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...
C Superelement approximation
In this case, the Euler-Bernoulli beam has been modeled using a number of superelements. Each superelement consists of a series of three rigid bodies connected by springs Cz and Cz3 as depicted in Fig. C.2. 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...
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...
Electrical module verification and validation
In this section the electrical module will be validated to justify the use of this model for model based control design purposes. First, a brief review of the existing literature on synchronous machine identification and parameter determination is given. Next, a new procedure is developed using ideas from Touhami et al. 291 for identifying the transfer functions of Park's dq-axis model of a synchronous generator from time-domain standstill step-response data. This procedure is applied to the...
Timedomain responses
In Fig. 4.20 and 4.21 the measured and simulated tower top acceleration response in x-direction are compared. To ensure that the simulation starts in steady-state, the equilibrium point has been determined, and the corresponding state vector has been saved. This state vector is used as initial condition in the performed simulation. From the figures it is clear that the SDLW1 model accurately describes the real response. Note that the time-domain response depends on the unknown viscous damper...
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...
Subproblem Modeling of flexible wind turbines 1
First of all, given the fact that considerable effort has been put in the development of DAWIDUM, a warm recommendation is given to fully exploit the potential of this new wind turbine design code. This requires the joint effort of all DUWIND members to develop and implement new models as well as wind turbine specific analysis and control design tools. In addition, the code must be extended with a wave and hydrodynamic module required to compute the water wave forces acting on the support...
Subproblem Model based control design 1
The model based control design sub-problem has been addressed only briefly. The main aspects that seem to be worthwhile to be investigated in more detail are listed below Electrical module. The robustness of for example different values of the rotational speed of the developed PI current controllers need to be assessed. In addition, attention must be paid to the minimization of power losses Economic control design. More effort must be put in the design of an economic control design criterion...
Literature review
The design of a robust frequency converter controller for high dynamic performance requires that the synchronous generator model parameters are known accurately. In principle, synchronous machine parameters may be determined either from design calculations or from measurements acquired at the factory or on site. For high dynamic performance control, however, the former approach is inadequate. A primary goal of this section is to address the latter issue. Many papers have been published on...
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...
Introduction Exk
Model parameter updating or model parameter tuning can be defined as a modelbased methodology for the reconciliation of measured and simulated data. In other words, the goal of model parameter updating is to improve the accuracy of mathematical models by adjusting the tunable parameters so that the differences between simulated and measured dynamic properties vanish. A question that can be asked is What is the relationship between model parameter updating and system identification Recall that...
G 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...
H Transfoshunt
The field winding is during the D-measurement short-circuited by a shunt. The name plate data of the used shunt is listed in Fig. H.2. Figure H.2 Name plate data of transfoshunt. Figure H.2 Name plate data of transfoshunt.
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...
Blackbox model structures
For single-input, single-output SISO systems, the general linear, time invariant LTI , black-box model structure is given by A q y t q -nk f u t Dq e t 5.3 where u t the input signal, y t the output signal, e t a white noise signal, A, B, C, D, and F are polynomials in the delay operator q -i The numbers na, nb, nc, nd, and nf are the orders of the respective polynomials. The number nk is the pure time delay the dead-time from input to output. Notice that for a sampled data system, nk is equal...
F Data acquisition system
Two supervisory control and data acquisition systems SCADAS II of Leuven Measurement Systems LMS with each 24 channels are used to store the time-domain as well as frequency domain data 249 . The name plate data of both SCADAS are listed in Fig. F.2. Figure F.2 Name plate data of LMS-DIFA SCADAS II data acquisition system. The programmable dual filter amplifier PDFA module in the LMS-DIFA SCA-DAS II is a universal signal conditioning module providing two identical, but each independently...
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...
Case EulerBernoulli beam verification
For verification of the proposed systematic structural modeling procedure, we will present here the exact solutions to the frequency equation for transverse vibrations of an Euler-Bernoulli beam for both the non-rotating and the rotating case 305 . That is, the Euler-Bernoulli beam will be analysed as an elastic body in which the mass and deformation properties are continuously distributed. In general, it is very difficult if not impossible to treat real mechanical structures as elastic...
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
Fig. 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...
Introduction Avv
The accurate computation of the aerodynamic forces is a very challenging problem. First of all, the wind environment in which wind turbines generally operate is variable both in space and time and has a strong stochastic content. Because the dimensions of atmospheric turbulence are of the same order as the rotor diameter, individual blades can be engulfed in coherent turbulence bells which lead to severe fatigue loading that significantly can reduce the lifetime of the structure. Secondly, the...
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...
Dawidum
Figure I.1 Welcome window of DAWIDUM. After starting up DAWIDUM, and subsequently pressing the Continue-button in the Welcome to DAWIDUM window, the main window is opened. This window is depicted in Fig. I.2. The main window has been divided into three parts Menu bar. At the top of the window you will find the menu bar. Via the options on the menu bar you can either create a new or modify an existing a wind turbine model, optimize model parameters using measured data, start a simulation,...
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...
Persistence of excitation
It is straightforward to understand that the character of the input signal that is applied during an experiment highly determines the amount of relevant information that is present in the data. For example, applying a constant input signal u t c, t e 0, ,tf c a constant, and tf the final time to the system will not result in an output signal that contains any information on the dynamics of the system. Observe that in this case only static behavior can be uniquely determined. Consequently, in...
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...
F Accelerometers
Three types of accelerometers are used, viz. Endevco model 2262A-25, Endevco model 2262A-200, and Sundstrand model QA-700. The Endevco accelerometers are rugged, fluid damped transducers of the piezoresistive type. The output range of model 2262A-25 is 25 g, and of model 2262A-200 200 g. Both models are light weight 28 gram , high-sensitivity 20 mV g and 2.5 mV g respectively at 100 Hz . The static acceleration limit is 250 g for model 2262A-25 and 1000 g for model 2262A-200. The frequency...
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...
X 1
Figure 4.7 Schematic of the APX-45 rotor blade and its two superelement approximation, with O 2 degrees of freedom rotational joints. The blade structural properties in reality differ from their designed values due to uncertain material parameters and manufacturing tolerances. The APX-45 rotor blades are produced by moulding processes using composite materials of which the material properties are not known exactly. The upper and lower blade surfaces are manufactured separately in two moulds by...
Model parametrization
The way in which the parameters enter into the model is determined by the parametrization. Formally, a parametrization n is a surjective mapping that maps the parameter vector 0 onto a specific model M 0 of a model class M as follows Clearly, different values of 0 produce different models. There are many different ways of parametrizing sets of models as meant above. For example, in black-box system identification the most common model set is described in terms of fractions of polynomials e.g....
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 APX rotor blade validation 1
As discussed in the previous subsection, the relative frequency error is most likely to be associated with the fact that the blades are manufactured by hand-lay-up and quality of the applied experiments and resulting eigenfrequency determination. In order to check those assumptions, the measured non-rotating eigenfrequencies of an APX-70 wind turbine rotor blade are in this subsection compared with those from the superelement approximation. The APX-70 rotor blade is suited for pitch controlled...
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...
A 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,...