Development of three-dimensional wind turbine wake models and offshore wind farm layout optimization strategies

Abstract

Wind energy plays an increasing important role in substituting fossil fuels and solving environmental issues all around world. Wake effect is a common problem in all wind farms, which decreases energy output as well as causes structural damages to wind turbines. If the knowledge of wake effect is well acknowledged, it will be helpful to improve the benefit of wind farms by optimizing layouts of wind turbines to avoid severe deficits and turbulences caused by upstream wind turbines. Therefore, this research project focuses on the investigations of three-dimensional (3-D) wind turbine wake models and new optimization strategies of wind farm layout. Novel 3-D wake models have been developed to describe the wake distribution in spatial, wind farm experiments have been conducted to study the characteristics of wakes and validate wake models, and new layout optimization strategies have been come up with to capture more wind energy and save the cost of offshore wind farms. The output of this project contributes to predicting the wake effect and improving the energy generation of wind farms. Firstly, the novel 3-D wake models have been developed. To solve the wind farm optimization problems spatially, an original analytical 3-D wind turbine wake model for a single wind turbine has been developed and validated. The newly presented 3-D wake model considers the wind variation in the vertical direction, therefore it is more accurate and closer to reality. The wake model is based on the flow flux conservation law and it assumes that the wind deficit downstream of a wind turbine is Gaussian-shaped. The wake model has been validated by the published wind tunnel measurement data. The adopted horizontal wake profiles were obtained from Marchwood Engineering Laboratory's atmospheric boundary-layer wind tunnel and were published by Schlez, Tindal, and Quarton (2003). The adopted vertical wake profile data were obtained from the atmospheric boundary-layer wind tunnel at St. Anthony Falls Laboratory and were published by Y.-T. Wu and Porte-Agel (2011). The relative errors are mostly within 5% in the horizontal profile validation and within 3% in the vertical profile validation. Based on the wake model, a series of wind prediction results have been demonstrated. For further consideration of the 3-D problems of wind farm optimization, the average wind speed of a single wind turbine has been investigated considering the influence of vertical wind distribution, and the 3-D wake model for multiple wind turbines have been developed. For one wind turbine, assuming the incoming wind is distributed as power law in the vertical direction, the average wind speed has a close relationship to the power exponent α, hub height h0 and rotor radius r0. When α = 0.4 , the average wind speed can decrease to 96% of the speed at the hub height, therefore, the wind variation in vertical direction should not be ignored. Then, the 3-D wake model for multiple wind turbines has been developed based on the wake model for single wind turbine. The method of Sum of Squares has been adopted to consider the wake adding principle. The wind tunnel data of two layouts have been used to validate the model. The experimental data come from the wind tunnel in the Saint Anthony Falls Laboratory at the University of Minnesota (L. P. Chamorro & Porte-Agel, 2011). For the first layout, most of the relative errors at the hub and the top heights are smaller than 6%. For the second layout, the largest errors are 8.5% at the top height, 17.8% at the bottom height and 21.2% at the hub height. The results predicted by the wake model for multiple wind turbines have also been presented. Secondly, the experimental study of wake effect and validations of wake models have been carried out by wind field measurements. An overview of available full-scale wind field measurements for investigating wake effect has been conducted. Typical measurements about wake effect in onshore wind farms, offshore wind farms and isolated wake effect have been studied. Information about the site, equipment and process of each experiment have been described in details. Significant results and experience from experiments are discussed. Thevalidations for wake models are the main purposes of some experiments, which have also been demonstrated. Our wind field measurements have been conducted for validating the developed wake models, which were conducted in a complex-terrain wind farm in northern China. The experiment of an upstream-and-downstream arrangement has been made to investigate how wakes of the upstream turbines affect the downstream turbines. It is observed that the range of the wake-influenced area expands, whereas the largest wind speed deficit decreases gradually in the downwind direction. Meanwhile, the wake centerlines of upstream and downstream wind turbines could be different. Another experiment of the side-by-side arrangement was also made to investigate how wake interactions distribute downwind of a row of wind turbines. It has been found that huge deficits of wind speed exist in all analyzing lines behind the wind turbines. The wind speeds reduced to as small as 2.8 m/s at 1D downwind position in Line 2. Fluctuations were observed in the far-wake zone. The range of the wake-influenced area was not easy to be identified in the far-wake zone, and the wakes of two adjacent turbines demonstrated a complicated interaction. The presented 3-D wake models have been validated by the on-site measured wind data. In the vertical direction, the wake model for a single wind turbine can predict the wind speeds with an acceptable accuracy, especially at positions beyond 10D downstream distance or over 100 m height. Because of the complex terrain, some large errors happened at positions less than 40 m height, and wind speeds in two symmetrical side sections showed different distributions at the same downwind positions. Whereas in the horizontal direction, the wake model for multiple wind turbines also has a reliable accuracy at the far wake positions and near the inflow measuring site, only except that wake model could not predict the wind deficits before an operating wind turbine, and it was not accurate enough in some particular complex-terrain positions. Suggestions have been given to improve the wake models in the future. Thirdly, for practical use of the proposed wind wake models, a new repowering strategy and a directional restriction method have been proposed to better optimize offshore wind farm layouts. In the repowering optimization strategy, the service time of the wind turbine foundation is extended to two generations' service time. The costs of removing the first-generation foundations and installing the second-generation foundations can be saved. With the layout optimization method, the wind loss caused by wake effect can decrease. Both aligned and optimized layouts are analyzed, and a case study (an offshore wind farm with the size of 3,740 m × 5,828 m) in Waglan Island seawater area in Hong Kong has been discussed as well. This offshore wind farm (the number of 4.2 MW wind turbine is 54) can generate 2.15 x 104 GWh electricity in 20 years. If the repowering strategy is applied, by reusing the wind turbine foundations and replacing the original wind turbines with the optimized wind turbine combination, the LCoE is expected to reduce by nearly 16.63% and to only 1.0310 HK$/kWh. An original directional spacing restriction method, Directional Restriction, has been presented to restrict the spacing between wind turbines. The new method considers the influence of wind directions, and the restriction for each wind turbine is related to its rotor diameter. With the Directional Restriction, a wind farm optimization process applying the Multi-Population Genetic Algorithm (MPGA) has been developed. Four representative cases are then studied and discussed. Through these cases, the utilization rate of a non-uniform wind farm with five types of wind turbines can increase to 99.21%, and the minimum utilization rate of a single wind turbine is 94.27%. A potential offshore wind farm in Sha Chau Island in Hong Kong is then analyzed. The results demonstrate that the proposed optimization method is practical in engineering design of local wind farms. In summary, this project has developed the novel 3-D analytical wind turbine wake models, carried out wind filed measurements and proposed two novel strategies for offshore wind farm optimization problems. The wake models can help to investigate the distributions and characteristics of wakes. The presented strategies combined with the optimization process can exploit the wind resource effectively and can be used to optimize the layout of non-uniform wind farms. It is expected that the work from this thesis can help develop wind power generation in Hong Kong, mainland China and in the world.