of wind generation and results in an increased load to the DPP and FD. Furthermore, the wind power plant is initialized at 0.70 p.u for the base case and onwards in this study. Figure 16 shows the performance of hybrid systems during increased load demand. Similarly, Table 2 presents the values of several parameters (NADIR, ISE, IAE) during a sudden increase in load demand. Figure 15: Flow chart of SPBA for tuning two-parameter controller. Case A: VSWT Contribution to FR Using Proposed Control Without Tuning Diesel Governor Gain Parameters  
In this case, the VSWT uses proposed inertial and proportional control loops and pitch compensation to provide synthetic inertia and pitch angle smoothing. However, the diesel governor gain parameters remain the same. To provide synthetic inertia, the gain parameters of the VSWT inertial and proportional control tuned by the proposed tuning methodology are discussed in Section 5. Using the SPBA tuning methodology, optimal tuning values for inertial and proportional control gains, i.e., \(\text{K}_{\text{dn}}=0.03\) and \(\text{K}_{\text{pn}}=0.1\), were calculated. Similarly, the BPAC was also tuned due to an additional pitch angle compensation controller. However, the BPAC (Figure 13) shows a better response with integral control instead of the proposed PI controller, in the pitch compensation loop (i.e., \(\text{K}_{\text{pc}}=0\)), which further simplifies the VSWT model. The new tuned gain parameters of the modified BPAC are given in Table 14. Therefore, with the proposed approach (without the variation in DG parameters), the new speed is 0.957646 p.u, and the NADIR is 57.45876 Hz. This clearly shows that the contribution of synthetic inertia is negligible (frequency improvement of 0.00222 Hz) when compared to the base case (Section 5.1). One of the main reasons for this negligible contribution is the optimally tuned diesel governor (we already tuned this in [30]), which mainly assists in providing inertia during transients in hybrid power systems. We finally conclude that the VSWT does not provide a significant contribution to synthetic inertia in hybrid mode with the diesel power plant when the diesel governor is optimally tuned. In other words, to benefit from the VSWT for FR, the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **With \(\text{K}_{\text{pn}}\), \(\text{K}_{\text{dn}}\), \(\text{K}_{\text{pc}}\), and \(\text{K}_{\text{ic}}=0\)** \\ \hline NADIR (p.u) & 0.957609 \\ IAE & 0.039205 \\ ISE & 0.001197 \\ C & 2 \\ Frequency (Hz) & 57.45654 \\ Z & 10,202.87614 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Base parameters of VSWT hybrid WDPS. Figure 16: VSWT hybrid WDPS base case response without proposed controller contribution. hybrid model will be tuned in combination when the DG works with optimally tuned gain parameters. Case B: VSWT Contributes to FR by Tuning the Proposed Controls and Diesel Governor Gain Parameters in Combination  
In this case, we considered both proposed control loops and diesel governor gain parameters and tuned the whole system in combination to make the hybrid power system effective during transients. The same proposed tuning methodology of the SPBA (discussed in Section 5) is used to simultaneously tune four parameters (K\({}_{\text{dn}}\), K\({}_{\text{pn}}\), K\({}_{\text{i,d}}\), and K\({}_{\text{p,d}}\)).