Wake steering optimization under uncertainty

Abstract

Abstract. Turbines in wind power plants experience significant power losses when wakes from upstream turbines affect the energy production of downstream turbines. A promising plant-level control strategy to reduce these losses is wake steering, where upstream turbines are yawed to direct wakes away from downstream turbines. However, there are significant uncertainties in many aspects of the wake steering problem. For example, infield sensors do not give perfect information, and inflow to the plant is complex and difficult to forecast with available information, even over short time periods. Here, we formulate and solve an optimization under uncertainty (OUU) problem for determining optimal plant-level wake steering strategies in the presence of independent uncertainties in the direction, speed, turbulence intensity, and shear of the incoming wind, as well as in turbine yaw positions. The OUU wake steering strategy is first examined for a two-turbine test case to explore the impacts of different types of inflow uncertainties, and it is then demonstrated for a more realistic 11-turbine wind power plant. Of the sources of uncertainty considered, we find that wake steering strategies are most sensitive to uncertainties in the wind speed and direction. When maximizing expected power production, the OUU strategy also tends to favor smaller yaw angles, which have been shown in previous work to reduce turbine loading. Ultimately, the plant-level wake steering strategy formulated using an OUU approach yields 0.48 % more expected annual energy production for the 11-turbine wind plant than a strategy that neglects uncertainty when considering stochastic inputs. Thus, not only does the present OUU strategy produce more power in realistic conditions, but it also reduces risk by prescribing strategies that call for less extreme yaw angles.

Experimental results of wake steering using fixed angles

“…First, using these models in the design of wind farm controllers produces different control strategies from prior deflection models and can be critical in the design of control strategies for large arrays, because of the secondary steering effects (see, for example, Zong and Porté-Agel (2021)). Second, the degree of power loss from wrong-way steering affects the design of robust control strategies, which are intended to address wind direction measurement uncertainty as well as the inability of the controller to track high-frequency wind direction variations because of slow yaw control dynamics (Rott et al, 2018;Simley et al, 2019;Quick et al, 2020). The penalty paid for wrong-way steering directly affects the magnitude of the yaw offsets applied for wind directions where wake steering is beneficial.…”

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

“…Further, after the turbine settles on a specific yaw position, the wind direction will vary until the yaw error is large enough for the turbine to yaw again, causing wind direction uncertainty. Quick et al (2017) and Quick et al (2020) investigated the impact of yaw position uncertainty on optimal wake steering performance by performing FLORIS simulations with a distribution of possible yaw positions for a given wind direction. Similarly, Rott et al (2018) and Quick et al (2020) included wind direction uncertainty when optimizing wake steering control using FLORIS by assuming a distribution of possible wind directions about the intended wind direction.…”

“…Quick et al (2017) and Quick et al (2020) investigated the impact of yaw position uncertainty on optimal wake steering performance by performing FLORIS simulations with a distribution of possible yaw positions for a given wind direction. Similarly, Rott et al (2018) and Quick et al (2020) included wind direction uncertainty when optimizing wake steering control using FLORIS by assuming a distribution of possible wind directions about the intended wind direction. Here, we model the uncertainty resulting from wind direction variability and controller limitations using the approach presented by Simley et al (2020b), wherein FLORIS simulations are performed assuming uncertainty in both yaw position and wind direction.…”

“…A good balance between energy production and the required yaw actuation was achieved by (1) updating the yaw offset command at least every 2 minutes, (2) filtering the wind direction input using a time constant similar to the update rate, and (3) including hysteresis on the yaw offset command to reduce yaw activity. The concept of robust wake steering control has been explored by several authors to address the challenge of operating in dynamic wind conditions (Rott et al, 2018;Simley et al, 2020b;Quick et al, 2020). Specifically, realizing that the wind direction can vary considerably while a turbine's yaw position remains fixed, the authors identified yaw offsets that maximize energy production assuming a certain degree of wind direction uncertainty.…”

Dynamic robust active wake control

“…They evaluated the performance of the robust AWC in case studies with different wind turbine spacings and turbulence intensities. The second work was published by Quick et al (2020), and considers robustness with respect to a range of uncertain parameters, namely wind speed, wind directions, turbulence intensity, wind shear and yaw angle. The authors used a polynomial chaos expansion approach to deal with the underlying high computational complexity of the resulting optimization, and demonstrated that the wind direction is the most significant contributor to uncertainty in the power predictions.…”