## 3 Relevant Research in Wind Farm Design and Optimization
### Financial Balance (FB)  
The most comprehensive FB model, shown in Equations (13) and (81), was provided by [PERSON] [279], which considers only relevant cost to the WFDO problem in a relative basis (_i.e._, fixed costs such as the price of WT, costs of planning and projecting, cost of the land, _etc._ are not taken into account since it is assumed that they don't influence the global optimum during the WFDO process):  
\[\text{FB}=WP-C_{\text{D}}-C_{\text{M}}-C_{\text{O}}-C\left(1+\frac{r_{\text{c 1}}-r_{\text{i}}}{n_{L}}\right)^{rn_{L}}-p_{sf}C\left(1+\frac{r_{\text{c2}}-r_{ \text{i}}}{n_{a}}\right)^{rn_{a}} \tag{81}\]  
where \(WP\) is the sales revenue of the expected electrical energy conversion over the wind farm operational lifetime (\(T\) [y]), \(C_{\text{D}}\) is the accumulated cost of components degradation, \(C_{\text{M}}\) is the cost of overall maintenance. \(C_{\text{O}}=p_{\text{t}}WP+p_{\text{lp}}WP\) is the cost of taxes and land payments, which are assumed proportional to the sales revenue. \(p_{\text{t}}\) and \(p_{\text{lp}}\) are the rate of taxation and rate of the land payment respectively. \(r_{\text{c1}}\) [%] is the interest rate that the wind farm consortium has to pay for loans (_i.e._, price of money in banks or by other investors), \(r_{\text{c2}}\) [%] is the investment rate (_i.e._, the interest rate that the consortium can obtain if investing their money alternatively in financial instruments/projects with identical risk profile compared to the wind farm), \(r_{\text{i}}\) [%] is the inflation rate, \(n_{L}\) is the number of times interests of loans has to be paid in a year, \(n_{a}\) is the number of times additional potential revenues from alternative investments are to be received in a year. \(p_{sf}\) describes the split of the total (variable) investment on consortium loans and consortium financial assets and is defined as the ratio between the consortium financial assets and \(C\). If no secondary investments are to be made, and no taxes and land payments are to be considered (e.g., offshore wind farms), Equation (81) can be simplified to Equation (13) as proposed by [PERSON] _et al._[166]. The variable part of the total wind farm investment costs (\(C\)) is expressed in Equation (82):  
\[C=C_{\text{F}}+C_{\text{I}}+C_{\text{T}}+C_{\text{E}} \tag{82}\]  
where \(C_{\text{F}}=\sum_{l=1}^{l}n_{l}CT_{i}\) is the total cost of foundations and \(n_{i}\) is the number of WTs erected on locations having foundation costs \(CT_{i}\). \(C_{\text{I}}=\sum_{j=1}^{l}n_{j}C_{l,j}\) is the total cost of WT installation, and \(n_{j}\) is the number of WTs having installation costs \(C_{l,j}\). \(C_{\text{T}}=\sum_{k=1}^{K}n_{k}CT_{k}\) is the total cost of civil engineering infrastructure, and \(n_{k}\) is the total length of the road having construction cost \(CT_{k}\). \(C_{\text{E}}=\sum_{l=1}^{L}n_{l}CC_{l}+\sum_{m=1}^{M}n_{m}CP_{m}\) is the total cost of electrical infrastructure (excluding transformer costs and the costs of connecting the wind farm with the main electrical grid, since these costs are considered independent of the wind farm topology). For the electrical infrastructure costs, two classes of grid elements are defined; one associated with cabling and the other associated with an overhead pole setup. \(n_{l}\) is the total length of the power grid having a cost per meter \(CC_{l}\) (including cables, trenching and laying of these, _etc._), and \(n_{m}\) is the total electrical elements with associated cost \(CP_{m}\) (including the price of overhead poles, the erection of these, cables, _etc._). Fatigue degradation is a stochastic process driven by stochastic loading of the WTs and is modeled as a linear process. For a WT structural member \(S\), the mean cost of fatigue load degradation is assumed to be proportional to the mean accumulated equivalent fatigue load, associated with a suitable component hot spot, caused by turbine operation during the lifetime of the wind farm.