scholarly journals Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1078 ◽  
Author(s):  
Jacob R. West ◽  
Sanjiva K. Lele
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Wind Turbine ◽  
Wind Farm ◽  
Wind Farms ◽  
Mean Flow ◽  
Thrust Coefficient ◽  
Turbine Performance ◽  
Trade Offs ◽  
Mean Kinetic Energy

The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.

scholarly journals Local and Mesoscale Impacts of Wind Farms as Parameterized in a Mesoscale NWP Model

2012 ◽  
Vol 140 (9) ◽  
pp. 3017-3038 ◽  
Author(s):  
Anna C. Fitch ◽  
Joseph B. Olson ◽  
Julie K. Lundquist ◽  
Jimy Dudhia ◽  
Alok K. Gupta ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Kinetic Energy ◽  
Wind Farm ◽  
Weather Prediction ◽  
Wind Farms ◽  
Mean Flow ◽  
Thrust Coefficient ◽  
Near Surface ◽  
Neutral Boundary Layer

Abstract A new wind farm parameterization has been developed for the mesoscale numerical weather prediction model, the Weather Research and Forecasting model (WRF). The effects of wind turbines are represented by imposing a momentum sink on the mean flow; transferring kinetic energy into electricity and turbulent kinetic energy (TKE). The parameterization improves upon previous models, basing the atmospheric drag of turbines on the thrust coefficient of a modern commercial turbine. In addition, the source of TKE varies with wind speed, reflecting the amount of energy extracted from the atmosphere by the turbines that does not produce electrical energy. Analyses of idealized simulations of a large offshore wind farm are presented to highlight the perturbation induced by the wind farm and its interaction with the atmospheric boundary layer (BL). A wind speed deficit extended throughout the depth of the neutral boundary layer, above and downstream from the farm, with a long wake of 60-km e-folding distance. Within the farm the wind speed deficit reached a maximum reduction of 16%. A maximum increase of TKE, by nearly a factor of 7, was located within the farm. The increase in TKE extended to the top of the BL above the farm due to vertical transport and wind shear, significantly enhancing turbulent momentum fluxes. The TKE increased by a factor of 2 near the surface within the farm. Near-surface winds accelerated by up to 11%. These results are consistent with the few results available from observations and large-eddy simulations, indicating this parameterization provides a reasonable means of exploring potential downwind impacts of large wind farms.

scholarly journals Set-point optimization in wind farms to mitigate effects of flow blockage induced by atmospheric gravity waves

2021 ◽  
Vol 6 (1) ◽  
pp. 247-271
Author(s):  
Luca Lanzilao ◽  
Johan Meyers
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Wind Farm ◽  
Wind Farms ◽  
Thrust Coefficient ◽  
Set Point ◽  
Coefficient Distribution ◽  
Atmospheric Gravity ◽  
Flow Blockage ◽  
Time Periodic

Abstract. Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer, causing detrimental consequences in terms of a farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm-induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution, which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Power gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the power gain to the atmospheric state is studied using the developed optimization tool for almost 2000 different atmospheric states. Overall, power gains above 4 % were observed for 77 % of the cases with peaks up to 14 % for weakly stratified atmospheres in critical flow regimes.

scholarly journals FLOWSTAR-Energy: a high resolution wind farm wake model

2016 ◽  
Author(s):  
Amy Stidworthy ◽  
David Carruthers
Keyword(s):  
Boundary Layer ◽  
Wind Turbine ◽  
Complex Terrain ◽  
Wind Farm ◽  
Wind Farms ◽  
Measured Data ◽  
Offshore Wind ◽  
Offshore Wind Farm ◽  
Wake Model ◽  
Turbine Wake

Abstract. A new model, FLOWSTAR-Energy, has been developed for the practical calculation of wind farm energy production. It includes a semi-analytic model for airflow over complex surfaces (FLOWSTAR) and a wind turbine wake model that simulates wake-wake interaction by exploiting some similarities between the decay of a wind turbine wake and the dispersion of plume of passive gas emitted from an elevated source. Additional turbulence due to the wind shear at the wake edge is included and the assumption is made that wind turbines are only affected by wakes from upstream wind turbines. The model takes account of the structure of the atmospheric boundary layer, which means that the effect of atmospheric stability is included. A marine boundary layer scheme is also included to enable offshore as well as onshore sites to be modelled. FLOWSTAR-Energy has been used to model three different wind farms and the predicted energy output compared with measured data. Maps of wind speed and turbulence have also been calculated for two of the wind farms. The Tjaæreborg wind farm is an onshore site consisting of a single 2 MW wind turbine, the NoordZee offshore wind farm consists of 36 V90 VESTAS 3 MW turbines and the Nysted offshore wind farm consists of 72 Bonus 2.3 MW turbines. The NoordZee and Nysted measurement datasets include stability distribution data, which was included in the modelling. Of the two offshore wind farm datasets, the Noordzee dataset focuses on a single 5-degree wind direction sector and therefore only represents a limited number of measurements (1,284); whereas the Nysted dataset captures data for seven 5-degree wind direction sectors and represents a larger number of measurements (84,363). The best agreement between modelled and measured data was obtained with the Nysted dataset, with high correlation (0.98 or above) and low normalised mean square error (0.007 or below) for all three flow cases. The results from Tjæreborg show that the model replicates the Gaussian shape of the wake deficit two turbine diameters downstream of the turbine, but the lack of stability information in this dataset makes it difficult to draw conclusions about model performance. One of the key strengths of FLOWSTAR-Energy is its ability to model the effects of complex terrain on the airflow. However, although the airflow model has been previously compared extensively with flow data, it has so far not been used in detail to predict energy yields from wind farms in complex terrain. This will be the subject of a further validation study for FLOWSTAR-Energy.

scholarly journals Set-point optimization in wind farms to mitigate effects of flow blockage induced by gravity waves

2020 ◽  
Author(s):  
Luca Lanzilao ◽  
Johan Meyers
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Wind Farm ◽  
Wind Farms ◽  
Thrust Coefficient ◽  
Set Point ◽  
Coefficient Distribution ◽  
Energy Gains ◽  
Flow Blockage ◽  
Time Periodic

Abstract. Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer causing detrimental consequences in terms of farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Energy gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the energy gain to the atmospheric state is studied using the developed optimization tool for almost two thousand different atmospheric states. Energy gains of up to 14 % are found for weakly stratified atmospheres in critical flow regimes.

Statistical calculation of thrust curve of a wind turbine based on available power curve and general specifications data

2021 ◽  
Author(s):  
Evgeny Atlaskin ◽  
Irene Suomi ◽  
Anders Lindfors
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Wind Farm ◽  
Wind Farms ◽  
Power Curve ◽  
Wake Effect ◽  
Thrust Coefficient ◽  
Simple Method ◽  
Wind Speeds ◽  
Power Curves

<p>Power curves for a substantial number of wind turbine generators (WTG) became available in a number of public sources during the recent years. They can be used to estimate the power production of a wind farm fleet with uncertainty determined by the accuracy and consistency of the power curve data. However, in order to estimate power losses inside a wind farm due to wind speed reduction caused by the wake effect, information on the thrust force, or widely used thrust coefficient (Ct), is required. Unlike power curves, Ct curves for the whole range of operating wind speeds of a WTG are still scarcely available in open sources. Typically, power and Ct curves are requested from a WTG manufacturer or wind farm owner under a non-disclosure agreement. However, in a research study or in calculations over a multitude of wind farms with a variety of wind turbine models, collecting this information from owners may be hardly possible. This study represents a simple method to define Ct curve statistically using power curve and general specifications of WTGs available in open sources. Preliminary results demonstrate reasonable correspondence between simulated and given data. The estimations are done in the context of aggregated wind power calculations based on reanalysis or forecast data, so that the uncertainty of wake wind speed caused by the uncertainty of predicted Ct is comparable, or do not exceed, the uncertainty of given wind speed. Although the method may not provide accurate fits at low wind speeds, it represents an essential alternative to using physical Computational Fluid Dynamics (CFD) models that are both more demanding to computer resources and require detailed information on the geometry of the rotor blades and physical properties of the rotor, which are even more unavailable in open sources than power curves.</p>

Spectra and Large Eddy Structures in the Double Log-Layer of a High Re Wind Turbine Array Boundary Layer

2016 ◽  
Author(s):  
Tanmoy Chatterjee ◽  
Yulia Peet
Keyword(s):  
Boundary Layer ◽  
Wind Turbine ◽  
Wind Farm ◽  
Scaling Laws ◽  
Numerical Models ◽  
Wind Farms ◽  
Large Eddy ◽  
Eddy Structures ◽  
Large Wind ◽  
Theoretical Conceptualization

Wind Turbine Array Boundary Layer (WTABL) is a relatively simple, yet useful theoretical conceptualization to study very large wind farms in atmospheric boundary layer (ABL). In the current paper, we perform a high-fidelity LES investigation of a 3 × 3 wind turbine array in a WTABL framework, with a main focus on extending the work beyond the simple analytical model and providing a rigorous fundamental understanding of the dynamic behaviour of length scales, their scaling laws and the anisotropic structure of the energy containing eddies responsible for power generation from the wind turbines. This is accomplished by studying the components of energy and shear-stress spectra in the flow. This knowledge can potentially provide an efficient way to control the wind farm power output as well as serve as a stepping stone to design efficient low order numerical models for predicting farm power and dynamics at reduced computational expense.

Mesoscale Influences of Wind Farms throughout a Diurnal Cycle

2013 ◽  
Vol 141 (7) ◽  
pp. 2173-2198 ◽  
Author(s):  
Anna C. Fitch ◽  
Julie K. Lundquist ◽  
Joseph B. Olson
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Diurnal Cycle ◽  
Wind Farm ◽  
Wind Farms ◽  
Temperature Perturbation ◽  
Mean Temperature ◽  
The Impact

Abstract Large wind farms are expected to influence local and regional atmospheric circulations. Using a mesoscale parameterization of the effects of wind farms that includes a momentum sink and a wind speed–dependent source of turbulent kinetic energy, simulations were carried out to quantify the impact of a wind farm on an atmospheric boundary layer throughout a diurnal cycle. The presence of a wind farm covering 10 km × 10 km is found to have a significant impact on the local atmospheric flow and on regions up to 60 km downwind at night. Daytime convective conditions show little impact of the wind farm on wind speeds, as the momentum deficits generated by the wind farm rapidly mix through the depth of the boundary layer. At night, the stable layer within the rotor area inhibits turbulent mixing of the momentum deficit, leading to a shallower wake and a greater reduction in the wind speed within the wake. Although a low-level jet forms at altitudes within the rotor area in the hours before dawn, it is completely eliminated within the wind farm. At night, a maximum warming of 1 K is seen at the bottom of the rotor area. Near the surface, there is less warming (0.5 K). Downwind, the surface temperature perturbation is small, with a cooling of up to 0.3 K. Over the simulation period, the mean temperature change over the wind farm area at 2 m is a very slight warming (0.2 K). Mean temperature changes downwind are negligible. Other influences on turbulent kinetic energy, surface heat fluxes, and boundary layer height, are discussed.

Overview of Subsynchronous Oscillation in Grid-connected Wind Farm

2020 ◽  
Vol 13 (7) ◽  
pp. 969-979
Author(s):  
Xu Pei-Zhen ◽  
Lu Yong-Geng ◽  
Cao Xi-Min
Keyword(s):  
Power Systems ◽  
Wind Turbine ◽  
Large Scale ◽  
Wind Farm ◽  
Wind Farms ◽  
Induction Generator ◽  
Future Research ◽  
Stable Operation ◽  
Subsynchronous Oscillation ◽  
Different Types

Background: Over the past few years, the subsynchronous oscillation (SSO) caused by the grid-connected wind farm had a bad influence on the stable operation of the system and has now become a bottleneck factor restricting the efficient utilization of wind power. How to mitigate and suppress the phenomenon of SSO of wind farms has become the focus of power system research. Methods: This paper first analyzes the SSO of different types of wind turbines, including squirrelcage induction generator based wind turbine (SCIG-WT), permanent magnet synchronous generator- based wind turbine (PMSG-WT), and doubly-fed induction generator based wind turbine (DFIG-WT). Then, the mechanisms of different types of SSO are proposed with the aim to better understand SSO in large-scale wind integrated power systems, and the main analytical methods suitable for studying the SSO of wind farms are summarized. Results: On the basis of results, using additional damping control suppression methods to solve SSO caused by the flexible power transmission devices and the wind turbine converter is recommended. Conclusion: The current development direction of the SSO of large-scale wind farm grid-connected systems is summarized and the current challenges and recommendations for future research and development are discussed.

scholarly journals Analysis of Wind Turbine Aging through Operation Data Calibrated by LiDAR Measurement

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2319
Author(s):  
Hyun-Goo Kim ◽  
Jin-Young Kim
Keyword(s):  
Power Generation ◽  
Wind Speed ◽  
Wind Turbine ◽  
Wind Farm ◽  
Free Stream ◽  
Turbine Blades ◽  
Wind Farms ◽  
Lidar Measurement ◽  
Wind Turbine Blades ◽  
Wake Effect

This study analyzed the performance decline of wind turbine with age using the SCADA (Supervisory Control And Data Acquisition) data and the short-term in situ LiDAR (Light Detection and Ranging) measurements taken at the Shinan wind farm located on the coast of Bigeumdo Island in the southwestern sea of South Korea. Existing methods have generally attempted to estimate performance aging through long-term trend analysis of a normalized capacity factor in which wind speed variability is calibrated. However, this study proposes a new method using SCADA data for wind farms whose total operation period is short (less than a decade). That is, the trend of power output deficit between predicted and actual power generation was analyzed in order to estimate performance aging, wherein a theoretically predicted level of power generation was calculated by substituting a free stream wind speed projecting to a wind turbine into its power curve. To calibrate a distorted wind speed measurement in a nacelle anemometer caused by the wake effect resulting from the rotation of wind-turbine blades and the shape of the nacelle, the free stream wind speed was measured using LiDAR remote sensing as the reference data; and the nacelle transfer function, which converts nacelle wind speed into free stream wind speed, was derived. A four-year analysis of the Shinan wind farm showed that the rate of performance aging of the wind turbines was estimated to be −0.52%p/year.

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