Pieter M. O. Gebraad

Evaluating wake models for wind farm control

Wind turbines are typically operated to maximize their own performance without considering the impact of wake effects on nearby turbines. There is the potential to increase total power and reduce structural loads by properly coordinating the individual turbines in a wind farm. The effective design and analysis of such coordinated controllers requires turbine wake models of sufficient accuracy but low computational complexity. This paper first formulates a coordinated control problem for a two-turbine array. Next, the paper reviews several existing simulation tools that range from low-fidelity, quasi-static models to high-fidelity, computational fluid dynamic models. These tools are compared by evaluating the power, loads, and flow characteristics for the coordinated two-turbine array. The results in this paper highlight the advantages and disadvantages of existing wake models for design and analysis of coordinated wind farm controllers.

A model-free distributed approach for wind plant control

By extracting kinetic energy from the wind flow, a wind turbine reduces the wind speed in the wake downstream of the wind turbine rotor. In a wind power plant, this wake effect reduces the power production of downstream turbines. This paper presents a control scheme for optimizing the total power output of a wind power plant by taking into account the wake effect. It is a distributed control scheme in which each wind turbine adapts its control settings based on information that it receives from neighbouring turbines. The total power optimization is performed using gradient-based optimization. The optimization is done in a model-free, data-driven manner, as the gradients are estimated from the past control actions, the measured power response of the turbine itself, and the power response of neighbouring turbines. The time-efficiency of the optimization scheme was improved by exploiting information on the locations of the turbines in the wind plant, and an estimate of the wind direction. The method is tested in a simulation of the Princess Amalia Wind Park. To be able to evaluate the time-efficiency of the scheme, in the simulation model a delay structure was included that models the wake traveling from one turbine to the next. The new control method results in a much faster convergence of the power optimization when compared with an existing model-free wind plant power optimization method that uses a game theoretic approach.

A data-driven model for wind plant power optimization by yaw control

This paper presents a novel parametric model that will be used to optimize the yaw settings of wind turbines in a wind plant for improved electrical energy production of the whole wind plant. The model predicts the effective steady-state flow velocities at each turbine, as well as the resulting electrical energy productions, as a function of the axial induction and the yaw angle of the different rotors. The model has a limited number of parameters that are estimated based on data. Moreover, it is shown how this model can be used to optimize the yaw settings using a game-theoretic approach. In a case study we demonstrate that our novel parametric model fits the data generated by a high-fidelity computational fluid dynamics model of a small wind plant, and that the data-driven yaw optimization control has great potential to increase the wind plants electrical energy production.

Investigation of the Impact of the Upstream Induction Zone on LIDAR Measurement Accuracy for Wind Turbine Control Applications using Large-Eddy Simulation

Several sources of error exist in lidar measurements for feedforward control of wind turbines including the ability to detect only radial velocities, spatial averaging, and wind evolution. This paper investigates another potential source of error: the upstream induction zone. The induction zone can directly affect lidar measurements and presents an opportunity for further decorrelation between upstream wind and the wind that interacts with the rotor. The impact of the induction zone is investigated using the combined CFD and aeroelastic code SOWFA. Lidar measurements are simulated upstream of a 5 MW turbine rotor and the true wind disturbances are found using a wind speed estimator and turbine outputs. Lidar performance in the absence of an induction zone is determined by simulating lidar measurements and the turbine response using the aeroelastic code FAST with wind inputs taken far upstream of the original turbine location in the SOWFA wind field. Results indicate that while measurement quality strongly depends on the amount of wind evolution, the induction zone has little effect. However, the optimal lidar preview distance and circular scan radius change slightly due to the presence of the induction zone.

LPV subspace identification using a novel nuclear norm regularization method

It is well-known that recently proposed Linear Parameter-Varying (LPV) subspace identification techniques suffer from a curse of dimensionality leading to an ill-posed parameter estimation problem. In this paper we will focus on regularization methods to solve the parameter estimation problem. Tikhonov and TSVD regularization are conventional general-purpose regularization methods. These general-purpose regularization methods give preference to a solution with a small 2-norm. In principle many other types of additional information about the desired solution can be incorporated in order to stabilize the ill-posed problem. The main contribution of this paper is that we propose a novel regularization strategy for LPV subspace methods: the nuclear norm regularization method. By applying state-of-the-art convex optimization techniques, the method stabilizes the parameter estimation problem by including information on the desired solution that is specific to the (LPV) subspace identification scheme. We will conclude the paper with a summarizing comparison between the different regularization techniques.

LPV Identification of Wind Turbine Rotor Vibrational Dynamics Using Periodic Disturbance Basis Functions

This brief presents an identification experiment performed on the coupled dynamics of the edgewise bending vibrations of the rotor blades and the in-plane motion of the drivetrain of three-bladed wind turbines. These dynamics vary with rotor speed, and are subject to periodic wind flow disturbances. This brief demonstrates that this time-varying behavior can be captured in a linear parameter-varying (LPV) model with the rotor speed as the scheduling signal, and with additional sinusoidal inputs that are used as basis functions for the periodic wind flow disturbances. By including these inputs, the predictor-based LPV subspace identification approach (LPV PBSIDopt) was tailored for wind turbine applications. Using this tailor-made approach, the LPV model is identified from data measured with the three-bladed Controls Advanced Research Turbine (CART3) at the National Renewable Energy Laboratorys National Wind Technology Center.

A Control-Oriented Dynamic Model for Wakes in Wind Plants

In this paper, we present a novel control-oriented model for predicting wake effects in wind plants, called the FLOw Redirection and Induction Dynamics (FLORIDyn) model. The model predicts the wake locations and the effective flow velocities at each turbine, and the resulting turbine electrical energy productions, as a function of the control degrees of freedom of the turbines (the axial induction and the yaw angle of the different rotors). The model is an extension of a previously presented static model (FLORIS). It includes the dynamic wake propagation effects that cause time delays between control setting changes and the response of downstream turbines. These delays are associated with a mass of air in the wake taking some time to travel from one turbine to the next, and the delays are dependent on the spatially- and time-varying state of the wake. The extended model has a state-space structure combined with a nonlinear feedback term. While including the control-relevant dynamics of the wind plant, it still has a relatively small amount of parameters, and the computational complexity of the model is small enough such that it has the potential to be used for dynamic optimization of the control reference signals for improved wind plant control.

A tutorial on control-oriented modeling and control of wind farms

Wind turbines are often sited together in wind farms as it is economically advantageous. However, the wake inevitably created by every turbine will lead to a time-varying interaction between the individual turbines. Common practice in industry has been to control turbines individually and ignore this interaction while optimizing the power and loads of the individual turbines. However, turbines that are in a wake experience reduced wind speed and increased turbulence, leading to a reduced energy extraction and increased dynamic mechanical loads on the turbine, respectively. Neglecting the dynamic interaction between turbines in control will therefore lead to suboptimal behaviour of the total wind farm. Therefore, wind farm control has been receiving an increasing amount of attention over the past years, with the focus on increasing the total power production and reducing the dynamic loading on the turbines. In this paper, wind farm control-oriented modeling and control concepts are explained. In addition, recent developments and literature are discussed and categorized. This paper can serve as a source of background information and provides many references regarding control-oriented modeling and control of wind farms.

Computational fluid dynamics simulation study of active power control in wind plants

This paper presents an analysis performed on a wind plants ability to provide active power control services using a high-fidelity computational fluid dynamics-based wind plant simulator. This approach allows examination of the impact on wind turbine wake interactions within a wind plant on performance of the wind plant controller. The paper investigates several control methods for improving performance in waked conditions. One method uses wind plant wake controls, an active field of research in which wind turbine control systems are coordinated to account for their wakes, to improve the overall performance. Results demonstrate the challenge of providing active power control in waked conditions but also the potential methods for improving this performance.

SOWFA + Super Controller User's Manual

SOWFA + Super Controller is a modification of the NRELs SOWFA tool which allows for a user to apply multiturbine or centralized wind plant control algorithms within the high-fidelity SOWFA simulation environment. The tool is currently a branch of the main SOWFA program, but will one day will be merged into a single version. This manual introduces the tool and provides examples such that a user can implement their own super controller and set up and run simulations. The manual only discusses enough about SOWFA itself to allow for the customization of controllers and running of simulations, and details of SOWFA itself are reported elsewhere Churchfield and Lee (2013); Churchfield et al. (2012). SOWFA + Super Controller, and this manual, are in alpha mode.