## L R

With R the length of the rotor blade and Nse the number of superelements the blade is subdivided in. The torsional spring constants in z-direction are determined analogously. Using the presented modeling approach a number of rotor blade models with different levels of complexity have been developed. The main features are listed in Table I.2. The integer appended to the basename Blade represents the number of superelements each blade has been subdivided in, while the characters xz indicate that...

## Summary main features in tabular form

The aformentioned features of the discussed state-of-the-art wind turbine design codes are summarized in two tables, Table 2.1, and Table 2.2, on the next two pages. The tabular form enables the reader to get quick and comparable information. It should be noted that the design codes are listed in alphabetical order i.e. the order does not express any rating. Design code features, with implemented in the design code, not not implemented in the design code, BEM Blade-Element-Momentum theory, FOS...

## Problem formulation

With this motivation and background in mind, the following problem can be formulated Develop a systematic methodology that generates accurate and reliable dynamic models suited for cost-effective design and operation of structurally flexible, variable speed wind turbines. It is recognized that solving the above problem is a huge challenge within the limited capacity and time available. As a consequence, we will confine our research to grid-connected, 3-bladed, horizontal-axis wind turbines...

## The future of wind power

The proliferation of wind turbines as a source of electricity in the future depends upon various economical, political, environmental, social and technical factors. The most important potential barriers for the large-scale development of both onshore and offshore wind energy are the relatively high kilowatt-hour price of wind-generated electricity, the public acceptance (especially in densely populated areas and coastal regions) and the impact on flora, fauna and landscape. On the other hand,...

## Stateoftheart of wind turbine design codes

In the introduction it was motivated that the availability of a dynamic model of a complete wind turbine is a necessity in view of the cost-effective design and operation of flexible, variable speed wind turbines. In the wind energy community there is a wide variety in different design codes that can be used to model a wind turbine's dynamic behavior. Each of them with advantages and disadvantages. In this chapter an inventory of the state-of-the-art of wind turbine design codes is made in...

## Costeffective wind turbine design and operation

Designing the cost-effective, grid-connected wind turbines that are required to materialize the presented outlook is a challenge given the fact these turbines are constantly competing with conventional power systems on the world market on the basis of the 2 Hereby assuming that the reduction in emissions is not counterbalanced by the expected increase in the worldwide electricity consumption. cost price of electricity per kilowatt-hour. At present, the conversion of wind power to electrical...

## Example three bladed wind turbine

For the purpose of illustration, Fig. 3.20 shows a superelement approximation of a three bladed wind turbine. Observe that both the tower and rotor blades are approximated by one superelement. Each superelement consists of three rigid bodies connected by two joints (marked o). Each joint (i.e. a universal joint since both blade and tower torsion is not considered in this thesis) has two degrees of freedom. This implies that this system has 18-DOF (exclusive pitch and azimuth). Obviously, the...

## Dynamic wind turbine model development

In Chapter 2 it has been concluded that the current wind turbine design codes are not suitable for design, and easy implementation of optimal operating strategies. Consequently, it is sensible to develop a new wind turbine design code. The models within this code should meet the requirements specified in Section 1.2. The fundamental requirement is, of course, that the models are suited for the design of optimal operating strategies. The layout of this chapter is as follows. Section 3.1 presents...

## Complete wind turbine

The main reasons are as follows the mechanical as well as the electrical module can be validated independently from both the aerodynamic and controller module. That is, under properly chosen experimental conditions, the bilateral couplings between these modules and the adjacent ones (see Fig. 3.14 on page 69) can be omitted. The aerodynamic module, on the other hand, can only be validated using data from an operating wind turbine. Observe that module verification can, for the greater part, be...

## Introduction

The DAWIDUM toolbox has been purpose-made to provide wind turbine designers and control engineers with a design tool that enables them to rapidly and easily build accurate dynamic models of wind turbines. The resulting non-linear dynamic models can be used to objectively compare and optimize different controllers to achieve improved performance and robustness. Because the models are fully parametric with physical meaningful parameters, the models can also be used to obtain an optimized wind...

## Stateoftheart variable speed wind turbine control

In a variable speed wind turbine, the rotor and the generator are decoupled from the grid by the power electronics implying that the rotor may rotate at (almost) any speed. Consequently, variable speed operation offers more control possibilities than constant rotational speed does. Variable speed operation has two main advantages over constant speed operation i) additional energy capture at partial load and ii) potential reduction of fatigue loads on the structure by absorbing torque...

## Modeling

In this section the main modeling options are discussed. We will start with the wind module library. DAWIDUM's wind module consists of two submodules, viz. deterministic and stochastic as illustrated in Fig. I.3. The deterministic submodule allows the following undisturbed wind inputs to be specified a uniform wind field (i.e. Vw is constant both in space and time), a sequence of upward and downward stepwise changes in the wind velocity, and the undisturbed wind velocity can be read from a user...

## Synchronous generator parameter identification

Synchronous machine identification and parameter determination can be performed either during normal operation (i.e. on-line), or during specially designed identification experiments (i.e. off-line) 90 . Each approach has advantages as well as disadvantages. For example, in the on-line case the measured input-output data reflect the actual operating conditions. A disadvantage is that it is not possible to manipulate the input signals arbitrarily in order to obtain the best identification...

## Motivation and background

The wind is a vast, worldwide renewable source of energy. Since ancient times, mankind has harnessed the power of the wind. The earliest known use of wind power is the sailboat. Wind energy propelled boats sailed up the Nile against the current as early as 5000 B.C. By 1000 A.D. the Vikings had explored and conquered the North Atlantic. The wind was also the driving force behind the voyages of discovery of the Verenigde Oost-Indische Compagnie (VOC) between 1602 and 1799. Windmills have been...

## Main wind turbine modes of operation

In this chapter the main wind turbine modes of operation will be discussed. In general, the following modes of operation can be distinguished 179 In the startup mode the rotor of the wind turbine is accelerated, and the generator is connected to the utility grid. In the power generation mode, power is extracted from the wind and converted to electricity. In this mode the wind velocity ranges from the cut-in wind velocity Vci, via the rated velocity Vr to the cut-out wind velocity Vco as...

## Overview wind turbine design codes

In the wind energy community the following design codes are commonly used to model and simulate the wind turbine dynamic behavior, as well as to carry out design calculations ADAMS WT (Automatic Dynamic Analysis of Mechanical Systems - Wind Turbine) 57 . ADAMS WT is an add-on package for the general-purpose, multibody package ADAMS. ADAMS WT is developed by Mechanical Dynamics, Inc. (MDI) under contract to the National Renewable Energy Laboratory (NREL), specifically for modeling...

## Frequency converter controller design

In the introduction it is stated that to reach economic viability, the design and operation of the complete wind turbine has to be optimized with respect to both cost and performance. Reduction of fatigue loads can significantly contribute to achieve this goal. The bandwidth of the active-pitch system, however, is in general too small to be able to achieve fatigue load reduction. As a result, pitch control should be used to follow minute-to-minute fluctuations in aerodynamic power, while the...

## Subproblem Modeling of flexible wind turbines

The wind turbine modeling sub-problem has been addressed in Part I (comprising Chapter 2 and Chapter 3). In Chapter 2 an inventory of the state-of-the-art of wind turbine design codes has been made. From this inventory it can be concluded that most of the design codes have been developed specially to deal with wind turbine design calculations and time-domain simulations, but are not suited to solve the main thesis problem. The main reasons are i) the absence of the indispensable bilateral...

## History of windmill and wind turbine control

Wind turbine control has a long history which was probably initiated by the regulation of the rotational speed of the Persian windmills in the tenth century A.D using a series of shutters. Another early example of a windmill regulation device is the mill-hopper which was used to regulate the flow of grain in a mill depending on the speed of rotation of the millstone by about 1588. The variability of the wind in both speed and direction was addressed and patented by the British blacksmith E. Lee...

## Flow states of a wind turbine rotor

In the previous chapters, a wind turbine is assumed to be operating in its intended state in which kinetic energy is extracted from the wind. The rotor converts the extracted energy into mechanical energy thereby producing a downwind force while slowing down the free-stream wind velocity accordingly. This operating state requires that the axial induction factor lies between zero and unity. This operating state comprises two so-called rotor flow states, notably the windmill and the turbulent...

## Introduction general wind turbine model

A horizontal-axis wind turbine basically consists of five physical components, viz. rotor, transmission, generator, tower including foundation and control system. The rotor converts wind power into mechanical power, which is represented by the product of torque and angular velocity of the rotor shaft. This velocity is increased by the transmission in order to come to an angular velocity well-suited for the generator. The generator in its turn converts the mechanical power into electrical power....

## Deterministic versus stochastic

For the design of an offshore wind turbine the wind generated waves are the most important 143 . The other types e.g. planetary waves, tsunamis, and capillary waves are either occurring beyond the relevant frequency range or their energy content is too small. Wind generated water waves are random in nature and contain energy in the frequency range of 0.05-0.5 Hz 144 . The wave velocity of these random waves is in the current design codes decomposed into a deterministic, and a stochastic wave...

## Mechanical module verification and validation

In this section DAWIDUM's systematic structural modeling procedure will be validated to justify the use of this procedure and the resulting models for both model based control design and design optimization purposes. Six cases are considered. In the first case the procedure is verified using a test case before applying it to real data. In the second till the fifth case measured non-rotating eigenfrequencies of wind turbine rotor blades are compared with those from the superelement...

## Blade tip and root effects

The BEM theory does not account for the effect of a finite number of rotor blades. Therefore a correction has to be applied for the interaction of the shed vorticity with the blade's bound vorticity. This effect is usually greatest near the blade tip, and it significantly affects the rotor torque and thrust. In principle, either an approximate solution by Prandtl 221 or a more exact solution by Goldstein 88 can be used to account for the non-uniformity of the induced axial velocity 55 . Both...

## Structural dynamics

In the early days of the wind industry, the effects of structural dynamics were either ignored completely, or included through the use of estimated dynamic magnification i.e. safety factors 228 . The increasing structural flexibility of wind turbines implies that their dynamic behavior, and our ability to model flexibility accurately, becomes more important 73 . Nowadays, the structural dynamics of wind turbines are approximated in three ways, notably using a multibody, finite element, and...

## Two degrees of freedom

Consider the two degrees of freedom 2-DOF system shown in Fig. G.4. The system consists of three rigid bodies connected by two ideal torsional springs Czi and Cz3 that model the elastic properties in bending direction. The damping is modeled by two viscous dampers, Keq 2 and Keq23 respectively. The input is the force F and the output is the displacement of the point action of F. Gravity is completely neglected. The equations of motion of the above 2-DOF system can be solved more easily using...

## Aerodynamic module

This section treats the aerodynamics. DAWIDUM's aerodynamic module has an input-output configuration as depicted in Fig. 3.4. The only input to this module is the undisturbed wind velocity Vw generated by the wind module. The aerodynamic module is bilaterally coupled to the mechanical module through the velocity vector x containing the blade movements with respect to the blade element reference frame , and the aerodynamic forces Faero. In other words, the interaction between the aerodynamics...

## Exact rotating eigenfrequencies

Now we will present exact solutions to the frequency equation for transverse vibrations of a rotating Euler-Bernoulli beam. The rotating beam is a particular case of the prestressed beam, of which the practical importance is considerable in the analysis of wind turbine rotor blades. It is a physical known fact that the eigenfre-quencies of a rotating beam raise due to the component of the centrifugal acceleration field along the beam leading to an additional stiffening term. This effect is in...

## Model verification and validation approach

In the first place, there is no single best approach to the assesment of the validity of a mathematical model. Statements about model validity must always been made in the context of the intended application. In this thesis, the developed models are intended to be used for both model based control design and design optimization of flexible wind turbines. This means that there is thus interest in model accuracy in predicting the steady-state conditions as well as in model accuracy with which the...

## History from windmill to wind turbine

The historic development of using wind as a source of power shows an evolution from simple drag-type vertical-axis windmills generating mechanical power for local use, via stand-alone wind turbines designed for battery charging and single grid-connected wind turbines producing AC power using aerodynamic lift, to wind farms supplying electricity to the utility grid for distribution to the consumers. In this subsection we shall briefly review this transition from windmills to wind turbines. The...

## Soil dynamics

Up to now, the effect of the flexibility of the foundation and its supporting soil has not been dealt with in this thesis. Soil is a non-linear material in which the stifness progressively decreases with increasing shear stress until, at a sufficient high stress level, plastic deformation takes place. Furthermore, when subjected to cyclic loading, soil exhibits damping which increases with increasing shear amplitude. Soil damping comprises two parts internal and radiation. The internal damping...

## Dynamic stall

Transient aerodynamics have another facet, called dynamic stall. Dynamic stall or stall hysteresis is a dynamic effect which occurs on aerofoils if the angle of attack changes more rapidly than the air flow around the blade or blade element can adjust. Dynamic stall was shown to occur under a variety of inflow conditions, including turbulence, tower shadow, and yawed flow 100 . The result is aerofoil lift and drag coefficients which depend not only on the instantaneous angle of attack...

## Wind field description

It has long been recognized that wind simulation should be an integral part of wind turbine structural design, and analysis. Now that the structural models become more sophisticated, adequate input to these models is essential in order to make full use of the increased accuracy. The wind input required to receive a license is laid down in design standards e.g. IEC-1400-1 standard 112 , NVN 11400-0 198 or Germanischer Lloyd 77 . In addition, a realistic wind input is also requisite in order to...

## Turbulent wake state

For high induced velocities exceeding approximately 40 of the free-stream velocity , the momentum and vortex theory are no longer applicable because of the predicted reversal of flow in the turbine wake. The vortex structure disintegrates and the wake becomes turbulent and, in doing so, entrains energetic air from outside the wake by a mixing process. Thereby thus altering the mass flow rate from that flowing through the actuator disk. The turbine is now operating in the so-called turbulent...

## Superelement approach

In the superelement approach, a part of a flexible body is approximated with a number of so-called superelements. Each symmetric superelement consists of 3 rigid bodies connected by joints marked o in Fig. 3.15 containing ideal torsional springs that model the elastic properties in bending direction. The attractive feature of modeling the flexibility by joint springs and dampers is that the spring and damper forces are readily incorporated into the standard rigid multibody body packages e.g. SD...

## D corrections

In the state-of-the-art design codes 2-D aerofoil data obtained from wind tunnel experiments at the appropriate Reynolds number is used to represent the aerodynamic properties of wind turbine rotor blades. Recall that wind tunnel data is obtained from measurements on non-rotating aerofoil sections, whereas the resulting lift, drag and moment coefficients are applied to rotating wind turbine blades. This approach leads to reasonable prediction of wind turbine loads for attached or equivalently...

## Propellor brake

B.1 indicates these five rotor flow states in the Cdax- a diagram. Wind turbines normally operate in the windmill state, with 0 lt a lt 0.5. Glauerts well-known, and well established blade element momentum theory is generally recommended for use in this flow state, resulting in the following relationship between the thrust coefficient and the axial induction factor This relationship can also be applied for negative axial induction factors i.e. a lt 0 . In this so-called propellor state...

## Synchronous generator physical description

In this subsection the physics of synchronous generators will be discussed since most electric power today is produced by synchronous generators 107 . In addition, the Lagerwey LW-50 750 is equipped with a synchronous generator. Synchronous generators are synchronous machines used to convert mechanical power into electrical power. Physically, most synchronous generators consist of a stationary part, called the stator, and a rotating part driven by an external torque, called the rotor. The...

## A Rotor blades

The rotor blades of the Lagerwey LW-50 750 - APX48 750 - are designed by the Stevin Laboratory of Delft University of Technology, The Netherlands 242 , and manufactured by Aerpac Special Products B.V., Hengelo, The Netherlands 241 . The rotor blades are designed for both full-span pitch-controlled and active stall regulated 3-bladed wind turbines. The APX-45 APX-48 rotor blade consists of two main parts a 3.75 m long non-aerodynamic part where the cylindrical contour is transformed into an...

## Automated structural modeling procedure

In Chapter 2 it has been observed that in most state-of-the-art wind turbine design codes an easy transfer from physical data available during the design of a new wind turbine to model parameters is missing. This situation should be changed in order to achieve an integrated and optimal wind turbine design. The superelement approach presented in Subsection 3.4.2 requires the specification of the mass, centroidal mass moment of inertia, length, location of the center of gravity, interconnection...

## Generation of the equations of motion of MBS

For a multibody system, the equations of motion are a set of ordinary differential equations ODE relating the accelerations to the time, the positions, the velocities, and the parameters of the system. There are various methods to derive the equations of motion of multibody systems. In order to be able to understand the differences between these methods, we will first highlight the roots of multibody system dynamics. As mentioned, the dynamics of multibody systems is based on classical...

## Dynamic inflow

The aerodynamic forces are, following the blade element momentum theory, calculated in a quasi-steady fashion, assuming at any instant in time an equilibrium between the load situation and the induced velocity. In other words the blade element momentum theory assumes that the induced velocity flow field react instantaneously to changes in blade loading. This treatment is in literature known as the equilibrium wake model. In the actual operation of a wind turbine its load situation is changing...

## Receptance Inertance Mobility Mass Examples

In structural and control engineering, the frequency response function is graphically plotted as log H s and arg H s against log w , which is called the Bode diagram or Bode plot. A few observations can be made. Examination of Eq. G.5 reveals that the natural frequency of a SDOF system with input and output configuration as selected, is equal to Furthermore, it is clear from Eq. G.6 that the DC-gain w 0 is equal to L 2 c, while for high frequencies w wn the asymptote has a slope of -2 on a...

## Superelement approximation

In this case, the Euler-Bernoulli beam has been modeled using a number of superelements. Again, the beam is built in at the base. The torsional spring constants for each superelement are determined as follows with E the modulus of elasticity, Iz the area moment of inertia, and Lse the length of the superelement which is, in turn, defined as with L the length of the Euler-Bernoulli beam and Nse the number of superelements the beam is subdivided in. The first four eigenfrequencies of the...

## Case APX rotor blade validation

In this subsection the measured non-rotating eigenfrequencies of an APX-45 wind turbine rotor blade are compared with those from the superelement approximation. The APX-45 rotor blades are designed by the Institute for Wind Energy of Delft University of Technology, The Netherlands 242 , and manufactured by Aerpac Special Products B.V., Hengelo, The Netherlands 241 . The rotor blades are designed for both full-span pitch-controlled and active stall regulated 3-bladed wind turbines. The blade has...

## Voorwoord

Promoveren Daaf gaat promoveren Deze reactie kreeg ik 6 jaar geleden vlak na mijn afstuderen te horen. Ik moest zelf ook even aan het idee wennen, maar de uitdaging om uit te zoeken of de stelling windenergie gratis en toch duur ontkrachtigd kon worden sprak mij zeer aan. De vrijheid en dus de mogelijkheden bij de sectie Systeem en Regeltechniek om dit doel te bereiken was voor mij de belangrijkste reden om voor de Technische Universiteit Delft en niet voor het ECN in Petten of Stork Product...

## Blade element momentum model

The combined blade element and momentum theory is an extension of the Rankine-Froude actuator disk theory described in Section 3.3.2. The blade element momentum theory divides the rotor blades into a number of radial blade sections elements , each at a particular angle of attack. These blade elements are assumed to have the same aerodynamic properties as an infinitely long or 2-D rotor blade with the same chord, and aerofoils. This implies that 2-D aerofoil data i.e. lift, drag and moment...

## Discussion

In the previous subsections four different rotor blades have been examined in order to justify the use of the proposed systematic structural modeling procedure and the resulting models for both model based control design and design optimization purposes. Measured non-rotating eigenfrequencies obtained via either hand-excited displacement measurements or a modal analysis are compared with those from both a finite element and the superelement approximation. The following observations can be made...

## Case Lagerwey LW wind turbine

The Lagerwey LW-50 750 wind turbine is located near Nieuwe-Tonge, Province of Zuid-Holland, The Netherlands. Fig. 4.13 shows a schematic of the measurement set-up of the full-scale modal test. The turbine was parked i.e. non-rotating during all testing. This implies that the bilateral coupling of the mechanical module to the electrical module, see Fig. 3.14 on page 69, can be omitted since the mechanical speed is equal to zero. Furthermore, the input from the aerodynamic module, Faero, is...

## The Lagerwey LW wind turbine

The Lagerwey LW-50 750 wind turbine is a 750 kW, variable speed wind turbine with an upwind rotor of 50.5-meter diameter. A picture of this turbine is shown in Fig. A.1. The LW-50 750 is located near Nieuwe-Tonge Province of Zuid-Holland, The Netherlands . The rotor consists of 3 blades that can be actively and individually pitched over the full span. The pitch control is used for power control at full load, and to stop the turbine if the safe operating limits are exceeded. The turbine is...

## Time series analysis

Figure 4.15 shows a typical tower top acceleration response in x-direction i.e. sensor A-05 from a parked modal test. Obviously, the stepwise change in the force applied to the tower top excites a wide range of natural frequencies. The relative high frequencies at the beginning of the response are damped out quickly, leaving eventually the single frequency associated with the lowest system mode of vibration. This mode is in literature often denoted with the misleading term first tower bending...

## Exact nonrotating eigenfrequencies

In Weaver et al. 305 it has been shown that the general solution for the transverse vibration of a uniform, non-rotating beam can be written as Y x Ci cos kx cosh kx C2 cos kx cosh kx 4.1 C3 sin kx sinh kx C4 sin kx sinh kx where Y defines the shape of the natural mode of vibration. The constants C1, C2, C3, and C4 in this expression are determined by satisfying boundary conditions at the ends of the beam. In the derivation of Eq. 4.1 it is assumed that the material is homogeneous, isotropic,...

## Rankine Froude actuatordisk model

The simplest and oldest mathematical model which describes the wind turbine dynamics is the Rankine-Froude actuator-disk model. The concept was introduced by R.E. Froude in 1889 68 , after W.J.M. Rankine 231 had introduced the momentum theory. In this model the rotor is replaced by an actuator-disk, which is a circular surface of zero thickness than can support a pressure difference, and thus decelerate the air through the disk. Physically, the disk could be approximated by a rotor with an...

## Calculation of the blade element forces

The aforementioned equations form the core of the aerodynamic description of the rotor behavior in DAWIDUM. Observe from Fig. 3.11 on page 58 or Eq. 3.27 on page 59 that the instantaneous undisturbed wind velocity W is composed of the vector sum of the perpendicular wind velocity Vp corrected for axial induction , and the tangential wind velocity Vt corrected for tangential induction . Obviously, Vp and Vt are expressed in the blade element local frame of reference and result from the...