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The dynamics of the turbulent atmospheric boundary layer play a fundamental role in wind farm energy production, governing the velocity field that enters the farm as well as the turbulent mixing that regenerates energy for extraction at downstream rows. Understanding the dynamic interactions among turbines, wind farms, and the atmospheric boundary layer can therefore be beneficial in improving the efficiency of wind farm control approaches. Anticipated increases in the sizes of new wind farms to meet renewable energy targets will increase the importance of exploiting this understanding to advance wind farm control capabilities. This review discusses approaches for modeling and estimation of the wind farm flow field that have exploited such knowledge in closed-loop control, to varying degrees. We focus on power tracking as an example application that will be of critical importance as wind farms transition into their anticipated role as major suppliers of electricity. The discussion highlights the benefits of including the dynamics of the flow field in control and points to critical shortcomings of the current approaches. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions. 

A quantitative understanding of the dominant mechanisms that govern the generation and decay of the counter-rotating vortex pair (CVP) produced by yawed wind turbines is needed to fully realize the potential of yawing for wind farm power maximization and regulation. Observations from large eddy simulations (LES) of yawed wind turbines in the turbulent atmospheric boundary layer and concepts from the aircraft trailing vortex literature inform a model for the shed vorticity and circulation. The model is formed through analytical integration of simplified forms of the vorticity transport equation. Based on an eddy viscosity approach, it uses the boundary-layer friction velocity as the velocity scale and the width of the vorticity distribution itself as the length scale. As with the widely used Jensen model for wake deficit evolution in wind farms, our analytical expressions do not require costly numerical integration of differential equations. The predicted downstream decay of maximum vorticity and total circulation agree well with LES results. We also show that the vorticity length scale grows linearly with downstream distance and find several power laws for the decay of maximum vorticity. These results support the notion that the decay of the CVP is dominated by gradual cancellation of the vorticity at the line of symmetry of the wake through cross-diffusion. 

Energy storage can generate significant revenue by taking advantage of fluctuations in real-time energy market prices. In this paper, we investigate the real-time price arbitrage potential of aerodynamic energy storage in wind farms. This under-explored source of energy storage can be realized by deferring energy extraction by turbines toward the front of a farm for later extraction by downstream turbines. In large wind farms, this kinetic energy can be stored for minutes to tens of minutes, depending on the inter-turbine travel distance and the incoming wind speed. This storage mechanism requires minimal capital costs for implementation and potentially could provide additional revenue to wind farm operators. We demonstrate that the potential for revenue generation depends on the energy arbitrage (storage) efficiency and the wind travel time between turbines. We then characterize how price volatility and arbitrage efficiency affect real-time energy market revenue potential. Simulation results show that when price volatility is low, which is the historic norm, noticeably increased revenue is only achieved with high arbitrage efficiencies. However, as price volatility increases, which is expected in the future as the composition of the power system evolves, revenues increase by several percent. 

Wake models play an integral role in wind farm layout optimization and operations where associated design and control decisions are only as good as the underlying wake model upon which they are based. However, the desired model fidelity must be counterbalanced by the need for simplicity and computational efficiency. As a result, efficient engineering models that accurately capture the relevant physics—such as wake expansion and wake interactions for design problems and wake advection and turbulent fluctuations for control problems—are needed to advance the field of wind farm optimization. In this paper, we discuss a computationally-efficient continuous-time one-dimensional dynamic wake model that includes several features derived from fundamental physics, making it less ad-hoc than prevailing approaches. We first apply the steady-state solution of the model to predict the wake expansion coefficients commonly used in design problems. We demonstrate that more realistic results can be attained by linking the wake expansion rate to a top-down model of the atmospheric boundary layer, using a super-Gaussian wake profile that smoothly transitions between a top-hat and Gaussian distribution as well as linearly-superposing wake interactions. We then apply the dynamic model to predict trajectories of wind farm power output during start-up and highlight the improved accuracy of non-linear advection over linear advection. Finally, we apply the dynamic model to the control-oriented application of predicting power output of an irregularly-arranged farm during continuous operation. In this application, model fidelity is improved through state and parameter estimation accounting for spanwise inflow inhomogeneities and turbulent fluctuations. The proposed approach thus provides a modeling paradigm with the flexibility to enable designers to trade-off between accuracy and computational speed for a wide range of wind farm design and control applications. 

Yawing wind turbines has emerged as an appealing method for wake deflection. However, the associated flow properties, including the magnitude of the transverse velocity associated with yawed turbines, are not fully understood. In this paper, we view a yawed turbine as a lifting surface with an elliptic distribution of transverse lift. Prandtl’s lifting line theory provides predictions for the transverse velocity and magnitude of the shed counter-rotating vortex pair known to form downstream of the yawed turbine. The streamwise velocity deficit behind the turbine can then be obtained using classical momentum theory. This new model for the near-disk inviscid region of the flow is compared to numerical simulations and found to yield more accurate predictions of the initial transverse velocity and wake skewness angle than existing models. We use these predictions as initial conditions in a wake model of the downstream evolution of the turbulent wake flow and compare predicted wake deflection with measurements from wind tunnel experiments. 

Improved integration of wind farms into frequency regulation services is vital for increasing renewable energy production while ensuring power system stability. This work generalizes a recently proposed model-based receding horizon wind farm controller for secondary frequency regulation to arbitrary wind farm layouts and augments the controller to enable power modulation through storage of kinetic energy in the rotor. The new design explicitly includes actuation of blade pitch and generator torque, which facilitates implementation in existing farms as it takes advantage of current wind turbine control loops. This generalized control design improves control authority by individually controlling each turbine and using kinetic energy stored in the rotor in a coordinated manner to achieve farm level control goals. Numerical results demonstrate the effectiveness of this approach; in particular, the controller achieves accurate power tracking and reduces loss of revenue in the bulk power market by requiring less setpoint reduction (derate) than the power level control range. 

This paper is an extended version of our paper presented at the 2016 TORQUE conference (Shapiro et al., 2016). We investigate the use of wind farms to provide secondary frequency regulation for a power grid using a model-based receding horizon control framework. In order to enable real-time implementation, the control actions are computed based on a time-varying one-dimensional wake model. This model describes wake advection and wake interactions, both of which play an important role in wind farm power production. In order to test the control strategy, it is implemented in a large-eddy simulation (LES) model of an 84-turbine wind farm using the actuator disk turbine representation. Rotor-averaged velocity measurements at each turbine are used to provide feedback for error correction. The importance of including the dynamics of wake advection in the underlying wake model is tested by comparing the performance of this dynamic-model control approach to a comparable static-model control approach that relies on a modified Jensen model. We compare the performance of both control approaches using two types of regulation signals, RegA and RegD, which are used by PJM, an independent system operator in the eastern United States. The poor performance of the static-model control relative to the dynamic-model control demonstrates that modeling the dynamics of wake advection is key to providing the proposed type of model-based coordinated control of large wind farms. We further explore the performance of the dynamic-model control via composite performance scores used by PJM to qualify plants for regulation services or markets. Our results demonstrate that the dynamic-model-controlled wind farm consistently performs well, passing the qualification threshold for all fast-acting RegD signals. For the RegA signal, which changes over slower timescales, the dynamic-model control leads to average performance that surpasses the qualification threshold, but further work is needed to enable this controlled wind farm to achieve qualifying performance for all regulation signals. 

The actuator disk model (ADM) continues to be a popular wind turbine representation in large eddy simulations (LES) of large wind farms. Computational restrictions typically limit the number of grid points across the rotor of each actuator disk and require spatial filtering to smoothly distribute the applied force distribution on discrete grid points. At typical grid resolutions, simulations cannot capture all of the vorticity shed behind the disk and subsequently overpredict power by upwards of 10%. To correct these modeling errors, we propose a vortex cylinder model to quantify the shed vorticity when a filtered force distribution is applied at the actuator disk. This model is then used to derive a correction factor for numerical simulations that collapses the power curve for simulations at various filter widths and grid resolutions onto the curve obtained using axial momentum theory. The proposed correction, which is analytically derived from first principles, facilitates accurate power measurements in LES without resorting to highly refined numerical grids or empirical correction factors.

 

Power tracking is an emerging application for wind farm control designs that allows farms to participate in a wider range of grid services, such as secondary frequency regulation. Control designs that enable large wind farms to follow a time-varying power trajectory are complicated by aerodynamic interactions that make it impossible to decouple upstream wind turbine control actions from downstream power production. This coupling is particularly important in applications where the reference trajectory is changing faster than, or at a similar rate as, the propagation of turbine wakes through the farm. In this work we overcome these difficulties by using a dynamic wake model that accounts for wake expansion, advection, and multi-wake interactions within a model-based receding horizon controller for coordinated control of a large multi-turbine wind farm. An ensemble Kalman filter is employed for state estimation and error correction at the turbine level. We implement the controller in high-fidelity numerical simulations of a wind farm with 84 turbines and then test the controlled farm's ability to track a power reference signal. The results demonstrate the ability of the control algorithm to track two types of power reference signals used by a US independent system operator.