Horns Rev Research Articles

Wind Turbine Wake Regulation Method Coupling Actuator Model and Engineering Wake Model

The wake effect is one of the main factors affecting the power generation of wind farms. Wake regulation is often used to reduce the wake interference between wind turbines. Accurate assessment of the wake flow of wind turbine is essential to wake regulation. Engineering wake models are widely used for rapid evaluation of the wake at present due to lower computational resource cost. However, the selection of empirical parameters of the wake model has significant influence on the prediction accuracy, especially in the case of yaw. The actuator model based on CFD simulation has less dependence on empirical parameters and higher simulation accuracy. However, the computational cost is too high for wake regulation for large wind farms. This paper proposed an improved wake regulation method that combines the advantages of the actuator line model (ALM) method and the engineering wake mode. The simulation results of the ALM is used to calibrate the empirical parameters of the engineering wake model. The calibrated wake model can be used to optimize the yaw angle of wind turbines during wake regulation. The accuracy of two models is compared using wind tunnel experimental data. The ALM results give better agreement to the experimental data. The Horns Rev wind farm case is used for the coupled method verification. The power generation increase using the engineering wake model is obviously greater than that of the ALM. After calibrating the wake model, the gap between the two power predictions is greatly narrowed, which proves the effectiveness of the proposed method. The proposed coupling method can be used to improve the credibility of the wake regulation with affordable computational cost.

Wind Farm Power Maximisation via Wake Steering: A Gaussian Process‐Based Yaw‐Dependent Parameter Tuning Approach

ABSTRACTMaximising the power production of wind farms is vital to meet the growing demand for wind energy and reduce its cost. Wake effects, resulting from the aerodynamic interactions between turbines in a wind farm, significantly impact farm efficiency, leading to substantial annual power losses. Wake steering, an influential control strategy, involves mitigating wake effects by strategically yaw misaligning upstream turbines to deflect their wakes. Conventional wake steering approaches typically rely on physics‐based analytical wake models with their parameters often calibrated using higher fidelity data. However, these approaches determine a fixed set of parameters prior to conducting wake steering, neglecting each parameter's dependency on yaw misalignment (i.e. the optimisation variables) exhibited throughout the optimisation process, potentially affecting its accuracy. To address this limitation, this paper introduces a novel data‐driven parameter tuning approach that integrates higher fidelity power measurements using Gaussian processes to continuously adapt parameters in lower fidelity wake models based on the current farm's yaw configuration. The effectiveness of the proposed approach is demonstrated on a wind farm and a layout corresponding to the Horns Rev wind farm, where various wind directions are investigated. The results reveal that the approach can enable a lower fidelity model to capture more complex physics, thereby improving its accuracy in wake steering optimisation, while maintaining robustness and computational efficiency. This method holds promise for real‐time control applications and can be extended to other control strategies and closed‐loop frameworks.

Wind farm power optimization using system identification

The wake effect reduces the total power production of wind farms. This paper presents a method for wind farm power optimization through wake effect reduction. The proposed method optimizes the yaw angle offsets and de-rating settings of all turbines to maximize total power generation. The optimization approach is gradient-based, with gradients at each iteration obtained through system identification using field test data, eliminating the need for physical models. In system identification, test signal design, model estimation and model validation problems are solved in a systematic manner; in the gradient-based optimization, in order to achieve fast convergence, methods for initial value and initial step-size determination, variable step-size iteration and iteration termination are developed. The method is verified using the FLORIS wind farm model developed by National Renewable Energy Laboratory (NREL), USA. The studied wind farm consists of 80 wind turbines configured similarly to the Horns Rev I offshore wind farm in Denmark. The result of the developed optimization method is highly consistent with those obtained using FLORIS's built-in optimization tool.

Integrated floating wind farm layout design and mooring system optimization to increase annual energy production

As we cluster wind turbines in wind farms to gain energy from sites with high wind speeds, wake losses occur within the wind farm. Wake loss is a term used to describe the lower energy production of a downwind turbine that is totally or partially in the wake of an upwind turbine. To decrease wake losses inside the wind farm, the wind farm’s layout is optimized. However, a variety of factors constrain the wind farm layout optimization, such as the size of the lease area relative to the number of turbines to be placed, or the shape of the lease area. Therefore, many wind farms end up with a regular grid layout, such as the Horns Rev 1 wind farm in the North Sea. The ability of a floating offshore wind turbine (FOWT) to change its position based on the wind direction and its mooring system design presents an opportunity to further decrease wake losses in floating wind farms. In this work, we integrate the design of the FOWT mooring systems with the floating wind farm layout design with the goal of increasing the farm’s annual energy production. We use the Horns Rev 1 wind farm as a case study to demonstrate our method. The results show that allowing the FOWT to relocate can decrease wake losses up to 18%. Moreover, the newly developed mooring systems are less stiff and therefore allow larger motion of the FOWT; hence, the material cost of the mooring system decreases by an estimated 17%.

Evaluating wind-farm power generation using a new direct integration of axisymmetric turbine wake

Engineering wake models enable fast calculation of wind-farm power generation including wake-turbine interactions, which is critical for annual energy yield calculations and for farm optimisation either at the design phase or during operation. The operating point of a turbine is determined based on its rotor-averaged wind speed, which is impacted by upstream wakes. The rotor-averaged deficit is typically calculated numerically by using a set of averaging points across the rotor disk, for which a Gaussian shape function is commonly evaluated. This numerical approach can have uncertainty based on the distribution of the averaging points. Also, a large number of averaging points can increase computational cost, which is detrimental for studies that rely on many individual calculations of farm power generation, e.g. layout optimisation. To avoid these drawbacks, we present a novel analytical solution to the circular-disk integration of a two-dimensional axisymmetric Gaussian function depicting upstream wakes for an arbitrary lateral offset between the rotor and the wake source. The analytical expression is compared against numerical averaging of an upstream wake, and is applied to the Horns Rev 1 wind farm showing excellent accuracy. Wind-farm layout optimisation models, especially methods based on gradient-descent optimisation, can benefit from the presented expression significantly, as this provides an analytically differentiable formulation for the rotor-averaged wind speed.

Inter-array cabling optimization in offshore wind power plants, a new reliability indicator for radial grids

The inter-array grid relates to a significant share of the investments into an offshore wind power plant (OWPP). Optimizing the cable connections regarding costs and reliability is a mathematically complex task due to the high variety of possible wind and component (wind turbine or cable) failure scenarios. This paper presents a novel mixed integer linear programming approach to support investment decisions into OWPPs by trading off cabling purchase and installation costs with power capacity risk (PCR), which is defined as a length-weighed cumulative power flow summation that reflects the consequences of cable failures. Then, quasi-random Monte Carlo simulations assess the optimized collection grids (CGs) to quantify their levelized cost of energy (LCOE). To construct relevant case studies, this work investigates the real OWPPs Ormonde, Horns Rev 1, Thanet, and London Array, which contain 30, 80, 100, and 175 wind turbines. The results reveal Pearson correlation coefficients around 0.99 between the proposed PCR and the expected energy not supplied. Furthermore, this paper’s findings indicate that minimum-cost CGs do not necessarily present the lowest LCOE.

Multi-objective layout optimization for wind farms based on non-uniformly distributed turbulence and a new three-dimensional multiple wake model

Wind farm layout optimization (WFLO) can reduce the turbulence intensity on the wind turbines while maximizing power generation. To accurately compute turbulence intensity distribution in the wind farm, we utilize the innovative three-dimensional cosine-shaped turbulence intensity (3D-COTI) model. By integrating the three-dimensional cosine-shaped linear entrainment (3DCLE) wake model previously developed by the authors, we introduce a new multiple wind turbine wake model (3DCLE-M). This model considers the wake superposition effect, enabling precise calculation of power generation. Building upon the 3D-COTI and 3DCLE-M models, we propose a multi-objective WFLO approach to maximize power generation and minimize streamwise turbulence intensity in the wind-turbine-swept area. The results indicate that under maximized power generation, this approach significantly reduces turbulence intensity and its non-uniform distribution in the wind-turbine-swept area. In two ideal cases, the maximum turbulence intensity in all wind-turbine-swept areas of the optimized layout is 25 % and 3.8 % lower than that of the selected benchmark layout. By optimizing the layout of the Horns Rev offshore wind farm, a new layout can be obtained with increased total power output by 1.58 % and the reduced total duration of high-fatigue-load wind turbines under high turbulence intensity by 25 % compared to the benchmark.

Time-domain fatigue damage assessment for wind turbine tower bolts under yaw optimization control at offshore wind farm

Yaw optimization control is recognized as the most effective active wake control strategy for enhancing the overall power generation of wind farms. However, the potential adverse effects of yaw optimization control on the fatigue life of wind turbines remain unclear. This study examined the effect of yaw optimization control on the fatigue life of offshore wind turbines using tower bolts. Initially, the yaw misalignment of the wind turbines was optimized using the open-source FLORIS package to maximize wind farm power generation. Subsequently, the time-varying load of the wind turbines was obtained through the OpenFAST software, using the optimal yaw misalignment, wind speed, and turbulence intensity at the hub height as inputs. The fatigue life of the wind turbines was then calculated by integrating the Schmidt–Neuper engineering stress algorithm, rain flow counting method, and Miner-Palmgren fatigue damage accumulation theory. Finally, a case study of the Horns Rev I large-scale offshore wind farm, comprising 80 wind turbines, revealed that yaw optimization control could significantly enhance the annual power generation of the wind farm by approximately 1.818%. However, optimization comes at the cost of reducing the fatigue life of wind turbine tower bolts by approximately 3–9 years.

An extended [formula omitted] model for wake-flow simulation of wind farms

The Reynolds-averaged Navier–Stokes approach coupled with the standard k−ɛ model is widely utilized for wind-energy applications. However, it has been shown that the standard k−ɛ model overestimates the turbulence intensity in the wake region and, consequently, overpredicts the power output of the waked turbines. This study focuses on the development of an extended k−ɛ model by incorporating an additional term in the turbulent kinetic energy equation. This term accounts for the influence of turbine-induced forces, and its formulation is derived through an analytical approach. To assess the effectiveness of the proposed model, we begin by analyzing the evolution of normalized velocity deficit and turbulence intensity in the wake region, and the normalized power of the waked turbines. This investigation involves a comparison of the predictions against results from large-eddy simulations in three validation cases with different layouts. We then simulate a wind farm consisting of 30 wind turbines and conduct a comparative analysis between the model-predicted normalized streamwise velocity and wind-tunnel measurements. Finally, to conclude our assessment of the proposed model, we apply it to the operational wind farm of Horns Rev 1 and evaluate the obtained normalized power with the results from large-eddy simulations. The comparisons and validations conducted in this study prove the superior performance of the extended k−ɛ model compared to the standard version.

A Wind Farm Power Maximization Method Based on Multi-Strategy Improved Sparrow Search Algorithm

Abstract For large-scale constructed wind farms, reducing wake loss and improving the overall output power are the main objectives for their optimal operation. Therefore, a wind farm power maximization method based on a multi-strategy improved sparrow search algorithm (MS-ISSA) is proposed in this paper. Integrating the wake propagation mechanism of wind turbines and the characteristics of the classic Jensen wake model, the Jensen–Gaussian wake model and wake superposition model were constructed to accurately calculate the wind farm wake distribution. The constructed Jensen–Gaussian wake model and wake superposition model can accurately describe the non-uniform distribution characteristics of wake velocity. The Sin chaotic model, Cauchy distribution, and hyperparameter adaptive adjustment strategy were used to improve the sparrow search algorithm (SSA), and the optimization ability, convergence speed, and stability of the SSA were improved. Accordingly, considering the maximum output power of the wind farm as the optimization target and axial induction factor as the optimization variable, a coordinated optimization model for wind turbines based on MS-ISSA was proposed to realize the coordinated optimal operation of wind turbines with reduced wake loss. Considering the Danish Horns Rev wind farm as the research object, the results of optimization using particle swarm optimization algorithm, whale optimization algorithm, basic sparrow search algorithm, and MS-ISSA were calculated and analyzed. The calculation results revealed that under different incoming wind conditions, the MS-ISSA exhibited better optimization results than the other optimization algorithms.

Wind Farm Blockage Revealed by Fog: The 2018 Horns Rev Photo Case

Fog conditions at the offshore wind farm Horns Rev 2 were photographed on 16 April 2018. In this study, we present the results of an analysis of the meteorological conditions on the day of the photographs. The aim of the study was to examine satellite images, meteorological observations, wind turbine data, lidar data, reanalysis data, and wake and blockage model results to assess whether wind farm blockage was a likely cause for the formation of fog upstream of the wind farm. The analysis indicated the advection of warm and moist air mass from the southwest over a cool ocean, causing cold sea fog. Wind speeds at hub height were slightly above cut-in, and there was a strong veer in the shallow stable boundary layer. The most important finding is that the wake and blockage model indicated stagnant air mass arcs to the south and west of the wind farm. In the photographs, sea fog is visible in approximately the same area. Therefore, it is likely that the reduced wind triggered the sea fog condensation due to blockage in this area. A discrepancy between the blockage model and sea fog in the photographs appears in the southwest direction. Slightly higher winds might have occurred locally in a southwesterly direction, which may have dissolved sea fog. The wake model predicted long and narrow wind turbine wakes similar to those observed in the photographs. The novelty of the study is new evidence of wind farm blockage. It fills the gap in knowledge about flow in wind farms. Implications for future research include advanced modeling of flow phenomena near large offshore wind farms relevant to wind farm operators.

Numerical simulations for a parametric study of blockage effect on offshore wind farms

AbstractThe paper presents a study of the upstream influence of wind farms on the wind speed, which is called blockage effect. A Reynolds Averaged Navier–Stokes (RANS) numerical model using an actuator disc method was devised and validated using the SCADA data from a Horns Rev 1 wind farm. The maximum difference between the average power in the first row for SCADA and the numerical model was 7.8%. The model was used to determine the impact of blockage effect on the wind farm parameters and the extent to which the wind speed and the power generation were reduced. A reference wind farm was defined, with a modified size, spacing, turbine height, and diameter that were used for comparison with other wind farm configurations. The results of the investigation of the wind farm parameter effects on the upstream wind speed reduction are presented in the paper. It has been established that increasing the turbine spacing from 5D to 6.7D reduces the power loss due to blockage by two. Blockage losses are almost eliminated when the spacing is increased two times. Similarly, the wind turbine thrust coefficient (CT) has a large impact on blockage, which is more pronounced, when CT is higher. In fact, the velocity deficit due to blockage is proportional to CT. The turbine tower height has small impact on blockage effect—the power reduction was changed by 0.3% due to blockage for the investigated range. The number of turbines in a row (with a constant number of turbines in a row) does not affect blockage significantly.

Prediction of multiple-wake velocity and wind power using a cosine-shaped wake model

It is well accepted the wakes induced by upstream turbines have an adverse impact on the power production of downstream turbines and this ubiquitous phenomenon severely affects wind farm performance. The aim of the study is to apply a new analytical wake model to prediction of multiple-wake velocity and power output inside wind farms and evaluate its performance. Unlike the classical top-hat model (Jensen model) widely embedded in industry-standard software, the newly proposed analytical wake model, which is derived based on the conservation of both mass and momentum, assumes a trigonometric distribution for the velocity deficit in the wakes of a stand-alone wind turbine and adopts a variable wake growth rate relating ambient turbulence as well as rotor-generated turbulence. Two superposition models including the SED (superposition of energy deficits) and the SVD (superposition of velocity deficits) are employed to simulate the wake-interaction flows and the performance of the new model with the superposition methods is evaluated in two cases: (1) wake interactions of two wind turbines; (2) power prediction of the Horns Rev offshore wind farm. The open-source wind-farm simulation tool FLORIS is employed to make a further comparison of different wake models. It is found that the new and the Gaussian models with the SED are in reasonably good agreement with large-eddy simulation (LES) and measurements compared with other wake models, whereas lower velocity as well as power output is predicted when using the SVD counterpart. This research proposes the SED model as an effective selection strategy for evaluating power output in wind farms when using the cosine and Gaussian models.

Layout and yaw optimisation of an offshore wind farm through analytical modelling

In this work, a computational tool for analytical large scale modelling of offshore wind farms is presented. Using Horns Rev 1 as a reference baseline, an optimal layout and yaw angle setting for one wind direction based on aerodynamic considerations is proposed. Based on a wake model presented by Qian & Ishihara, flow velocities as well as turbulence intensities are predicted when several wake flows are superimposed. Subsequently, the aerodynamic performance of the wind turbines is calculated. The proposed tool shows good agreement with measurement and LES data. The influence of performance-driving parameters, namely turbine spacing, ambient turbulence intensity and yaw angle are investigated. The axial spacing and ambient turbulence are identified as the most significant factors. Based on these results, the proposed optimal layout solution suggests a higher power yield of up to 57 %, while the optimal yaw angles found in this work show a power increase of over 6% compared to the baseline layout.

A short note on turbulence characteristics in wind-turbine wakes

Analytical wake models need formulations to mimic the impact of wind turbines on turbulence level in the wake region. Several correlations can be found in the literature for this purpose, one of which is the formula proposed in A. Crespo, J. Hernández, Turbulence characteristics in wind-turbine wakes, Journal of Wind Engineering and Industrial Aerodynamics 61 (1) (1996) 71–85, which relates the added turbulence to the induction factor of the turbine, ambient turbulence intensity, and normalized distance from the rotor through an equation with one coefficient and three exponents for the effective parameters. Misuse of this formula with an incorrect exponent for the ambient turbulence intensity is propagating in the literature. In this note, we implement the original and the incorrect formulation of turbine-induced added turbulence in a Gaussian wake model to quantify its impact by studying the Horns Rev 1 wind farm. The results reveal that the turbulence intensity and the normalized power of the waked turbines predicted by the wake model with the correct and the incorrect implementation of turbine-induced added turbulence correlation have a difference equal to 1.94% and 3.53%, respectively, for an ambient turbulence intensity of 7.7%. For an ambient turbulence intensity of 4%, these discrepancies grow to 2.7% and 4.95%.

Turbulence in waked wind turbine wakes: Similarity and empirical formulae

Turbulence of wind turbine wakes increases the power fluctuations and dynamic loads of downwind turbines. In this work, we analyze the large-eddy simulation (LES) data of the Horns Rev wind farm, and find that the streamwise variations of the Reynolds normal stresses in the wakes of the waked wind turbines located in different rows collapse well with each other for both rise and decay portions when they are normalized using the maxima. Empirical formulae in the form of a power function are then proposed to describe the streamwise variations of the Reynolds normal stresses for different blade spanwise positions. Notably, linear relations are observed between the exponent and the coefficient. The LES data of the two tandem wind turbine cases with different inflows and turbine spacings are then employed to test the proposed empirical formulae. The tests show that the empirical formulae can capture the downstream variations of the Reynolds normal stresses especially for the streamwise component.

Layout optimization for renovation of operational offshore wind farm based on machine learning wake model

In the past, offshore wind farms commonly had a large wind turbine distance to avoid power loss induced by the wake effects. For this reason, the operational offshore wind farms with such a large wind turbine distance are relatively low in capacity density and have a great potential to include more wind turbines. This paper aims to provide a suitable renovation plan for those operational wind farms. Different from traditional wind farm layout optimization, the purpose of the renovation is to install new wind turbines while maintaining the status quo, which is an optimization problem with the constraint of initial wind turbines. Therefore, the renovation plan can be applied flexibly without waiting for the decommissioning of initial wind turbines. In this paper, the renovation plan is provided by a robust wind farm layout optimization framework based on a machine learning wake model, which can evaluate overall power production more accurately than traditional analytical models. Both heuristic and gradient-based optimization algorithms are applied and compared. Horns Rev wind farm is analyzed for demonstration. The differences between the two algorithms are limited to 1%. Furthermore, the renovation and freeform optimizations are successfully applied to the cases with 12.5%∼50% more wind turbines. According to the results, the freeform optimizations without the constraint of initial wind turbines have similar performance to renovation plans with an error smaller than 0.3%. When the number of wind turbines is added from 80 to 120, the normalized AEP (annual energy production) slightly decreases from 96.6% to 93.4%, which means the power loss increases by 3%∼4%. In the meantime, the capacity density increases significantly by 50% as the area remains the same. In conclusion, the renovation plan is recommended for aging wind farms with a low capacity density like Horns Rev wind farm.

GPU simulation of wake effects at the Horns Rev 1 offshore wind farm using the CFD porous disk wake model

To verify the effectiveness of the GPU simulation of wake effects at a large-scale offshore wind farm, we ran an in-house large-eddy simulation (LES) solver with a CFD porous disk wake model for the Horns Rev 1 wind farm. For this numerical research, we prepared the latest workstation equipped with a Xeon W-2265 CPU and an NVIDIA RTX A6000 GPU. We clarified that the calculation speed of the single GPU of the NVIDIA RTX A6000 is approximately 10 times faster than the calculation speed of the Xeon W-2265. Careful data analysis and visualization of the unsteady turbulent flow fields obtained in the current LES study suggest that the mutual interference of the wakes developed by wind turbines may frequently form a local speed-up region around wind turbines, located on the downstream side of large offshore wind farms.

An innovative method of investigating the wind turbine’s inflow speed in a wind farm due to the multiple wake effect issue

In order to produce more power, several turbines are grouped in a wind farm, resulting in the wake interaction. Therefore, in a complex wind farm layout with multiple wakes affecting, determining the turbine’s velocity is essential. It is especially critical in solving wind farm layout optimization problems since it takes plenty of testing layouts to find the optimal one. This article presents an innovative method that calculates the turbine’s inflow speed through the wake interactions in a wind farm. As its main feature, the proposed method generates mesh on every turbine and calculates each cell’s speed based on the upstream wake, which affects it. Then the mass conservation applies to all cells, and an equivalent velocity for the turbine is obtained. This procedure is implemented for a hypothetical wind farm to calculate the wind farm’s output power for three different wind directions. Moreover, the gained energy is optimized through the PSO algorithm to discover the optimal wind farm layout. The proposed method is also tested on the Horns Rev offshore wind farm as the validation case, showing that it is compatible with the experimental and numerical results.

Construction of offline predictive controller for wind farm based on CNN–GRNN

In order to reduce Levelized Cost of Energy(LCOE), the wind farm development trend includes mainly two points: (1) rotor diameter of wind turbines will be larger, (2) density of offshore facilities will be higher. Consequently, the wake interference effect will be more severe, and predictive control has become one of the main studies for reducing wake disturbance. However, most of these strategies are usually computationally expensive and have limitations for large-scale wind farms since the optimization cost tends to increase exponentially with prediction horizons and number of wind turbines, which is unfavorable for real-time control. Considering control effectiveness and online computational efficiency, an offline predictive controller using convolutional neural network-general regression neural network (CNN–GRNN) is proposed for wind farm power control considering fatigue load. A CNN–GRNN hybrid network is trained to carry out the mapping between system states and optimal control settings calculated by particle swarm optimization (PSO) algorithm under various wind directions and wind speeds, and CNN–GRNN acts as an offline optimizer to provide ideal control laws with negligible online computation workload. The power at Horns Rev 1 can be improved up to 5.6% in comparative experiments with lookup table (LUT) strategy while keeping the fatigue load within the preset limitation, and the extensive simulation results under various wind conditions indicate that this proposed strategy can provide a more desirable performance for wind farm power control with fatigue constraint while retaining the advantage of negligible online computational burden.