###### Abstract  
The construction and gradual installation of turbines on wind farms has been hindered by the high cost of the energy production. An effective way to minimize energy costs is via the optimal design of wind turbines and their layout, but relevant and synthetic studies are lacking. This paper proposes a method to minimize the energy cost of offshore wind farms by simultaneously optimizing the rated wind speed, the rotor radius of wind turbines and their layout. Firstly, a new, mixed mathematical formulation of the energy cost is presented, considering the Weibull distribution for wind, the characterizing parameters of wind turbines and the distance between two turbines. Secondly, to obtain the minimum energy cost, a composite optimization algorithm was developed, which consists of an iterative method and an improved particle swarm optimization algorithm. The former was used to search the minimal energy costs that relate to the design parameters of a single wind turbine, while the latter was adopted for optimizing the layout of the wind turbines iteratively. Finally, the proposed method was applied to three case studies with variable wind speed and constant wind direction. Results of the case studies show that the reduced energy cost after optimization has a range of 0-0.001 $/kWh, which confirms the effectiveness of the proposed approach. Meanwhile, the layout of the wind turbines after optimization tends to locate the two wind turbines with the biggest spacing in the wind direction, which justifies the utilization of layout optimization. Furthermore, exploring the optimally designed parameters of wind turbines revealed that the wind farms with a high mean wind speed can have a wider range of turbine capacity than those with a low wind speed, which offers more freedom for the designers when constructing offshore wind farms at wind sites with rich wind resources. Keywords:offshore wind farm; cost of energy; layout; optimal design; particle swarm optimization +
Footnote †: journal: Applied Soft  
As the COE of the whole offshore wind farm is relevant to the total annual cost and the annual energy production (AEP), the COE is optimized by considering two aspects: reducing the production cost and increasing the AEP. Considering the design of the offshore wind farm, the approaches to optimize the COE can be categorized into main two types: wind farm layout optimization (WFLO) and wind turbine design optimization (WTDO). The WFLO aims to study the optimal layout of wind turbines on a certain wind farm, so that the maximum AEP and the minimum cost can be realized. Much existing research revealed that the WFLO has a significant impact on the performance of the offshore wind farm and the total produced energy when using a specific kind of wind turbine. In these studies, WFLO is achieved by considering two main factors: the wake effect and the optimization algorithm. The wake effect has a great influence on the AEP. Wakes from upstream turbines can severely affect the performance of downwind turbines, and the wake losses typically reduce the power generated by 10-20% compared with the undisturbed turbines [2]. In order to describe the complex, non-linear phenomena, many wake loss models have been developed describing the real flow field with relative accuracy. So far, the existing wake loss models can be categorized as Jensen models [3], Larsen models [4], Frandsen models [5], Gaussian models [6] and corresponding extended wake loss models. Among these wake loss models, the Jensen model has been widely applied to describe the turbine wake, for it is a simple model and needs less computational resources. On the other hand, the optimal algorithm is necessary to find the optimal number and location of wind turbines. Many non-conventional algorithms have been applied to extract maximum energy output corresponding to the optimization layout with regard to wind energy exploitation.