Analytical model for the power–yaw sensitivity  of wind turbines operating in full wake

Liew, Jaime; Urbán, Albert M.; Andersen, Søren Juhl

doi:10.5194/wes-5-427-2020

Cited by 40 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The uncertainties and sensitivities in this study associated with the wall model, subfilter-scale model, wind turbine model, and ABL characteristics such as boundary layer inversion height were not investigated in detail and are left for future work. More reliable and generalizable estimates for P p (Liew et al, 2020), or generally C p as a function of γ , should be investigated. Future work should also investigate the influence of latitude and geostrophic wind direction on wake steering control performance (Howland et al, 2020b).…”

Section: Discussionmentioning

confidence: 99%

“…However, simulations have shown for the NREL 5 MW turbine that P p equals 1.88 (Gebraad et al, 2016a). Recent work has shown that P p differs for freestream and waked turbines (Liew et al, 2020). The value of P p that results in a satisfactory agreement with experimental data depends on the wind turbine model, ABL shear and veer, and atmospheric stability.…”

Section: Lifting Line Wake Modelmentioning

confidence: 97%

“…The incident velocity is projected into the rotor disk plane, and therefore the dependence of thrust on the yaw misalignment γ in uniform inflow conditions would be cos 2 (γ ), although it may deviate from this in sheared and veered inflow conditions. While the actuator disk model is lower fidelity than the actuator line methods, it captures the far wake (far wake is approximately x/D 3; see, e.g., Bastankhah and Porté-Agel, 2017) accurately for both aligned (Martínez-Tossas et al, 2015) and yaw misalignment wind turbines (Lin and Porté-Agel, 2019). Since the goal of the present study is controller synthesis and sensitivity experiments, more computationally expensive actuator line simulations are left for future work given the large volume of simulations that are run.…”

Section: Large Eddy Simulation Setupmentioning

confidence: 99%

See 2 more Smart Citations

Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

et al. 2020

View full text Add to dashboard Cite

Abstract. Strategies for wake loss mitigation through the use of dynamic closed-loop wake steering are investigated using large eddy simulations of conventionally neutral atmospheric boundary layer conditions in which the neutral boundary layer is capped by an inversion and a stable free atmosphere. The closed-loop controller synthesized in this study consists of a physics-based lifting line wake model combined with a data-driven ensemble Kalman filter (EnKF) state estimation technique to calibrate the wake model as a function of time in a generalized transient atmospheric flow environment. Computationally efficient gradient ascent yaw misalignment selection along with efficient state estimation enables the dynamic yaw calculation for real-time wind farm control. The wake steering controller is tested in a six-turbine array embedded in a statistically quasi-stationary, conventionally neutral flow with geostrophic forcing and Coriolis effects included. The controller statistically significantly increases power production compared to the baseline, greedy, yaw-aligned control provided that the EnKF estimation is constrained and informed with a physics-based prior belief of the wake model parameters. The influence of the model for the coefficient of power Cp as a function of the yaw misalignment is characterized. Errors in estimation of the power reduction as a function of yaw misalignment are shown to result in yaw steering configurations that underperform the baseline yaw-aligned configuration. Overestimating the power reduction due to yaw misalignment leads to increased power over the greedy operation, while underestimating the power reduction leads to decreased power; therefore, in an application where the influence of yaw misalignment on Cp is unknown, a conservative estimate should be taken. The EnKF-augmented wake model predicts the power production in yaw misalignment with a mean absolute error over the turbines in the farm of 0.02P1, with P1 as the power of the leading turbine at the farm. A standard wake model with wake spreading based on an empirical turbulence intensity relationship leads to a mean absolute error of 0.11P1, demonstrating that state estimation improves the predictive capabilities of simplified wake models.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Lifting Line Wake Modelmentioning

confidence: 97%

Section: Large Eddy Simulation Setupmentioning

confidence: 99%

See 1 more Smart Citation

Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

et al. 2020

View full text Add to dashboard Cite

show abstract

“…The power-yaw loss coefficient α is implemented as suggested by the paper of Liew et al [51]. This paper describes how α should be adjusted based on whether a turbine is in the wake of another turbine and what the spacing is between those two turbines.…”

Section: Calibration Methodsmentioning

confidence: 99%

Sensitivity and Uncertainty of the FLORIS Model Applied on the Lillgrund Wind Farm

2021

Self Cite

View full text Add to dashboard Cite

Wind farms experience significant efficiency losses due to the aerodynamic interaction between turbines. A possible control technique to minimize these losses is yaw-based wake steering. This paper investigates the potential for improved performance of the Lillgrund wind farm through a detailed calibration of a low-fidelity engineering model aimed specifically at yaw-based wake steering. The importance of each model parameter is assessed through a sensitivity analysis. This work shows that the model is overparameterized as at least one model parameter can be excluded from the calibration. The performance of the calibrated model is tested through an uncertainty analysis, which showed that the model has a significant bias but low uncertainty when comparing the predicted wake losses with measured wake losses. The model is used to optimize the annual energy production of the Lillgrund wind farm by determining yaw angles for specific inflow conditions. A significant energy gain is found when the optimal yaw angles are calculated deterministically. However, the energy gain decreases drastically when uncertainty in input conditions is included. More robust yaw angles can be obtained when the input uncertainty is taken into account during the optimization, which yields an energy gain of approximately 3.4%.

show abstract

“…For example, Fleming et al ( 2017) estimate p P = 1.43 using data from a commercial wind plant, Gebraad et al (2016) find that a value of p P = 1.88 fits results from LES simulations, and Medici ( 2005) determines a value of p P = 2 from a wind tunnel experiment. But as discussed by Liew et al (2020), blade element momentum theory predicts p P = 3. Note that p P and the value of p v used in FLORIS (see Eq.…”

Section: Impact Of Yaw Misalignment On Power Productionmentioning

confidence: 95%

Results from a Wake Steering Experiment at a Commercial Wind Plant: Investigating the Wind Speed Dependence of Wake Steering Performance

Simley¹,

Fleming²,

Girard³

et al. 2021

Preprint

View full text Add to dashboard Cite

Abstract. Wake steering is a wind farm control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, thereby increasing the net wind plant power production and reducing fatigue loads generated by wake turbulence. In this paper, we present results from a wake steering experiment at a commercial wind plant involving two wind turbines spaced 3.7 rotor diameters apart. During the three-month experiment period, we estimate that wake steering reduced wake losses by 5.7 % for the wind direction sector investigated. After applying a long-term correction based on the site wind rose, the reduction in wake losses increases to 9.8 %. As a function of wind speed, we find large energy improvements near cut-in wind speed, where wake steering can prevent the downstream wind turbine from shutting down. Yet for wind speeds between 6–8 m/s, we observe little change in performance with wake steering. However, wake steering was found to improve energy production significantly for below-rated wind speeds from 8–12 m/s. By measuring the relationship between yaw misalignment and power production using a nacelle lidar, we attribute much of the improvement in wake steering performance at higher wind speeds to a significant reduction in the power loss of the upstream turbine as wind speed increases. Additionally, we find higher wind direction variability at lower wind speeds, which contributes to poor performance in the 6–8 m/s wind speed bin because of slow yaw controller dynamics. Further, we compare the measured performance of wake steering to predictions using the FLORIS (FLOw Redirection and Induction in Steady State) wind farm control tool coupled with a wind direction variability model. Although the achieved yaw offsets at the upstream wind turbine fall short of the intended yaw offsets, we find that they are predicted well by the wind direction variability model. When incorporating the predicted achieved yaw offsets, estimates of the energy improvement from wake steering using FLORIS closely match the experimental results.

show abstract

Analytical model for the power–yaw sensitivity of wind turbines operating in full wake

Cited by 40 publications

References 31 publications

Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

Optimal closed-loop wake steering – Part 1: Conventionally neutral atmospheric boundary layer conditions

Sensitivity and Uncertainty of the FLORIS Model Applied on the Lillgrund Wind Farm

Results from a Wake Steering Experiment at a Commercial Wind Plant: Investigating the Wind Speed Dependence of Wake Steering Performance

Contact Info

Product

Resources

About