Simplified Wind Turbine Model Research Articles

A Positive Position Feedback controller for vibration control of wind turbines

Wind energy has become one of the most important energy sources in the last decades. Most of this type of energy comes from turbines installed onshore though there has been a paradigm shift in this field with the installation of offshore wind turbines, anchored to the seabed or floating ones. Both offshore and onshore technologies have a set of associate problems which sometimes can compromise the turbine integrity, such as environmental disturbances or harmful vibrations. Most of these vibrations and loads are actively compensated in commercial wind turbines through strategies which can modify the turbine power reference to reduce the tower and blades oscillations, at the expense of compromising efficiency. In this work, a new type of control vibration for wind turbines based on piezoelectricity is proposed. A closed loop control is developed from the sensing of the tower vibrations, followed by an in-house designed Positive Position Feedback (PPF) controller, and with a control signal applied to the piezoelectric transducers working as actuators. To design the PPF controller, a simplified wind turbine model is created in COMSOL Multiphysics. A state-space model is obtained, parametrized, validated and used for the tuning of the PPF controller presented in this paper. Simulation results show that with a set of piezoelectric transducers located along the turbine tower, significant reduction of the tower vibrations can be achieved.

Data-based Identifiability and Observability Assessment for Nonlinear Control Systems using the Profile Likelihood Method

This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Data-Based Identifiability and Observability Assessment for Nonlinear Control Systems Using the Profile Likelihood Method

Abstract This paper introduces the profile likelihood method in order to assess simultaneously the parameter identifiability and the state observability for nonlinear dynamic state-space models with constant parameters. While a formal definition of a parameter’s identifiability has been used before, the novel idea is to investigate also the state’s observability by the identifiability of its initial value. Using the profile likelihood, both qualitative as well as quantitative statements are drawn from the analysis based on the nonlinear model and (possibly noisy) sensor data. A simplified wind turbine model is presented and used as an application example for the profile likelihood approach in order to investigate the model’s usability for state and parameter estimation. It is shown that the critical model parameters and initial states are identifiable in principle. The analysis with more complex models and realistic data reveals the limitations when assumptions are deliberately violated in order to meet reality.

Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

AbstractWith the ever increasing power rates of wind turbines, more advanced control techniques are needed to facilitate tall towers that are low in weight and cost‐effective but in effect more flexible. Such soft‐soft tower configurations generally have their fundamental side‐side frequency in the below‐rated operational domain. Because the turbine rotor practically has or develops a mass imbalance over time, a periodic and rotor‐speed dependent side‐side excitation is present during below‐rated operation. Persistent operation at the coinciding tower and rotational frequency degrades the expected structural life span. To reduce this effect, earlier work has shown the effectiveness of active tower damping control strategies using collective pitch control. A more passive approach is frequency skipping by inclusion of speed exclusion zones, which avoids prolonged operation near the critical frequency. However, neither of the methods incorporates a convenient way of performing a trade‐off between energy maximization and fatigue load minimization. Therefore, this paper introduces a quasi‐linear parameter varying model predictive control (qLPV‐MPC) scheme, exploiting the beneficial (convex) properties of a qLPV system description. The qLPV model is obtained by a demodulation transformation and is subsequently augmented with a simple wind turbine model. Results show the effectiveness of the algorithm in synthetic and realistic simulations using the NREL 5‐MW reference wind turbine in high‐fidelity simulation code. Prolonged rotor speed operation at the tower side‐side natural frequency is prevented, whereas when the trade‐off is in favor of energy production, the algorithm decides to rapidly pass over the natural frequency to attain higher rotor speeds and power productions.

Wind farm interference and terrain interaction simulation by means of an adaptive actuator disc

Wind turbine wake interference is a relevant phenomenon that involves speed losses and turbulence increments which greatly affect downstream turbines, and power efficiency of wind farms. To precisely simulate wake interaction, the most common simplified wind turbine model, the Actuator Disc (AD) model, is improved adding the capability to adapt the thrust force distribution to a non-uniform velocity field over the disc, and the orientation to different local wind directions. These situations are typically found in wind farm situation where turbines interact with wakes of upstream turbines and the terrain. This development is based on the OpenFOAM open source finite volume parallel software. The improved AD model is first validated against wind tunnel experiments. Then, an onshore wind farm case is presented, in which the complex interaction of the turbines and terrain is studied. Comparing with power efficiency of field measurements, the simulations succeed to capture the characteristic values for low and high wake impact situations, with differences of 2.5% and 1.3%, respectively. Results show that this improved AD model produces a better solution for wake interaction cases. Its usefulness to predict the wind farm power output at feasible computational cost is also evidenced.

Optimization of a tuned liquid column damper subject to an arbitrary stochastic wind

The current Brazilian energy scenario is undergoing impactful changes. There is a clear need to adjust the current energy sector that presents an imbalance due to the almost exclusively dependency on hydroelectric power. This brings the need of diversifying the Brazilian energy matrix, including other energy sources that are both efficient and renewable. Amongst the available options, the wind energy stands out. Remarkable progress in wind turbine technology has been made over the past years, allowing the design of higher and slender structures for increasing efficiency in energy production. Parameter optimization for tuned liquid column dampers (TLCD), a class of passive structural control, has been previously proposed in the literature for reducing vibration in wind turbines and several other applications. However, most of the available work considers the wind excitation as either a deterministic harmonic load or random load with white noise spectra, which might not be representative of the actual wind load. This paper proposes an optimization approach for the TLCD parameters subjected to an arbitrary wind spectrum, given that its power spectral density is know. Finally, a numerical example is given in which a simplified wind turbine model is loaded by different stochastic wind profiles. Satisfactory reduction in the response vibration levels is found, and it is shown that different wind profiles can significantly affect the optimization results, i.e. the best TLCD parameters are dependent on the wind model.

Scaling of wind energy conversion system for time-accelerated and size-scaled experiments

This paper presents a scaling methodology based on dimensional analysis and applicable to systems’ mathematical models. The main goal of this research is to propose time-accelerated and size-scaled HIL (Hardware In the Loop) experiments, while keeping similarity with respect to the dynamics of the original system. The scaling process is presented using a simple wind turbine model. The scaling method is validated through simulations in which a wind turbine model and an electrochemical battery model are connected together. Finally, an experimental real-time validation is performed using physical emulators.

Modal dynamics of structures with bladed isotropic rotors and its complexity for two-bladed rotors

Abstract. The modal dynamics of structures with bladed isotropic rotors is analyzed using Hill's method. First, analytical derivation of the periodic system matrix shows that isotropic rotors with more than two blades can be represented by an exact Fourier series with 3/rev (three per rotor revolution) as the highest order. For two-bladed rotors, the inverse mass matrix has an infinite Fourier series with harmonic components of decreasing norm; thus, the system matrix can be approximated by a truncated Fourier series of predictable accuracy. Second, a novel method for automatically identifying the principal solutions of Hill's eigenvalue problem is introduced. The corresponding periodic eigenvectors can be used to compute symmetric and antisymmetric components of the two-bladed rotor motion, as well as the additional forward and backward whirling components for rotors with more than two blades. To illustrate the use of these generic methods, a simple wind turbine model is set up with three degrees of freedom for each blade and seven degrees of freedom for the nacelle and drivetrain. First, the model parameters are tuned such that the low-order modal dynamics of a three-bladed 10 MW turbine from previous studies is recaptured. Second, one blade is removed, leading to larger and higher harmonic terms in the system matrix. These harmonic terms lead to modal couplings for the two-bladed turbine that do not exist for the three-bladed turbine. A single mode of a two-bladed turbine will also have several resonance frequencies in both the ground-fixed and rotating frames of reference, which complicates the interpretation of simulated or measured turbine responses.

Aerodynamic Modeling of NREL 5-MW Wind Turbine for Nonlinear Control System Design: A Case Study Based on Real-Time Nonlinear Receding Horizon Control

The work presented in this paper has two major aspects: (i) investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory) 5-MW reference wind turbine; (ii) nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.

A Simplified Electro-Mechanical Model of a DFIG-based Wind Turbine for Primary Frequency Control Studies

In recent years, world-wide power systems are experiencing a steadily growth of wind power penetration. A common concern in the operation of such systems is related to the frequency stability. Modern variable speed wind turbines have a limited capacity in providing ancillary services, such as fast-frequency response and primary frequency regulation. Recent developments in wind plant controllers allow performing active power control from all its units to respond to system frequency deviations. It is thus important to study the effects of the presence of these plants in the system frequency response. Existing detailed models of wind turbines are not suitable to this goal because their complexity makes them impractical for system-wide studies. This paper presents a simplified model of a wind turbine with Doubly-Fed Induction Generator specifically conceived for such studies, along with its validation with a detailed model.

Power System Voltage Control Using Wind Farms Based on a Doubly Fed Induction Generation (DFIG)

This paper shows the modeling and the effectiveness of wind turbine for voltage improvement of power systems. The wind turbine is based on a doubly-fed induction generator (DFIG). A field-oriented control is used to control of the power flow exchanged between the DFIG and the power system. A simplified wind turbine model based on independent control of active and reactive powers is used in this paper. The proposed methodology is tested in the single machine power system connected to a wind farms in the case of sudden voltage variations.

Investigation of a Speed Exclusion Zone to Prevent Tower Resonance in Variable-Speed Wind Turbines

A speed exclusion zone algorithm to prevent the rotor rotational frequency from exciting the side-side tower mode in a variable-speed wind turbine was designed. The algorithm was first tested on a simple wind turbine model developed in Simulink and then implemented and tested on an experimental test rig. Different speed exclusion zone widths were tested to observe how the performance of the wind turbine is affected. Results obtained from both simulations and experiments showed the effectiveness of the speed exclusion zone algorithm in preventing excitation of tower resonance. Results from different speed exclusion zone widths showed that with a wider exclusion zone, the tower mode is excited less at the expense of a larger power loss.

Research on the Compensation Coefficients of the Improved MPPT Control Based on Reduction of Tracking Range

The improved maximum power point tracking (MPPT) control based on the reduction of tracking range could reduce the tracking distance of wind turbine effectively, and improve the tracking efficiency. In this study, the relationship between the compensation coefficient of the improved MPPT control and several factors was investigated. Based on simulations of the simplified wind turbine model, wind conditions, air density and wind turbine parameters were used in the studies to investigate the relationship between the optimum compensation coefficients and these corresponding conditions. It can be indicated that in the fact, compensation coefficient is majorly determined by the tracking targets of MPPT and the dynamic performance of wind turbines that determined by the conditions mentioned above. The results also provide guidance for further studies in this area.

Wind turbine wake properties: Comparison between a non-rotating simplified wind turbine model and a rotating model

Experimental results on the wake properties of a non-rotating simplified wind turbine model, based on the actuator disc concept, and a rotating model, a three-blade wind turbine, are presented. Tests were performed in two different test sections, one providing a nominally decaying isotropic turbulent inflow (turbulence intensity of 4% at rotor disc location) and one providing a neutral atmospheric boundary layer above a moderately rough terrain at a geometric scale of 1:300 (determined from the combination of several indicators), with 13% of turbulence intensity at hub height. The objective is to determine the limits of the simplified wind turbine model to reproduce a realistic wind turbine wake. Pressure and high-order velocity statistics are therefore compared in the wake of both rotor discs for two different inflow conditions in order to quantify the influence of the ambient turbulence. It has been shown that wakes of rotating model and porous disc developing in the modeled atmospheric boundary layer are indistinguishable after 3 rotor diameters downstream of the rotor discs, whereas few discrepancies are still visible at the same distance with the decaying isotropic turbulent inflow.

Torsional Damping considering Both Shaft and Blade Flexibilities

A three-mass mechanical model that considers both shaft and blade flexibilities was used for the design of a torsional damper to damp drive-train vibrations in a wind turbine. Two torsional dampers were designed: one considering only the drive-train mode and another considering both the drive-train and blade in-plane symmetrical modes. The dampers performance was tested on a simple wind turbine model in Simulink® and then implemented in a more complete model in GH Bladed®. The simulation results on both wind turbine models correlate very well. This result indicates that a three-mass model is a good model for representing the shaft and blade flexibilities for designing a torsional damper. Simulation results show that considering both drive-train and blade in-plane mode frequencies when designing the torsional damper can lead to a better performance in damping torsional vibrations.

Fault Detection and Isolation and Fault Tolerant Control of Wind Turbines using Set-Valued Observers

Research on wind turbine Operations & Maintenance (O&M) procedures is critical to the expansion of Wind Energy Conversion systems (WEC). In order to reduce O&M costs and increase the lifespan of the turbine, we study the application of Set-Valued Observers (SVO) to the problem of Fault Detection and Isolation (FDI) and Fault Tolerant Control (FTC) of wind turbines, by taking advantage of the recent advances in SVO theory for model invalidation. A simple wind turbine model is presented along with possible faulty scenarios. The FDI algorithm is built on top of the described model, taking into account process disturbances, uncertainty and sensor noise. The FTC strategy takes advantage of the proposed FDI algorithm, enabling the controller reconfiguration shortly after fault events. Additionally, a robust controller is designed so as to increase the wind turbine's performance during low severity faults. Finally, the FDI algorithm is assessed within a publicly available benchmark model, using Monte-Carlo simulation runs.

Gust load reduction concept in wind turbines

AbstractA concept is presented of gust alleviation in wind turbines by using the blade aerodynamic torsional moment as an actuator for forcing the blade to feather in order to reduce aerodynamic loads. The pitching to feather is implemented through a temporary release of the blade‐hub torsional connection after that the blade rotates freely until it reaches the assumed pitch angle. To describe this process, a simple wind turbine model with three elastic blades is formulated and some numerical simulations are performed. The results of the simulations include, among others, the time‐history of the out‐of‐plane blade bending moment in response to the uniform gust, showing that, in this way, it is possible—at least theoretically—to reduce this moment by approximately 2/3 of its peak value. Moreover, the blade pitch angle changes faster than increased by a regular control actuator. Copyright © 2009 John Wiley & Sons, Ltd.

Identification of equivalent modal damping for a wind turbine at standstill using Fourier and wavelet analysis

The current paper presents approaches to evaluate the equivalent modal viscous damping ratios for a wind turbine tower, using Fourier and wavelet analysis based linear regression. In the Fourier analysis, the estimated damping ratios are constant, but in the wavelet analysis, temporally varying damping ratios using a time-segmented least squares approach can be identified. The estimation of time varying damping is important in assessing the risk of negative aeroelastic damping in wind turbines. In absence of experimental data, the proposed approaches have been illustrated on numerically simulated response obtained from a simple wind turbine model. The model used for generating the response time history data for the wind turbine tower is composed of a flexible tower and rotor blade system, inter-connected using a substructuring technique, which facilitates the blade/tower coupling. A model order reduction technique is first used to model each of the two substructures (tower/nacelle and rotor system) as single-degree-of-freedom systems (DOF), allowing both systems to be later coupled together to form an equivalent two-DOF coupled tower/blade wind turbine tower model with equivalent viscous damping. A wind-induced forced vibration analysis of the coupled system is then carried out using artificially generated wind drag time histories. Two identification procedures based on (a) Fourier and (b) wavelet analysis, and linear regression, are used to solve the inverse problem for evaluating the first- and second-equivalent modal damping ratios of the coupled system. For the numerical example presented in order to demonstrate the applicability of the proposed approaches, good agreement was observed between the originally specified modal damping ratios and the subsequently estimated values. The estimation of damping using wavelet analysis techniques can be applied to situations where damping may vary with time. The proposed approaches can be used without any limitation on response data obtained for more complex models of turbines and loadings or on experimentally measured data from wind turbines.

Modelling and control of synchronous generators for wide‐range variable‐speed wind turbines

AbstractThe modelling and control of a wide‐range variable speed wind turbine based on a synchronous generator are presented. Two different methods to control the operation of the synchronous generator are investigated, i.e. load angle control and instantaneous vector control. The dynamic performance characteristics of these control strategies are evaluated and compared using three model representations of the generator: a non‐reduced order model including both stator and rotor transients, a reduced order model with stator transients neglected, and a steady‐state model that neglects generator electrical dynamics. Assessment on the performance of grid‐side controller is shown during network fault and frequency variation. A simplified wind turbine model representation is also developed and proposed for large‐scale power system studies. Simulation results in Matlab/Simulink are presented and discussed. Copyright © 2007 John Wiley & Sons, Ltd.