J.W. van Wingerden

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.

Closed-loop control wind tunnel tests on an adaptive wind turbine blade for load reduction

Wind tunnel tests on a non-rotating, dynamically scaled wind turbine blade equipped with variable trailing edge geometry were carried out. The effectiveness of the system for active load reduction purposes, with the interaction between structural dynamics, aerodynamics and control was tested. The actuation of the adaptive trailing edge was based on a piezoelectric bender actuator. The full aeroservoelastic system was identified based on input and output measurement signals. A feedback controller, using strain signals on the blade root, was designed, tuned and applied on the system in order to minimize root bending moments. The results show remarkable performance in reduction of blade root strains for both open-loop and closed-loop tests. The sensitivity of various design and control parameters are analyzed both in the prescribed cases and in the feedback-controlled system.

Linear Parameter Varying Identification of Freeway Traffic Models

This paper deals with linear parameter varying (LPV) modeling and identification of a generic, second-order freeway traffic flow model. A non-conventional technique is proposed to transform the nonlinear freeway traffic flow model into a parameter-dependent form. The resulting exact LPV model is equivalent to the original nonlinear dynamics. Simplification of the nonlinear model gives rise to the introduction of an approximate LPV description. The application of parameter varying identification approaches are made possible by the transformation. Closed-loop predictor-based subspace identification for LPV systems (PBSID LPV) is applied to estimate the affine parameter matrices of the LPV freeway models developed. If the model structure of the original plant is assumed to be known, this paper shows a solution how to estimate LPV model parameters based on the identified model. Parameter-dependent models are identified and validated using real detector measurement data in order to emphasize the applicability of the kernel PBSID LPV methodology. Comparison with traditional nonlinear parametric identification, generally used in traffic identification, is also provided.

Fast-Array Recursive Closed-Loop Subspace Model Identification

Abstract In this paper a subspace model identification algorithm is presented that can be implemented recursively to track slowly time-varying linear systems operating in open loop and closed loop. Particular attention is paid to the computational cost and tracking performance of the developed identification algorithm. The identification problem is described by only two linear problems. The computational complexity is reduced by using array algorithms to solve these linear problems and exploiting the structure in the vectors. This results in a fast implementation of the developed recursive identification algorithm. The effectiveness of the proposed algorithm in comparison with existing methods is emphasized with a simulation study on a time-varying closed-loop system.

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.

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.

Subspace IDentification of MIMO LPV systems: The PBSID approach

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence operating under open and closed-loop conditions. A factorization is introduced which makes it possible to form predictors which are based on past inputs, outputs, and scheduling data. The predictors contain the LPV equivalent of the Markov parameters. Using the predictors, ideas from Predictor Based Subspace IDentification (PBSID) are developed to estimate the state sequence from which the LPV system matrices can be constructed. A numerically efficient implementation is presented.

Subspace identification of multivariable LPV systems: a novel approach

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence. Ideas from closed-loop LTI subspace identification are used to formulate the input-output behavior of an LPV system. From this input-output behavior the LPV equivalent of the Markov parameters can be estimated. We show that with this estimate the product between the observability matrix and state sequence can be reconstructed and an SVD can be used to estimate the state sequence and consequently the system matrices. The curse of dimensionality in subspace LPV identification will appear and the kernel method is proposed as a partial remedy. The working of the algorithm is illustrated with two simulation examples.