## 3 Relevant Research in Wind Farm Design and Optimization
### Electromagnetic Interference (EMI)
#### 3.2.6 Economic Modeling of Wind Farms
The O&M cost was considered constant over the wind farm operational time and calculated as a percentage of the initial capital cost (\(C_{\rm Inv}=C_{\rm RNA}+C_{\rm SS}+C_{\rm Elect}+C_{\rm Decom}\)). Net Present Value (NPV)  
The most comprehensive NPV model was defined by [PERSON] [56] and [PERSON] _et al._[135, 278, 310]. The model considers that wind farms require initial investments or capital costs (\(I_{\rm WF}\)[S], which represent the WT acquisition and infrastructure costs) to operate. Once in operation, the wind farm delivers a stream of both financial benefit, which represent the sales revenue of the energy, and O&M costs during its expected operational lifetime (\(LT\)[y]) from which net cash flows \(N_{K}\) of the \(k\)th year, representing the net income (energy sale minus O&M costs), are obtained. At the end of the operational lifetime of the wind farm additional present value expenses arise for the installation decommissioning (\(C_{\rm D}\)[S]), and an additional income might come from present residual values (\(V_{\rm R}\)[S]) as shown in Equations (14) and (73):  
\[{\rm NPV}(x_{\rm F})=-I_{\rm WF}(x_{\rm F})-C_{\rm D}(x_{\rm F})+V_{\rm R}(x_{ \rm F})+\sum\
olimits_{k=1}^{LT}\frac{N_{k}(x_{\rm F})}{(1+r)^{k}} \tag{73}\]  
where \(x_{\rm F}\) is a wind farm configuration, and \(r\) is the equivalent discount rate or real interest rate (annual depreciation of money), which can be calculated using the Fisher equation, which accounts for the nominal interest rate (\(i\)) and the expected inflation rate (\(p\)), shown in Equation (74):  
\[r=\frac{1+i}{1+p}\cong i-p \tag{74}\]  
The previous model was extended by [PERSON] _et al._[278] in order to include both the energy price and the O&M costs evolution in time. In addition, the costs of civil engineering and electric infrastructure as well as the energy losses were taken into account during the NPV calculation as shown next:  
\[ \begin{split}{\rm NPV}(x_{\rm F})=-I_{\rm WT}-I_{\rm CW}(x_{\rm F })-I_{\rm EI}(x_{\rm F})-C_{\rm D}(x_{\rm F})+V_{\rm R}(x_{\rm F})\\ +\sum\
olimits_{k=1}^{LT}\frac{\left(E_{\rm G}(x_{\rm F})-E_{\rm EI }(x_{\rm F})\right)k_{\rm AV}p_{\rm kWh}(1+\Delta p_{\rm kWh})^{k+1}-C_{0 \rm B,M}(x_{\rm F})(1+\Delta C_{0\rm B,M})^{k+1}}{(1+r)^{k}}\end{split}  \tag{75}\]where \(I_{\text{WT}}\)[S] is the initial investment for the acquisition of WTs, \(I_{\text{CW}}\)[S] is the civil infrastructure cost, \(I_{\text{EI}}\)[S] is the electrical infrastructure cost, \(E_{\text{G}}\)[kWh] is the gross converted energy, \(E_{\text{EL}}\)[kWh] is the energy losses in the electric system, \(p_{\text{kWh}}\)[S/kWh] is the energy sale price, \(k_{\text{AV}}\) is the availability factor [%], \(\Delta p_{\text{kWh}}\)[%] is the annual increase of the wholesale price of energy, \(C_{0\&M}\)[S] is the cost of operation and maintenance, and \(\Delta C_{0\&M}\)[%] is the annual increase of \(C_{0\&M}\). The civil engineering infrastructure cost (\(I_{\text{CW}}\)) is composed of the WT foundations costs and costs derived from the construction of auxiliary roads, which are assumed proportional to the total length of the auxiliary road. The foundation costs are modeled considering the bearing capacity of the land. The electrical infrastructure of the wind farm has three main components: the internal MVAC collection network, substations, and the HVAC transmission lines. Given a certain electrical configuration \(y(x_{F})\), the total present cost of the execution and commissioning of the electrical infrastructure can be calculated using Equation (76):  
\[\text{NPV}\big{(}y(x_{\text{F}})\big{)}=-I_{\text{E}}\big{(}y(x_{\text{F}}) \big{)}-\frac{\sum_{k=1}^{LT}C_{\text{EL},k}\big{(}y(x_{\text{F}})\big{)}}{(1+ r)^{k}} \tag{76}\]  
where \(I_{\text{E}}\)[S] is an initial capital investment. The electrical infrastructure generates running costs related to electrical losses (\(C_{\text{EL},k}\)[S]), which are modeled as simple Joule-based power losses, depending on the power line's resistance and the amount of current flowing through the conductor.