## 2 Proposed Energy Cost Model for Offshore Wind Farms
### Annual Production Cost  
On the offshore wind farm, two types of support platforms were applied, namely, the bottom-fixed platform and floating platform. Usually, the bottom-fixed platform is installed when the offshore wind farm is near the coastline, namely, the shallow-water sea, while the floating platform is employed on sites far from the coastline or beyond, namely, the deep-water sea. As the cost is a key factor in determining the COE, the detailed cost model of the bottom-fixed offshore wind turbine developed by the National Renewable Energy Laboratory (NREL) was utilized and is expressed as [25]:  
\[Cost_{i}=FCR\times ICC_{i}+AOE_{i}, \tag{2}\]  
where \(Cost_{i}\) is the total cost of turbine \(i\), \(ICC_{i}\) is the initial capital cost, and \(AOE_{i}\) is the annual operating expense. \(FCR\) is the fixed charge rate, which is set to 0.1158 per year [25].  
In the NREL cost model, the cost data of turbine components was available for different years. For the purpose of consistency, all cost data were converted to 2002 dollars before the cost and scaling factors were developed. \(ICC_{i}\) consists of the turbine system cost and the support platform station cost. The detailed costs are listed below.  
(1) The turbine system cost.  
The turbine system is divided into four main subsystems, the mechanical system (such as blade, gearbox and so on), electrical system (including generator, power converter and electrical connection), control system (safety system, yaw control, torque control and pitch control), and auxiliary system, such as hydraulic cooling equipment, hub and tower. Since the number of blades is three, the turbine system cost, \(ICC_{turb}\), is given by:  
\[\begin{array}{ll}ICC_{turb}&=209.526P_{r}+16.45P_{r}^{1.249}+206.69R+11.9174( 2R)^{1.953}-0.01069(2R)^{2.5}+11.4354R^{2.5025}\\ &+2.00617R^{2.53}+0.48017(2R)^{2.6578}+0.01(2R)^{2.887}+0.0678(2R)^{2.964}+1.6 7458R^{3}\\ &+0.00432(2R)^{3.5}+0.59595\pi R^{2}H+73990.5\end{array} \tag{3}\]  
According to Equation (3), the value of \(ICC_{turb}\) is determined by the parameters of the wind turbine corresponding to the rated power, rotor radius and hub height. So \(ICC_{turb}\) can be expressed as a function of \(P_{r}\), \(R\) and \(H\), namely, \(ICC_{turb}=f_{1}(P_{r},R,H)\).  
(2) The support platform station cost.  
The \(ICC_{BoP}\) involves the cost of infrastructure and offshore engineering, and the detailed mathematical models are shown in Reference [25]. According to the report of NREL, the \(ICC_{BoP}\) can be summarized as  
\[ICC_{BoP}=0.311325 ICC_{turb}+755.402P_{r}+1.62843\times 10^{-5}P_{r}^{3}-0.038625P _{r}^{2}+56.341P_{r}+58710 \tag{4}\]  
From Equation (4), the \(ICC_{BoP}\) is determined by the turbine system cost and rated power, and \(ICC_{BoP}\) can be expressed as \(ICC_{BoP}=0.311325f_{1}(P_{r},R,H)+f_{2}(P_{r})\).  
(3) The annual operating expense.  
The annual operating expense \(AOE\) consists of the land lease, levelized operation and maintenance (OM), and the levelized replacement costs. Its mathematical formula is  
\[AOE_{i}=17P_{r}+0.02108 AEP_{i} \tag{5}\]  
According to Equation (5), the \(AOE_{i}\) is determined by the rated power and the annual energy production. So, referring to Equations (2)-(5), the wind turbine \(i\) cost can be expressed as  
\[Cost_{i}=f_{costi}(P_{r},R,H,AEP)=0.151851435f_{1}(P_{r},R,H)+0.1158f_{2}(P_{r} )+17P_{r}+0.02108 AEP_{i} \tag{6}\]  
In the above equation, Equation (6), \(Cost_{i}\) was estimated based on the empirical model, which is related to the rated power, rotor radius, tower height, and AEP of the wind turbine \(i\). Since the AEP of the wind farm is determined by the parameters and layout of wind turbines, it is possible to minimize the cost of the wind farm by designing the appropriate wind turbine parameters and their layout.