## 3 Relevant Research in Wind Farm Design and Optimization
### Electromagnetic Interference (EMI)  
In none of the reviewed works the wind farm EMI effects were considered. However, other literature works have reported different models and methods for calculating the EMI effects produced by wind farms [36, 311]. Most approaches assume that signal scattering is the most important source of EMI from WTs [36, 312], among the factors described in Section 2.2.3. The common procedure to determine the overall EMI effects is to calculate all the possible attenuations of original signal and compare the resultant signal with the original signal. The amplitude of a useful electromagnetic signal reaching a receiver (\(C_{S}\)) can be approximated using Equation (43):  
\[C_{S}=P_{\mathrm{T}}-A_{\mathrm{TR}}+G_{\mathrm{TR}} \tag{43}\]  
where \(P_{\mathrm{T}}\) [dB] is the transmitter power, \(A_{\mathrm{TR}}\) [dB] is the attenuation between the transmitter and receiver, and \(G_{\mathrm{TR}}\) [dB] is the receiver antenna gain in the direction of transmitted signal. A WT interfering signal, (\(I_{S}\)) can be calculated using Equation (44):  
\[I_{S}=P_{\mathrm{T}}-A_{\mathrm{TW}}+10\log_{10}\left(\frac{4\pi\sigma_{S}}{ \lambda^{2}}\right)-A_{\mathrm{WR}}+G_{\mathrm{WR}} \tag{44}\]  
where \(A_{\mathrm{TW}}\) [dB] is the attenuation between the transmitter and the WT, \(A_{\mathrm{WR}}\) [dB] is the attenuation between the WT and the receiver, \(G_{\mathrm{WR}}\) [dB] is the receiver antenna signal gain in the direction of the reflected signal, \(10\log_{10}(4\pi\sigma_{S}/\lambda^{2})\) [dB] is the contribution to the signal scattering by the WT, \(\sigma_{S}\) [m\({}^{2}\)] is commonly known as the radar cross section (and can be considered a function of the WT geometry, WT dielectric properties and the incident signal wave length) and \(\lambda\) [m] is the signal wavelength. The difference between the useful and the interfering signals is:  
\[C_{S}-I_{S}=A_{\rm TW}-10\log_{10}\left(\frac{4\pi\sigma_{S}}{\lambda^{2}} \right)+A_{\rm WR}-A_{\rm TR}+G_{\rm TR}-G_{\rm WR} \tag{45}\]  
If a forward scattering case is considered, where a WT is between transmitters and receivers, and if the distance between the transmitter and receiver (\(d_{\rm TR}\)) is much larger than the distance between the WT and the receiver (\(d_{\rm WR}\)) then \(A_{\rm TW}\approx A_{\rm TR}\). Furthermore, the free space loss is commonly approximated as \(A_{\rm WR}=20\log_{10}(4\pi d_{\rm WR}/\lambda)\), resulting in:  
\[C_{S}-I_{S}=10\log_{10}(4\pi)+20\log_{10}(d_{\rm WR})-10\log_{10}(\sigma_{S})+ G_{\rm TR}-G_{\rm WR} \tag{46}\]  
Equation (46) suggests that the difference between the useful signal and the interference signal may be improved by: (1) increasing the distance between WT and receivers; (2) reducing the radar cross section (\(\sigma_{S}\)); (3) enhancing the signal gain between the transmitter and the receiver; and (4) reducing the signal gain between the WT and the receiver. Some of the suggested improvements, however, have strong impacts in the WT energy conversion (e.g., separating WT from key locations) and induce the need to spend more capital costs for mitigation (e.g., by incorporating amplifiers, re-transmitters or additional transmitting antennas). Equation (46) can be rearranged to define a forbidden zone, in terms of the distance \(Fz\), within which a WT may not be located if an adequate interference level (\(I_{S,Req}\)) is to be maintained:  
\[Fz=20\log_{10}(d_{\rm TR})=\left(C_{S}-I_{S,Req}\right)+10\log_{10}(\sigma_{S} )-G_{\rm TR}+G_{\rm WR}-11 \tag{47}\]  
The term \(Fz\) is highly dependent of the radar cross section (\(\sigma_{S}\)), which, unfortunately, is not easy to calculate and is dependent on the direction the signal is transmitted. Different approaches in literature have suggested how to calculate \(\sigma_{S}\)[36, 129, 312, 313, 314], where the method of moments is applied to calculate the EMI contributions of both the WT tower and the WT rotor, assumed to be composed of perfect electric conductor materials (which, however, is not the case in practice).