# An Optimization Framework for Wind Farm Design in Complex Terrain
## 4 Case Study and Results
As discussed in Section 3.3, this parameter should be set large enough to explore the design space more thoroughly and thus find a better solution after a sufficient large number of evaluations. This is supported by the comparison of optimization runs with the same \(E_{\text{max}}\), but different \(M_{\text{max}}\), as shown in the second to fourth rows of Table 2.  
The best optimized design found by all the optimization runs summarized in Table 2 is under the optimization setting: \(E_{\text{max}}=10,000\), \(M_{\text{max}}=5000\) m, with the optimized AEP as 166.21 GWh, representing a 2.70% increase to the original wind farm design. This design is found by the Random Search algorithm starting from the initial design obtained by the Heuristic Fill algorithm, and shown in Figure 1.0 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Opt. Setting**} & \multicolumn{2}{c}{**AEP [GWh] (Increase [\%])**} & \multicolumn{2}{c}{**CPU Time [s]**} \\ \hline \(E_{\text{max}}\) [-] & \(M_{\text{max}}\) [\(m\)] & **Initial** & **Opt. min** & **Opt. mean** & **Opt. max** & **Mean** \\ \hline
1000 & 5000 & 161.83 & 164.62 (1.72) & 165.03 (1.98) & 165.67 (2.37) & 2137.5 \\
1000 & 50 & 164.61 & 165.18 (2.07) & 165.27 (2.12) & 165.30 (2.14) & 1824.6 \\
1000 & 500 & 164.61 & 165.17 (2.06) & 165.28 (2.13) & 165.41 (2.21) & 1923.7 \\
1000 & 5000 & 164.61 & 165.17 (2.06) & 165.45 (2.24) & 165.79 (2.45) & 2272.3 \\
5000 & 5000 & 164.61 & 165.76 (2.42) & 166.02 (2.58) & 166.17 (2.68) & 12,042.6 \\
10,000 & 5000 & 164.61 & 165.95 (2.55) & 166.11 (2.64) & **166.21 (2.70)** & 24,613.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of the framework in multiple runs with different settings. Figure 9: Best optimized design found by the framework with \(E_{\text{max}}=10,000\), \(M_{\text{max}}=5000\) m.  
To better compare the performance of the original, initial, and optimized designs as shown in Figures 6, 8 and 9, their gross and net AEP values are listed in Table 3.  
As Table 3 shows, the initial design found by the Heuristic Fill algorithm has both higher gross AEP and higher net AEP than the original design. Although the wake loss is higher for the initial design than the original one (6.16% versus 4.67%), the larger increase (3.34%) of gross AEP thanks to the higher mean wind speed of the sites found by the Heuristic Fill algorithm compensates the higher wake loss and still yields a substantial increase (1.72%) of net AEP. Note that the higher wake loss of the initial design can also be seen from the layout shown in Figure 8, as the turbines are placed much closer to each other than the original layout shown in Figure 6.  
Since the optimized design in Figure 9 is obtained by the optimization run starting from the initial design in Figure 8, we can also compare these two designs. Apparently, the optimization algorithm makes a small sacrifice in gross AEP, i.e., allowing the gross AEP to decrease by 0.28% from 175.42 GWh to 174.91 GWh, while decreasing the wake loss percentage from 6.16% to 4.97%. The combined effect allows the optimized design to gain a 0.97% increase of net AEP to the initial design (from 164.61 GWh to 166.21 GWh), representing a 2.70% increase of net AEP when compared to the original design (from 161.83 GWh to 166.21 GWh). Examining the layout of the initial design in Figure 8 and the layout of the optimized design in Figure 9, we can see that the turbines are scattered away from each other while most of the turbines are still located at high elevation sites. This shows that the optimization algorithm tries to lower wake effects while not sacrifice too much on the gross AEP, as suggested by the net and gross AEP comparison. To show the performance of the framework in multiple runs, the evolution histories of the 10 runs under the optimization setting: \(E_{\max}=10,000\), \(M_{\max}=5000\) m are shown in Figure 10, which demonstrate the random nature of the RS algorithm. As Figure 10 shows, different runs of the optimization process yield different results.