# An Optimization Framework for Wind Farm Design in Complex Terrain
## 4 Case Study and Results  
As a demonstration, a case study for an anonymous wind farm in complex terrain using the proposed framework is presented here. This wind farm is located in Northwest China, and has a total capacity of 50 MW with 25 turbines. This wind farm has been studied in [23; 32] to investigate the wake flow simulation in complex terrain using CFD, and the preliminary results of the layout optimization  
Figure 5: Architecture of the framework. study of this wind farm have been presented in [18]. Some of this wind farm's site conditions have already been shown in Figure 1. Its original layout is shown in Figure 6 and the turbine characteristics are shown in Figure 7. This type of turbine is variable speed, pitch regulated and has a rotor diameter of \(D=93\) m and a hub height of \(H=67\) m. The cut-in, rated, and cut-out wind speeds are 3 m/s, 12 m/s, and 25 m/s, respectively. Note that constraints on inclusive and exclusive boundaries and bounds on parameters that are considered in this case study are shown in Figure 3. Additionally, the minimal distance requirement used in Equation (14) is chosen as the minimal distance between the turbines in the original layout, which is \(D_{min}=403.8\) m. The inclusive boundary shown with red line in Figure 6 is set as the minimal convex polygon that covers all the turbines, and the exclusive boundary (the green line) is arbitrarily set to test the modelling capacity of the exclusive boundary of the framework. The choice of the inclusive boundary is to make sure the optimized wind farm occupies the same or a smaller area and the required cost of electrical cables and access roads that connect all turbines stays at the same level, so that the comparison of AEP with the original wind farm makes sense. To find a good feasible initial design, the Heuristic Fill algorithm is applied in this wind farm, which obtains an initial design with \(\text{AEP}=164.61\) GWh, as shown in Figure 8.  
Figure 8: Initial design obtained by the Heuristic Fill algorithm. Figure 6: Original design of the anonymous wind farm in complex terrain. Figure 7: Turbine characteristics. Compared to the original wind farm, the design found by the Heuristic Fill algorithm obtains an impressive 1.72% increase of AEP (from 161.83 GWh to 164.61 GWh). Note that this increase is achieved by a deterministic filling process without any searching process, thus can be done in several seconds. To show the performance of the proposed framework, multiple runs of Random Search with different settings of the optimization algorithm are carried out, i.e., optimization runs with different numbers of total evaluation number, \(E_{\text{max}}\), and maximal step size, \(M_{\text{max}}\). For each of these parameter combinations, 10 optimization runs are done to obtain the statistics. Cases starting from the original design (as shown in Figure 6) and the initial design found by the Heuristic Fill algorithm (as shown in Figure 8) are both tried. The results are summarized in Table 2. Note that the percentages of AEP that increase in the optimized wind farm design compared to the original wind farm (161.83 GWh) are marked with underlines inside the parentheses, and the CPU time shown here is the mean value per run for 10 runs by a Python 3.6 implementation of the framework on a laptop with an Intel(r) i5-2520M CPU @2.50 GHz. As shown in Table 2, allowing the optimization process to run longer, i.e., with a larger number of evaluations, generally obtains better results (see the last three rows in Table 2). The other advantage for an optimization process is starting from a better initial design, as the results from the initial design obtained by the Heuristic Fill algorithm are much better than those from the original design using the same optimization setting (see the first and fourth rows of the results in Table 2). The maximal step size also has an effect on the results, as it controls the degree of change that can be made to the current best design in each step.