## 4 Conclusions  
In this paper, a real two-dimensional wind farm layout optimization was carried out using the superior unrestricted coordinate method with continuous variation of wind turbine placements. In order to verify the effectiveness of wind farm layout optimization on improving the total output power, different wind conditions including the ideal and realistic wind scenarios were investigated. The ideal wind scenario included constant wind speed and constant wind direction, constant wind speed and variable wind directions, and variable wind speeds and variable wind directions. The realistic wind scenario included a Weibull distribution. A newly developed Jensen-Gaussian wake model, which considers the variation of wake velocity in the radial direction as Gaussian distribution, was employed for the optimization study. The means of handling the irregular wind farm boundary were proposed in conjunction with the discretization method to calculate the wind farm power output under the Weibull distribution. The results showed that as the number of wind turbine increased from 40 to 46, the total wind farm power output showed a linearly increasing pattern. In comparison, the total wind farm power losses variation as a function of the number of wind turbines was dependent  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Wind Scenario** & **Layout Properties** & **Minimum Distance of** \\
**Wind Turbines** & **Average Distance of** \\
**Wind Turbines** & **Wind Turbines** \\ \hline Constant speed and direction & 7D & 37.3D \\ Constant speed and variable directions & 7 & 36.27D \\ Variable speeds and directions & 7.28D & 36.1D \\ Weibull distribution & 7D & 35.2D \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of optimized wind farm layouts in terms of minimum and average distances between wind turbines (in the unit of turbine diameter, D) for different wind scenarios studied.  
Figure 14: Rule of thumb layout of wind farm with fixed spacing of potential wind turbine locations on the cross-wind direction.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**LayoutNumber** & **40** & **41** & **42** & **43** & **44** & **45** & **46** \\ \hline Rule of thumb & 8373 & 8584 & 8785 & 8982 & 9199 & 9395 & 9598 \\ Optimized & 9821 & 10,056 & 10,303 & 10,540 & 10,782 & 11,017 & 11,263 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of total wind farm power output (in kW) with different number of wind turbines for rule of thumb layout and optimized wind farm layout.  
on the wind conditions. In general, the total power losses increased with more installed wind turbines. However, for some particular wind conditions, e.g., the Weibull distribution, it showed a different trend with nearly the same power losses when an adjacent number (41 and 42, 45 and 46) of wind turbines were installed. By imposing the boundary constraint on the objective function for optimization, all the optimized wind turbine positions were inside the wind farm boundary. The distribution of wind turbines was dependent on the wind conditions. A common feature of wind turbine positions regardless of wind conditions was that they are distributed along the wind farm boundary as much as possible to alleviate the wake effect.  
Data curation, Y.Z. and J.X.; Writing-review & editing, L.W.  
This research is funded by the China Postdoctoral Science Foundation (Grant No.: 2018M632244), Natural Science Foundation of Jiangsu Province (Grant No.: BK20180879), High-level Talent Research Foundation of Jiangsu University (Grant No.:18 JDG012), Australia Endeavour Scholarships and Fellowships, and Canada Future Energy Systems Program. The financial support from the Jiangsu University of China and Department of Education and Training of Australia are particularly acknowledged. The high performance computational (HPC) resources provided by the Queensland University of Technology (QUT) are also greatly appreciated.  
The authors declare no conflicts of interest.