Design against buckling 1
Given perfect geometry, the strength of a cylindrical steel tube in axial compression is the lesser of the yield strength and the elastic critical buckling stress, given by where r is the cylinder radius and t is the wall thickness. Yield strength governs for r 1 less than 0.605E fy, which equates to 506 for mild steel, with fy 245 MPa. However, the presence of imperfections, particularly those introduced by welding, means that the tower-wall compression resistance is significantly reduced,...
Connection of embedded wind generation
Distribution utilities have an obligation to operate the electrical distribution networks in such a way as to provide power to their customers at an agreed quality. At present, power quality requirements are based on national standards although a common European position is emerging described in British Standard 1995b . However, it should be noted that this document describes minimum standards of supply which a customer may expect and is not directly applicable to the connection of embedded...
Info Oha
Evaluate the dynamic factor, QD, for the blade root bending moment for a 20 m long stationary blade under extreme loading. Consider a trial 20 m long blade design designated Blade TR utilizing NACA 632XX aerofoil sections with the chord and thickness distributions shown in Figure 5.2 a . The thickness distribution has a pronounced knee near mid span to minimize the thickness to chord ratio in the outer half of the span. Assuming a uniform skin thickness along the blade, apart from local...
Control of tower vibration
For both fixed and variable-speed machines the influence of the pitch controller on tower vibration and loading, described in Section 8.2.1, is one of the major constraints on the design of the control algorithm. The first tower fore-aft vibra-tional mode is essentially very lightly damped, exhibiting a strong resonant response which can be maintained at quite a high level even by a small amount of excitation which is naturally present in the wind. The strength of the response depends...
Nacelle Bedplate
The functions of the nacelle bedplate are to transfer the rotor loadings to the yaw bearing and to provide mountings for the gearbox and generator. Normally it is a separate entity, although in machines with an integrated gearbox, the gearbox casing and the nacelle bedplate could, in principle, be a single unit. The bedplate can either be a welded fabrication consisting of longitudinal and transverse beam members or a casting sculpted to fit the desired load paths more precisely. One fairly...
Braking loads
Most turbines have the mechanical brake located on the high-speed shaft, with the result that braking loads are transmitted through the gearbox. If, as is usually the case, the mechanical brake is one of the two independent braking systems required, then it must be capable of decelerating the rotor to a standstill from an overspeed, e.g., after a grid loss. This typically requires a torque of about three times rated torque. The mechanical brake is only required to act alone during emergency...
Constraints on firstmode natural frequency
As noted in Section 6.14, it is important to avoid the excitation of resonant tower oscillations by rotor thrust fluctuations at blade-passing frequency or, to a lesser extent, at rotational frequency. Dynamic magnification impacts directly on fatigue loads, so the further the first-mode tower natural frequency is from the exciting frequencies, the better. Unfortunately, it is generally the case that the natural frequency of a tower designed to be of adequate strength for extreme loads is of...
Project finance
Large companies e.g., power utilities or major energy companies may choose to develop small wind-farm projects using their own capital resources. The costs of the project are met from the general equity raised by the company with the liabilities of the project secured against the main corporate assets. The cost of borrowing, which influences the required discount rate for the project, depends on the financial strength of the company and it is possible to avoid the considerable expense involved...
R Nuo
My.CF r - m r Q2r p r - r dr 5 . 74 6 calculate combined bending moment distribution 7 calculate new deflected profile resulting from this bending moment distribution 8 calculate revised estimate of natural frequency from Tip deflection calculated for new deflected profile 9 repeat steps 2 - 8 with revised mode shape and frequency until calculated mode shape converges. It is important to note that the lateral loads and deflections of a centrifugally loaded beam do not conform to Betti's Law,...
A Definition of Drag
The drag on a body immersed in an oncoming flow is defined as the force on the body in a direction parallel to the flow direction. In a very slow-moving fluid the drag on a body may be directly attributable to the viscous, frictional shear stresses set up in the fluid due to the fact that, at the body wall, there is no relative motion. This type of flow is known as Stokes' flow after Sir George Stokes. Two centuries before Stokes, Isaac Newton showed that that the shear stress t at a boundary...
C 1
tangential flow induction factor at the blade tip two-dimensional lift curve slope, dCi da constant defining magnitude of structural damping upstream and downstream stream-tube cross-sectional areas face width of gear teeth blade chord Weibull scale parameter damping coefficient per unit length generalized damping coefficient with respect to the ith mode decay constant Theodorsen's function, where v is the reduced frequency C v F v iG v sectional drag coefficient sectional force coefficient...
Stationary Blade Loading Lift and drag coefficients
Maximum blade loadings are in the out-of-plane direction and occur when the wind direction is either approximately normal to the blade, giving maximum drag, or at an angle of between 12 and 16 to the plane of the blade when the angle of attack is such as to give maximum lift. In the absence of data on drag coefficients for airflow normal to the blade, designers formerly utilized the drag coefficient for an infinitely long flat plate of 2.0, with an adjustment downwards based on the aspect...
Drivetrain Mounting Arrangement Options Lowspeed shaft mounting
The functions of the low-speed shaft are the transmission of drive torque from the rotor hub to the gearbox, and the transfer of all other rotor loadings to the nacelle structure. Traditionally the mounting of the low-speed shaft on fore and aft bearings has allowed these two functions to be catered for separately the gearbox is hung on the rear end of the shaft projecting beyond the rear bearing and the drive torque is resisted by a torque arm. The front bearing is positioned as close as...
Fatigue properties
When expressed in terms of stress, the fatigue properties of composite laminates extend over a wide range, depending on fibre volume fraction and the number of plies with fibres in the longitudinal direction. However, data from constant stress amplitude fatigue test results become much more intelligible if stress ranges are converted into initial strain ranges, allowing the fatigue properties of composites with different lay-ups to be compared. The Young's modulus of a composite reduces over...
h Xpk
The derivation of these expressions parallels that for the absolute values of displacement and velocity at the end of the time step, given in Section 5.8.5. Similar expressions obtain for the displacement and velocity increments at the hub due to tower flexure. 5 Solve Equations 5.108 and 5.114 for the accelerations at the end of the time step. 6 Solve the incremental equations of motion again - this time including the changes in the coupled terms on the right hand side over the time step - to...
Rotor Diameter
The issue of what size of turbine produces energy at minimum cost has been fiercely debated for a long time. Protagonists of large machines cite economies of scale and the increase in wind speed with height in their favour. From the other camp, the 'square-cube law', whereby energy capture increases as the square of the diameter, whereas rotor mass and therefore cost increases as the cube, is advanced as an argument against. In reality, both arguments are correct, and there is a trade-off...
Harmonics
Only variable-speed wind turbines inject significant harmonic currents into the network. Fixed-speed wind turbines, particularly those with power-factor correction capacitors, alter the harmonic impedance of the distribution network and, in some circumstance, create resonant circuits. This may be important if fixed- and variable-speed wind turbines are installed in the same wind farm. It is noted in IEC 2000b that harmonic currents have been reported from a few installations of fixed-speed,...
Voltage flicker
Voltage flicker describes dynamic variations in the network voltage which may be caused either by wind turbines or by varying loads Bossanyi, Saad-Saoud and Jenkins, 1998 . The origin of the term is the effect of the voltage fluctuations on the brightness of incandescent lights and the subsequent annoyance to customers Mirra, 1988 . Human sensitivity to variations of light intensity is frequency dependent and Figure 10.14 indicates the magnitude of sinusoidal voltage changes which laboratory...
Earthing Grounding of Wind Farms
All electrical plant require a connection to the general mass of earth in order to minimize shock hazards to personnel and animals, establish a low-impedance path for earth-fault currents and hence satisfactory operation of protection, improve protection from lightning and retain voltages within reasonable limits, and prevent large potential differences being established which are potentially hazardous to both personnel and equipment. In the UK this subject is referred to as 'earthing' while in...
Active stall control
Active stall control achieves power limitation above rated wind speed by pitching the blades initially into stall, i.e., in the opposite direction to that employed for active pitch control, and is thus sometimes known as negative pitch control. At higher wind speeds, however, it is usually necessary to pitch the blades back towards feather in order to maintain power output at rated. A significant advantage of active stall control is that the blade remains essentially stalled above the rated...
Info Bwt
across the disc caused by the rate of change of axial momentum as developed in Section 3.2.1 Equation 3.9 is additional to the pressure drop associated with the rotation of the wake and is uniform over the whole disc. If the wake did not expand as it slows down the rotational wake structure together with the rotational pressure gradient would not change as the wake develops whereas the pressure loss caused by the change of axial momentum will gradually reduce to zero in the fully-developed...
Pitching blade tips
Blade tips which pitch to feather have become the standard form of aerodynamic braking for stall-regulated turbines. Typically the tip blade is mounted on a tip shaft, as illustrated in Figure 6.13, and held in against centrifugal force during normal operation by a hydraulic cylinder. On release of the hydraulic pressure which is triggered by the control system, or directly by an overspeed sensor , the tip blade flies outwards under the action of centrifugal force, pitching to feather...
The Kp curve
An alternative performance curve can be produced for a turbine controlled at constant speed. The CP - curve shows, non-dimensionally, how the power would vary with rotational speed if the wind speed was held constant. The KP - 1 curve describes, again non-dimensionally, how the power would change with wind speed when constant rotational speed is enforced. KP is defined as The CP - and KP - 1 curves for a typical fixed-pitch wind turbine are shown in Figure 4.6. The KP - 1 curve, as stated...
Passive pitch control
An attractive alternative to active control of blade pitch to limit power is to design the blade and or its hub mounting to twist under the action of loads on the blades in order to achieve the desired pitch changes at higher wind speeds. Unfortunately, although the principle is easy to state, it is difficult to achieve it in practice, because the required variation in blade twist with wind speed generally does not match the corresponding variation in blade load. In the case of stand-alone wind...
Power Control Passive stall control
The simplest form of power control is passive stall control, which makes use of the post-stall reduction in lift coefficient and associated increase in drag coefficient to place a ceiling on output power as wind speed increases, without the need for any changes in blade geometry. The fixed-blade pitch is chosen so that the turbine reaches its maximum or rated power at the desired wind speed. Stall-regulated machines suffer from the disadvantage of uncertainties in aerodynamic behaviour...
Info Ujt
Therefore, in terms of parameter , from Equation 3.192 rf Rf 2 2 irUi 3.198 It should be noted that the axial acceleration distribution is axi-symmetric and independent of the yaw angle. The mean value of axial acceleration over the area of the disc is The non-dimensional form of the acceleration can be expressed as 97 ur Ht 256 ctd 3 .200 where ao Mo Ul, axial flow factor and r tR UM which is called non-dimensional time. Fx 1 pU1QOn R2 ctd Substituting for CTD from Equation 3.199 gives...
Wind farm and generator protection
Figure 10.20 shows a typical protection arrangement for a wind farm of fixed-speed wind turbines with generator voltages of 690 V and with a collection circuit voltage of 11 kV. The 11 kV circuit is fed from a 33 11 kV Delta Star wound transformer with the 11 kV neutral grounded either directly or through a resistor. The 11 0.69 kV transformers are also wound Delta Star and so the 690 V neutral points of each circuit may be directly grounded. The neutral point of the generators is not connected...
T 1
Equation 3.36 is not quite the same as Equation 3.23 of Section 3.3.3 and it can be shown that this is a result of ignoring the wake expansion. The torque on an annulus of radius r and radial width r is d P4nrU a 1 - a 2 Q r pWt r sin t r - r CP TT-f 4 .' lt 1 - a 2 3.40 The reduced efficiency compared with the simple actuator disc result, CP 4a 1 - a 2, is caused by the energy required to spin the wake, as a rigid body, with an angular velocity 2a'Q. It should be noted that any additional...
Historical Development
Windmills have been used for at least 3000 years, mainly for grinding grain or pumping water, while in sailing ships the wind has been an essential source of power for even longer. From as early as the thirteenth century, horizontal-axis windmills were an integral part of the rural economy and only fell into disuse with the advent of cheap fossil-fuelled engines and then the spread of rural electrification. The use of windmills or wind turbines to generate electricity can be traced back to the...
Tower tiedown
The tower is normally fitted with a base flange, which can either be attached to the foundation by screwed rods cast into the concrete or bolted to an embedded tower stub. This sub section is concerned with the former arrangement. The screwed rods are normally anchored in some way at their base, and their capacity to resist overturning moment is determined by the pull-out resistance of the semi-circle of bolts on the upwind side. As this is governed by the concrete shear strength, the rods have...
Z 1
Deutscher Ingenieure, 1986 , VDI 2230, gives a method for calculating the bolt load increment as a proportion of the load increment in the 'tributary' width of tower wall under these conditions. The axial loading on the flanged joint and the effect of the moment due to the eccentricity of loading are considered separately. The axial load is assumed to be shared between the bolt and the preloaded flanges in proportion to the stiffnesses of the load paths, which, in the case of the flanges, is...
Active pitch control
Active pitch control achieves power limitation above rated wind speed by rotating all or part of each blade about its axis in the direction which reduces the angle of attack and hence the lift coefficient - a process known as blade feathering. The main benefits of active pitch control are increased energy capture, the aerodynamic braking facility it provides and the reduced extreme loads on the turbine when shut-down see also Sections 4.2.5,4.2.7 and 8.2.1 . The pitch change system has to act...
Rotor Position with Respect to Tower Upwind configuration
The upwind configuration is the one most commonly chosen. The principal advantage is that the tower shadow effect is much less for the same blade-tower spacing, reducing both dynamic loads on the blade and rhythmic noise effects. Set against this is the need to take great care to avoid the risk of blade-tower strikes with upwind machines, requiring accurate prediction of blade deflections under turbulent wind loading. The clearance between the undeflected blade and the tower can be increased by...
Teeter stability on stallregulated machines
At first sight, it might be thought that the teeter motion of a stalled rotor would be unstable because of negative damping resulting from the negative slope of the Ci-a curve post-stall. However, two-dimensional aerodynamic theory is a poor predictor of post-stall behaviour, and it has proved possible to design teetered rotors that are stable in practice, such as the Gamma 60 Falchetta et al., 1996 and Nordic 1000 Blade 'A' pitch change due to Section J - J teeter angle Z Engstrom et a ., 1997...
Pitchteeter coupling
As described in Section 5.8.8, the magnitude of teeter excursions can be reduced by coupling blade pitch to teeter angle, in order to generate an aerodynamic restoring moment proportional to the teeter angle. This can be done simply by setting the teeter hinge at an angle, known as the Delta 3 angle, to the perpendicular to the rotor axis. Alternatively, on pitch-controlled machines, pitch-teeter coupling can be introduced by actuating the blade pitch by the fore-aft motion of a rod passing...
Tower Stiffness
A key consideration in wind turbine design is the avoidance of resonant tower oscillations excited by rotor thrust fluctuations at rotational or blade-passing frequency. The damping ratio may be only 2-3 percent for tower fore-aft oscillations and an order of magnitude less for side-to-side motion, so unacceptably large stresses and deflections could develop if the blade-passing frequency and tower natural frequency were to coincide. Rotational frequency is less of a concern, because cyclic...
Variableslip operation
Variable slip represents a compromise between fixed- and variable-speed operation Bossanyi and Gamble 1991, Pedersen 1995 . The variable-slip generator is essentially an induction generator with a variable resistor in series with the rotor circuit, controlled by a high-frequency semiconductor switch. Below rated, this acts just like a conventional fixed-speed induction generator. Above rated, however, control of the resistance effectively allows the air-gap torque to be controlled and the slip...
R Jxd
QQ , R ry , x m , y __, Di 1 - y - D1 D2 mo l m4 vmml mi n Sa n dn S0 n is the power spectrum of stress, Jo Although the Dirlik cycle range p.d.f. was not intended to apply to signals containing periodic components, several investigations Hoskin et al. 1989 , Morgan and Tindal 1990 , Bishop et al. 1991 have been carried out to determine its validity for wind turbine fatigue damage calculations, using monitored data for flapwise bending from the MS1 wind turbine on Orkney. Cycle range p.d.f.s...
Info Anm
Figure 5.7 Blade In-plane and Out-of-plane Aerodynamic Bending Moment Distributions for Typical 40 m Diameter Stall-regulated Machine Operating in a Steady, Uniform 10 m s Wind Figure 5.7 Blade In-plane and Out-of-plane Aerodynamic Bending Moment Distributions for Typical 40 m Diameter Stall-regulated Machine Operating in a Steady, Uniform 10 m s Wind aerodynamic blade bending moments. The variation of these moments with radius is shown in Figure 5.7 for the example above. The blade bending...
Info Mel
The maximum achievable value of the power coefficient is known as the Betz limit after Albert Betz the German aerodynamicist 119 and, to date, no wind turbine has been designed which is capable of exceeding this limit. The limit is caused not by any deficiency in design, for, as yet, we have no design, but because the stream-tube has to expand upstream of the actuator disc and so the cross section of the tube where the air is at the full, free-stream velocity is smaller than the area of the...
Closedloop Control Issues and Objectives Pitch control see also Sections and
Pitch control is the most common means of controlling the aerodynamic power generated by the turbine rotor. Pitch control also has a major effect on all the aerodynamic loads generated by the rotor. Below rated wind speed, the turbine should simply be trying to produce as much power as possible, so there is generally no need to vary the pitch angle. The aerodynamic loads below rated wind speed are generally lower than above rated, so again there is no need to modulate these using pitch control....
Pitching to stall
Figure 4.9 shows the power curves for a turbine rated at 60 kW, which is achieved at 12 m s. At wind speeds below the rated level the blade pitch angle is kept at 0 . As rated power is reached only a small negative pitch angle, initially of about 2 , is necessary to promote stalling and so to limit the power to the rated level. As the wind speed increases small adjustments in both the positive and negative directions are all that are needed to maintain constant power. The small sizes of the...
Info Kam
The ratio of the steady moment at radius r to that at the root is Jr c r r _ r dr JQR c r r dr, so the ratio of the standard deviation of the quasistatic fluctuations at radius r to the steady value there is amb r _ amb r amb 0 M 0 amb 0 Ksmb r A5 59 M r a mb 0 M 0 M r M 0 V Ksmb 0 ' Generally, the square root will be close to unity, so a MB r M r will be nearly constant. In Section A5.5 it was shown that the standard deviation of the first mode resonant root bending moment is equal to 0ax1 J m...
References Wpo
Armstrong, J. R. C. and Hancock, M., 1991 . 'Feasibility study of teetered, stall-regulated rotors'. ETSU Report No. WN6022. Bossanyi, E. A. and Gamble, C. R., 1991 . 'Investigation of torque control using a variable slip induction generator' ETSU WN-6018, Energy Technology Support Unit, Harwell, UK. Burton, A. L., Mill, P. W. and Simpson, P. B., 1990 . 'LS1 post-synchronization commissioning'. Proceedings of the 12th BWEA Conference, pp 183-193. Mechanical Engineering Publications, Bury St...
Stall regulation
An important feature of this KP - 1 curve is that the power, initially, falls off once stall has occurred and then gradually increases with wind speed. This feature provides an element of passive power output regulation, ensuring that the generator is not overloaded as the wind speed increases. Ideally, the power should rise with wind speed to the maximum value and then remain constant regardless of the increase in wind speed this is called perfect stall regulation. However, stall regulated...
Islanding and selfexcitation of induction generators
Fixed-speed wind turbines use induction generators to provide damping in the drive train and, as there is no direct access to the field of an induction generator, the magnetizing current drawn from the stator leads to a requirement for reactive power. In order to reduce the reactive power supplied from the network it is conventional to fit fixed-speed wind turbines with local power factor correction PFC capacitors. As long as the induction machine is connected to a distribution network its...
Info Rre
Here, PRB and QB are the baseline values of rated power and rotational speed, 500 kW and 30 r.p.m. respectively. The two design options can now be examined. a Planform and rotational speed unchanged from baseline The maximum output power drops by almost exactly one third due to the reduction in the number of blades, but the reduction in energy yield is less severe at 19 percent. This is because, although the coefficient of performance CP for the two-bladed machine is very nearly two thirds that...
W Syn
Figure 7.16 a Velocity Diagram for Vibrating Blade Looking Towards Hub b Out-of-plane and In-plane Components of Lift and Drag Forces c Directions of Vibration, x and y Figure 7.16 a Velocity Diagram for Vibrating Blade Looking Towards Hub b Out-of-plane and In-plane Components of Lift and Drag Forces c Directions of Vibration, x and y Here is the free stream wind speed and U1 1 a the reduced wind speed at the rotor plane as usual. The damping coefficients per unit length for vibrations in the...
Gear arrangements
Parallel axis gears may be arranged in one of two ways in each gear stage. The simplest arrangement within a stage consists of two external gears meshing with each other and is commonly referred to as 'parallel shaft'. The alternative 'epicyclic' arrangement consists of a ring of planet gears mounted on a planet carrier and meshing with a sun gear on the inside and an annulus gear on the outside. The sun and planets are external gears and the annulus is an internal gear as its teeth are on the...
U Hwi
Figure 3.32 Prandtl's Wake-disc Model to Account for Tip-losses Figure 3.32 Prandtl's Wake-disc Model to Account for Tip-losses Rw r is a distance measured from the wake edge. Distance d between the discs should be that of the distance travelled by particle three between successive vortex sheets. Glauert 1935 takes d as being the normal distance between successive helicoidcal vortex sheets. The helix angle of the vortex sheets is the flow angle 0 s and so with N sheets intertwining from N...