1. Introduction
Renewable energy has been very attractive since the end of last century, as there have been ever-growing concerns over limited fossil-fuel resources, serious environmental regulations, and heavy energy demand. Among various types of renewable energy, wind energy is one of the most economical sources. The wind energy development has been rapidly developed in recent years. In 2017, the global cumulative installed wind turbine capacity has reached a new peak value of 539.58 GW [
1]. On the other side, there is a new trend for the development of wind energy, that is, the installation of wind turbines has gone from onshore sites to offshore sites [
2]. Despite the rapid growth of wind energy utilization, the challenge still exists, especially for the offshore-site turbines. The high cost of energy (COE) for offshore wind power (compared to the onshore wind power and traditional sources) has hindered the utilization of offshore wind energy across the world.
As the turbine COE is relevant to the total annual cost and the annual energy production (AEP) [
3], optimizing COE reduces the production cost and increases the production efficiency. Considering the overall procedure of the wind turbine development, the potential approaches for minimizing COE can be accordingly categorized into three types: design optimization, manufacturing process optimization, and on-site optimization. Since the manufacturing procedure depends on the manufacture technology which is normally scheduled during a certain period, its optimization is hard to employ in practice. By comparison, the on-site optimization is utilized as a common practice in the wind energy industry [
4]. The on-site optimization is to optimize the turbine controller and its parameters matching the wind characteristics, so the AEP is enhanced by optimizing the energy capture efficiency below rated wind speeds. Two types of approaches are available for the on-site optimization. One approach is to control the rotor speed to follow the changing wind speed, so that the known principle of the optimal tip speed ratio tracking can be fulfilled [
5]. To do this, the advanced wind estimator-based torque controller has been utilized by industrial turbines [
6,
7,
8], and the Lidar-based previewer controllers have gradually been payed attention to [
9]. Meanwhile, some researchers have proposed to optimize the performance by adjusting the controller parameter according to the wind condition [
10], as it has been revealed that the controller performance is significantly affected by the wind conditions [
11,
12]. Furthermore, the energy production efficiency can be improved by considering a hybrid wind-hydro power plant for the isolated power system [
13,
14]. The other approach of improving the energy capture efficiency is to control the yaw system to track the wind direction, so that the yaw error can be minimized. In some recent studies, the previewed yaw controller and its parameter optimizations have been proposed, which have been proven to be efficient in enhancing the energy capture efficiency [
15,
16]. Despite these on-site optimizations being cost-effective and convenient to carry out, the achieved profit is quite limited as the energy capture efficiency is only improved in some control regions.
Many efforts have been made towards improving the performance of the wind turbines through design optimization. A comprehensive review of wind turbine optimization technologies is given in [
17], in which a few of works have been referred for wind turbines towards minimizing the COE by optimizing the aerodynamics shape of airfoils. As a key wind turbine component, the blade is a determining factor for energy harvesting efficiency and its aerodynamic shape optimization is very momentous. The aerodynamic shape optimization involves many objectives, such as the AEP, the air loads of the blades and rotors, and the blade mass. Improving one objective inevitably deteriorates the others, and thus the aerodynamic shape optimization widely uses multi-objective functions. A numerical optimization method for the design of horizontal axis wind turbines is presented in [
18], in which the fatigue and extreme loads and the AEP are considered. A multi-objective optimization method is proposed for the turbine blade using the lifting surface method as the performance prediction model [
19]. The first study on the external axis wind turbines is conducted to optimize blade count and operating point to simultaneously maximize power, while minimizing power fluctuating and the peak point reaching time [
20]. When these researches optimize the aerodynamic shape, most of them only concerned with the open-loop static aerodynamic performance, that is, the AEP is calculated under the implicit assumption that the turbines can keep operating at the optimal TSR. But in practice, the large-scale wind turbines cannot instantly respond to the wind fluctuation and the performance is influenced by the wind conditions [
21]. In this regard, the closed-loop optimal design should be considered, which has been presented in a recent study [
22]. Nevertheless, the blade aerodynamic optimization is a small portion of the turbine design, and the optimal design involving the most important parameters of the overall design may achieve a low COE in an effective way.
As the first step of design process of wind turbines, the conception design defines the most important parameters, of which the optimizations have been proven to be highly efficient in minimizing the COE [
23,
24,
25,
26,
27]. The dominant ingredient of designing a satisfactory turbine with low COE includes the suitable physical and operational parameters, which are determined by the wind conditions on the erected site of the turbines, but there have been very few studies conducted. An optimization method is presented for the concept design of a grid-connected onshore wind turbine, in which the blade number, rotor diameter, tower height, rotor rotational speed, the rated wind speed, and the rated power have been optimized to match the wind condition described by the Weibull parameters [
28]. Based on the case study results, it has been shown that some of the existing onshore turbines appear to be well designed, and others do not. An iterative approach is presented to optimize the turbine design based on a simple COE model, which is a function of rotor diameter, tower height, rated power, and the TSR. In their results, it is revealed that the onshore turbines about 1–2 MW can achieve minimum COE for considered cases [
29]. Another design study is conducted on onshore turbines, in which the COE model is described relevant to rotor diameter, hub height, capacity factor, rated power, and rotor diameter [
30]. Recently, a mathematical approach is proposed to minimize the COE of onshore turbines, in which the COE model is expressed as a function of rated power and rated wind speed [
31]. When compared with the referenced turbines, a noticeable profitability has been gained by the optimized turbines. The above references have shown that the site-specific turbine design can achieve a low COE for onshore turbines, but the studies for the offshore wind turbines are lacking.
Currently, the offshore wind turbines are designed towards the large-size trend, but whether the offshore turbines with large capacity and long blades will have a low COE remains unclear. This paper aims at clarifying this issue. For this purpose, the relation among the COE, the rated wind speed, and the rotor radius is established, a method to achieving optimal COE of the offshore turbines is proposed, and the optimal results are obtained and analyzed. Since the cost model is important to determine the COE results, the detail cost model of the bottom-fixed offshore wind turbines developed by NREL is employed in this study [
32]. By comparison to the literature, the contribution of this study is twofold: on one hand, a method to minimizing the COE of offshore turbines through optimizing the rated wind speed and rotor radius is proposed, which can be extended to other types of wind turbines; on the other hand, the optimal design parameters achieving the minimal COE of offshore wind turbines are obtained and explored under different wind conditions, which can be used as references for offshore wind turbine designers. The remaining sections are organized as follows: the design process of wind turbines is summarized in
Section 2. The COE model of onshore turbines is discussed in
Section 3, and
Section 4 presents the method of optimizing COE by selecting the optimal rated wind speed and rotor radius, and the optimal results through the case studies. Finally,
Section 5 concludes the study.