## 3 Relevant Research in Wind Farm Design and Optimization
### Electromagnetic Interference (EMI)
#### 3.2.6 Economic Modeling of Wind Farms
The cost of gravity bases is given by:  
\[C_{\rm GB}=m_{\rm GB}\ cc_{\rm concrete}\ (1+cl_{\rm GB}) \tag{63}\]  
where \(m_{\rm GB}\) [kg] is the mass of the gravity base, which is obtained based on an iterative procedure, which includes the soil bearing capacity, maximum horizontal forces (created by wind and wave loads), buoyant forces and downward forces [55]. \(cc_{\rm concrete}\) [S/kg] is the price of the material used to manufacture the gravity base (e.g., reinforced concrete), and \(cl_{\rm GB}\) is the labor factor including the cost of installation. The cost of monopile bases is:  
\[C_{\rm pile}=m_{\rm pile}\ cc_{\rm steel}\ (1+cl_{\rm MP}) \tag{64}\]  
\[m_{\rm pile}=\rho_{\rm steel}\ L_{\rm pile}\frac{\pi}{4}\left[D_{\rm pile}^{2} -\left(D_{\rm pole}-2t_{\rm wall}\right)\right] \tag{65}\]  
where \(m_{\rm pile}\) [kg] is the mass of the monopile, which depend on the density of the material used (\(\rho_{\rm steel}\) [kg/m\({}^{3}\)]), the diameter of the monopile (\(D_{\rm pile}\) [m]), the thickness of the monopile wall (\(t_{\rm wall}=0.011\)\(D_{\rm pile}\) [m]) and the length of the pile (\(L_{\rm pile}\) [m]), which depend on the expected axial and lateral loads [55]. \(cc_{\rm steel}\) [S/kg] is the price of the material used to manufacture the monopile (e.g., steel), and \(cl_{\rm MP}\approx 1.8\) is the labor factor including the cost of installation. The cost of tripod bases is:  
\[C_{\rm tripod}=m_{\rm tripod}\ cc_{\rm steel}\left(1+cl_{\rm tripod}\right)+3C _{\rm pile} \tag{66}\]  
where \(m_{\rm tripod}\) [kg] is the mass of the tripod, which depends on the expected loads, and \(cl_{\rm tripod}\approx 1.5\) is the labor factor including the cost of installation. The electrical interconnection cost model is decomposed in two separated models; the first model quantifies the costs of collection power lines (MVAC), and the second model quantifies the costs of transmission power lines (HVAC). The MVAC collection system cost (\(C_{\rm MVAC}\) [S]) is a function of the total cable length (\(L_{\rm MVAC}\) [m]) and the rated voltage (\(V_{\rm MAC}\) [V]) as shown in Equation (67):  
\[C_{\rm MVAC}=L_{\rm MVAC}(a_{1}V_{\rm MAC}+b_{1}) \tag{67}\]  
where \(a_{1}=0.0105\) and \(b_{1}=95\). The HVAC collection system cost (\(C_{\rm HVAC}\) [S]) depends on the wind farm power (\(P_{F}\) [W]), the cable voltage (\(V_{\rm HAC}\) [V]) and the cable length (\(L_{\rm HVAC}\) [m]). The number of cables required to transmit the wind farm power is estimated using Equation (68):  
\[N_{\rm cable}={\rm ceil}(6.03\times 10^{-4}\ P_{F}/V_{\rm HAC}+0.464) \tag{68}\]  
where ceil is a function that rounds its argument towards infinity. The cost of the switch gear (\(C_{\rm switch}\) [S]), and the transformer (\(C_{\rm xfrm}\) [S]), used to rise the voltage of the collection network, is given in Equations (69) and (70):  
\[C_{\rm switch}=0.668\ V_{\rm HAC}+36{,}000 \tag{69}\]\[C_{\rm xfrm}=1.035P_{F}^{0.751} \tag{70}\]  
The cost of the HVAC transmission system is given in Equation (71):  
\[C_{\rm tower}=1.5\ m_{\rm tower}=1.5\ \left(c_{\rm tower}\ D^{2.8}\left(\frac{Z_{\rm H }}{D}\right)^{1.7}\left(\frac{P_{\rm rated}}{A}\right)^{0.6}\right) \tag{62}\]0  
where the price per unit length of the cable itself is \(cc_{\rm cable}=0.00168\,V_{\rm HAC}+1280\,\) and \(cc_{\rm laying}=100\,\). The decommissioning cost model depend on the type of foundation and can be expressed in terms of cost per WT or cost per MW installed, as shown in Equation (72):  
\[C_{\rm decom}=\left\{ \begin{array}{l}(cc_{\rm WT}N_{\rm WT})(1+cc_{\rm cable })\\ (P_{F}cc_{\rm MW})(1+cc_{\rm cable})\end{array} \right. \tag{72}\]  
where \(cc_{\rm WT}=200,000\)[S] is the decommission cost for each WT in the wind farm, \(cc_{\rm MW}=55,000\)[S] is the cost for decommission per MW installed, and \(cc_{\rm cable}=12\)[S] is the cost of decommissioning of power lines (_i.e._, for both collection lines and transmission lines).