## 6 Scenario Study
### Qualitative Feasibility Analysis for Possibly Considering Wake Effect within the Wind Farm  
The WPPs' design optimization is necessary as this influences the wind farm's annual energy production (AEP) [38]. The optimal performance of a wind farm, which involves maximizing the area's wind energy potential and minimizing the turbulence loading on the rotors of downstream WPPs, is closely connected to the optimal WPP distribution throughout the available site [38; 39]. The wake effect is a dominant factor that influences the wind farm's AEP. As the wind moves past each WPP's rotor, axial and radial pressure drops occur and energy is extracted, which causes pertinent turbulence to rise downstream of the WPP.  
The [PERSON] wake model is a well-known one-dimensional (1D) wake model that makes use of two formulas based on the assumptions of a linearly growing wake diameter, constant wind speed recovery which is proportional to the downstream distance, and a \"top-hat\" distribution [38; 40]. This can be further expressed in a constant wind speed in the cross-wind direction, with changes appearing only in a streamwise direction. The expressions below apply to the [PERSON] wake model [38; 40]:  
\[D_{wk}=2(k_{wk}x_{d}+R_{d}) \tag{18}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Technique I** & **Technique II** & **MPPT** & **Proposed** & **Proposed** \\  & **(Hz)** & **(Hz)** & **(Hz)** & **Technique** & **Technique** \\  & & & & **w/o Battery (Hz)** & **(Hz)** \\ \hline A & 59.624 & 59.697 & 59.521 & 59.709 & 59.728 \\ B & 59.574 & 59.601 & 59.469 & 59.602 & 59.630 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Obtained frequencies by the proposed technique and conventional approaches under each scenario.  
Figure 19: Results for Scenario B: (**a**) WPP\({}_{1}\)’s auxiliary power output; (**b**) WPP\({}_{2}\)’s auxiliary power output; (**c**) WPP\({}_{1}\)’s gain; (**d**) WPP\({}_{2}\)’s gain; (**e**) speed of WPP\({}_{1}\) rotor; (**f**) speed of WPP\({}_{2}\) rotor.  
\[V_{usd}=V_{up}\left[1-\frac{4}{6}\left(\frac{R_{d}}{R_{d}+k_{u\rightleftharpoons k}x_{d}} \right)^{2}\right] \tag{19}\]  
where \(D_{u\
less}\), \(k_{u\
less}\), \(x_{d}\), \(R_{d}\), \(V_{usd}\), and \(V_{up}\) represent the wake's diameter, downstream distance, WPP rotor distance, wind speed deficit, and upstream wind speed, respectively. The schematic Jensen wake model representation is shown in Figure 20.  
From the wake model above, the following equations can be expressed as follows:  
\[u=(1-a)v_{upt},\ v_{1}=(1-2a)v_{upt},\ \alpha=\frac{1}{2\text{ln}\left(\frac{z}{z _{0}}\right)} \tag{20}\]  
\(a\) is a defined 'axial interference factor', which is utilized to express the ratio between the speed reduction at the plane of the blade disc and the undistributed wind speed well upstream of the turbine. The wind's course through the turbine blades is depicted by a cone on the assumption that the wake will expand linearly. Thus, the radius of this cone \(R_{x}\) is obtained as seen in the model figure. The dimensionless scalar \(\alpha\) determines how quickly the wake expands with distance and is defined in Equation (20). \(z\) is the hub height of the turbine generating the wake and \(z_{0}\) is a constant called surface roughness, which depends on the characteristics of the local landscape. Due to assumptions on the turbulent wake and the minimal tip vortices contribution, it can be said that the [PERSON] wake model is suitable for downstream distances greater than three times the WPP rotor diameter [38; 40]. For this study, the WPPs within the wind farm will tend to have such a wake effect, and thus the analysis with the combination of the battery system for frequency regulation operation is very necessary. This is due to the operation condition that the battery system might set into operation, dependent on the selection of the WPP based on the rotor speed being measured.