Burton T. (et. al.) Wind energy Handbook

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is the annulus radius and r

is the sun radius. Hence, putting a ¼ r

, the

volume of a planet is

LSS

1:15(a  1)

(a þ 1)



lim

and the volume of the sun is 4=(a  1)

times as big. The total volume of planets and

sun becomes

V ¼ k

LSS

a þ 1



lim

1 þ

(a  1)



(7:56)

Substituting a ¼ 2, we obtain

¼ r

and N ¼

3

1:15

¼ 8:195

which is rou nded down to 8, giving

V ¼ k

LSS

3

lim

1 þ



¼ k

LSS

=

lim

Hence the volume of the sun and planets of the epicyclic stage is only one eighth of

the volume of the gearwheel and pinion of the equivalent parallel stage, assuming

the designs are governed by gear tooth bending stress. If contact stress were to

govern, the relative volume of the epicyclic stage would be even less.

The dramatic materials savings obtainable with epicyclic gearboxes depend on

equal sharing of loads between the planets. Although this is theo retically achievable

through accuracy of manufacture, it is in practice desirable to introduce some

ﬂexibility in the planet mountings to take up any planet position errors – for

example by supporting the planets on slender pins cantilevered out from the planet

carrier. Note that the fatigue design of such pins is, like the design of intermediate

shafts, governed by torque ﬂuctuations rather than by torque absolute magnitude.

7.4.8 Gearbox noise

The main source of gearbox noise arises from the meshing of individual teeth.

Loaded teeth deﬂect slightly, so that if no tooth proﬁle correction is made, unloaded

teeth are misaligned when they come into contact, resulting in a series of impacts at

the meshing frequency. It is therefore standard practice to adjust the tooth proﬁle –

usually by removing material from the tip area of both gears, referred to as ‘tip

relief’ – to bring the unloaded teeth back into alignment at the rated gear loading.

In the case of wind turbines, the gear loading is variable, so it is necessary to select

the load level at which the tip relief provides the correct compensation. If the tip

relief load level is too high, there will be exce ssive loss of toot h contact near the tips

at low powers, while if it set too low the noise level at rated power will be too high.

GEARBOX 435

However, if gearbox noise is expected to be more intrusive at low wind speeds,

when it is less likely to be masked by aerodynamic noise, then a low compensation

load level should be selected.

Helical gears are usually quieter than spur gears (with teeth parallel to the gear

axis) because the width of the tooth comes into mesh over a ﬁnite time interval

rather than all at once. Moreover, the peak tooth deﬂections of helical gears are less

than those of spur gears because there are always at least two teeth in contact rather

than one, and because the varying bending moment across the tooth width means

that the less heavily loaded portions of the tooth can provide restraint to the part

that is most heavily loaded. As a result, the tooth misalignments due to insufﬁ-

cient/excessive tip relief at a particular load level will be reduced .

Epicyclic gears are normally quieter than parallel shaft gears because the reduced

gear size results in lower pitch line velocities. However, this beneﬁt is lost if spur

gears are used rather than helical gears, in order to avoid problems with planet

alignment. One way of maintaining the alignment of helical planet gears is to

provide thrust collars on the sun and annulus.

As the annulus of an epicyclic gear stage is often ﬁxed, it would be convenient to

integrate it with the gearbox casing. However, this would enable annulus gear

meshing noise to be radiated directly from the casing, so it is preferable to make the

annulus a separate element, supported on resilient mountings. Similarly, resilient

gearbox mountings should be used to attenuate the transmission of gearbox noise

to the nacelle structure and tower.

The noise produced by gear tooth meshing can reach the environment outside

the wind turbine by a variety of routes:

• through the shaft directly to the blades, which may radiate efﬁciently,

• through the resilient mounts of the gearbox to the support structure and thereby

to the tower, which can radiate efﬁciently under some circumstances,

• through the resilient mounts of the gearbox to the support structure and thereby

to the nacelle structure, which can also radiate,

• through the casing wall to the nacelle air and then via air intake and exhaust

ducts,

• through the casing wall to the nacelle air and then via the nacelle structure.

All these paths are modally dense and it is virtually impossible to design out a

selected frequency. If noise is a problem then the options are to reduce the source

sound level, perhaps by improving the tip relief as described above, or to modify

the major path to reduce transmission. Identiﬁcation of the major path is not

straightforward, but one way of doing so is to use Statistical Energy Analysis (SEA),

which combines a theoretical model with extensive ﬁeld measurements. The path

may not be simple, as non-linearity in the system can make one path the predomi-

nant one at low wind speeds and another path critical at higher wind speeds.

Treatment of a radiating path can invo lve damping treatment such as shear layer

436 COMPONENT DESIGN

damping or even just sand or bitumen layers added to the tower wall, for instance.

In some cases the treatment can have more than one effect. When blades are the

major source of radiation and damping material is added inside the blades then this

material can act as a stiffening material as well as a damping mechanism. Some-

times it is useful to add tu ned absorbers to parts of the structure to damp out one

particular frequency. An alternative use of such tuned absorbers is to design them

to raise the impedance at the tuned freque ncy so that the offending vibration does

not pass that point on the structure.

7.4.9 Integrated gearboxes

As noted in Section 6.11.1, the cases of integrated gearboxes must be very robust, in

order to transmit the rotor loads to the nacelle structure without exp eriencing

deﬂections which would impair the proper functioning of the gears. In view of the

complex shape of the casing, stress distributions due to each load vector usually

have to be det ermined using ﬁnite-element (FE) analysis – these can then be

superposed in line with the different extreme load combinat ions. The fatigue

analysis will require the superposi tion of stress histories resulting from simultane-

ous time histories of rotor thrust, yaw moment and tilt moment derived from

simulations at different wind speeds.

7.4.10 Lubrication and cooling

The function of the lubrication system is to maintain an oil ﬁlm on gear teeth and

the rolling elements of bearings, in order to minimize surface pitting and wear

(abrasion, adhesion and scufﬁng). Varying levels of the elastohydrodynamic lubri-

cation provided by the oil ﬁlm can be identiﬁed, depending on oil ﬁlm thickness.

These range from full hydrodynamic lubrication, which exists when the metal

surfaces are separated by a relatively thick oil ﬁlm, to boundary lubrication when

the asperities of the metal surfaces may be separated by lubricant ﬁlms only a few

molecular dimensions in thickness. Scufﬁng, which is a severe form of adhesive

wear involving localized welding and particle transfer from one gear to the other,

can occur under boundary lubrication conditions, which are promoted by high

loading and low pitch line velocity and oil viscosity.

Two alternative methods of lubrication are available: splash lubrication and

pressure fed. In the former, the low-speed gear dips into an oil bath and the oil

thrown up agains t the inside of the casing is channelled down to the bearings. In

the latter, oil is circulated by a shaft driven pump, ﬁltered and delivered under

pressure to the gears and bearings. The advantage of splash lubrication is its

simplicity and hence reliability, but pressure fed lubrication is usually preferred for

the following reasons:

• oil can be positively directed to the locations where it is required by jets,

• wear particles are removed by ﬁltration,

GEARBOX 437

• the churning of oil in the bath, which can result in a net efﬁciency loss, is avoided,

• the oil circulation system enables heat to be removed much more effectively from

the gearbox by passing the oil through a cooler mounted outside the nacelle,

• it allows for intermittent lubrication when the machine is shut-down if a standby

electric pump is incorporated.

With a pressure fed system, it is normal practice to ﬁt temperature and pressure

switches downstream of the ﬁlter to trip the machi ne for excessive temperature or

insufﬁcient pressure.

Guidance on the selection of lubricant, which has to take into account the ambient

temperatures at the site in question, is given in the AGMA/AWEA (1996) docu-

ment. Sump heaters may be needed to enable oil to be circulated when the turbine

starts up at low temperatures.

7.4.11 Gearbox efﬁciency

Gearbox efﬁciency can vary between about 95 percent and 98 percent, depending

on the relative number of epicyclic and parallel shaft stages and on the type of

lubrication.

7.5 Generator

7.5.1 Induction generato rs

The induction generators commonly used on ﬁxed-speed wind turbines are very

similar to conventional industrial induction motors. In principle the only differ-

ences between an induction machine operating as a generator and as a motor are

the direction of power ﬂow in the connecting wires, whether torque is applied to or

taken from the shaft and if the rotor speed is slightly above or below synchronous.

The size of the market for induction motors is very large and so, in many cases, an

induction generator design will be based on the same stator and rotor laminations

as a range of induction motors in order to take advantage of high manufacturing

volumes. Some detailed design modiﬁcations, e.g., changes in rotor bar material,

may be made by the machine manufacturers to reﬂect the different operating

regime of wind turbine generator, particularly the need for high efﬁciency at part

load, but the principles of operation are those of conventional ind uction motors.

The synchronous speed, which is determined by the number of magnetic poles

will be in the range of 1500 r.p.m. (4 pole), 1000 r.p.m. (6 pole) or 750 r.p.m. (8 pole)

for connection to a 50 Hz network. For commercial reasons it is common to use a

voltage of only 690 V even for large generators and in some very large wind

turbines the resulting high currents have led to the decision to locate the turbine

transformer in the nacelle. The physical protection of the generator is arranged to

avoid the ingress of moisture, i.e. a totally enclosed design, and in some wind

438 COMPONENT DESIGN

turbines liquid cooling is used to reduce air-borne noise. A high slip at rated power

output is often requested by the wind turbine designer as this increases the

damping in the wind turbine drive train but at the expense of losses in the rotor.

Figure 7.28 shows the conventional equivalent circuit of an induction machine

that may be used to analyse its steady-state behaviour (Hindmarsh, 1984, and

McPherson, 1990). The slip (s) is the difference between the angular velocity of the

stator and rotor:

s ¼

 ø

(7:57)

and so for motor operation it is positive and for generator operation negative.

Figure 7.29 shows how the active power varies with slip for a 1 MW induction

machine. A convention has been chosen with the current ﬂowing into the circuit

and so the norm al operating region for a generator is between O and A. At 1 MW

generation (A) the slip is around 0.8 percent with the rotor rotating faster than the

stator ﬁeld. It may be seen that the maximum power that may be generated before

the peak of the curve is reached is only some 1.3 MW. This is because the generator

⫺jX

(1 ⫺ s)/s

Figure 7.28 Equivalent Circuit of an Induction Machine with Power Factor Correction

Capacitors

1.5

0.5

1.5

10% 5% 0 5% 10%

Real power

(MW)

Slip

motoring

generating

Figure 7.29 Variation of Active Power with Slip of a 1 MW Induction Machine

GENERATOR 439

has been represented as connected to a distribution network with a low short-circuit

level (and hence a high impedance) and the impedance of the local turbine

transformer is included in the calculation. This source impedance acts to lower the

maximum power which may be exported before the peak of the curve is reached,

and instability occurs. It also leads to asymmetry in the torque–slip curve.

Figure 7.30 shows how the reactive power drawn by the generator varies with

slip. The normal generating operating region is again shown as O–A. At point A

(1 MW output) the generator (with its ﬁxed local power factor correction capacitors)

draws some 600 kVAr. It may be seen that the reactive power requirement increases

very rapidly if the output power rises above its rated value.

Figures 7.29 and 7.30 may be combined to give the conventional ‘circle diagram’

representation of an induction machine shown in Figure 7.31. Again the normal

generating region is shown as O–A. The ﬁxed power factor correction capacitors

act to reduce the requirement for reactive power and so translate the circle diagram

on the y-axis towards the origin.

Reactive power

(MVAr)

0.5

1.5

2.5

10% 5% 0 5% 10%

Slip

Figure 7.30 Variation of Reactive Power with Slip for a 1 MW Induction Machine

Reactive power

(MVar)

0.2

0.4

0.6

0.8

1.5 1 0.5 0 0.5 1 1.5

Real power (MW)

Figure 7.31 Circle Diagram of 1 MW Induction Machine

440

COMPONENT DESIGN

The equations used to describe the steady-state performance of induction gen-

erators are given in any standard undergraduate textbook (e.g. Hindmarsh, 1984,

and McPherson, 1990). Dynamic analysis is more complex but is dealt with by

Krause (1986).

7.5.2 Variable-speed generators

There are two fundamental approaches to electrical variable-speed operation. Either

all the output power of the wind turbine may be passed through the frequency

converter to give a broad range of variable speed operation or a restricted speed

range may be achieved by converting only a fraction of the output power.

Figure 7.32 shows in schematic form how a broad range, variable-speed genera-

tion system may be conﬁgured. Early broad range variable-speed wind turbines

used a diode rectiﬁer bridge in the generator converter and a naturally commu-

tated, thyrist or, current source, converter on the network side (Freris, 1990). How-

ever, naturally commutated thyristor converters consume reactive power and

generate considerable characteristic harmonic currents. On weak distribution sys-

tems it is difﬁcult to provide suitable ﬁltering and power factor correction for this

type of equipment. Hence modern practice is to use two voltage source converters

(Heier, 1998) with either a synchronous or induction generator. Each converter

consists of a Graetz Bridge (as shown in Figure 10.17) with Insulate d Gate Bipolar

Transistors (IGBTs) as the switching elements. The bridges are switched rapidly

(typically between 2–6 kHz) with some form of Pulse Width Modulation to produce

a close approximation to a sine wave. The generator converter rectiﬁes all the power

to DC, which is then inverted by the network converter. Ope ration of this type of

voltage source converter is described in Mohan, Undeland and Williams (1995).

Control strategies vary but one appr oach is to control the generator converter to

maintain the DC link voltage at a constant value and then use the network converter

to control the power ﬂowing out of the system and hence the torque on the

generator (Jones and Smith, 1993). A power bandwidth of 200–500 radians/s is

quoted in this paper indicating the very fast control possible with such equipment

with an overall efﬁciency of 92.1 percent consisting of 95.9 percent for the generator

and 96 percent for the power electronics. The network side converter may be

Generator

converter

Network

converter

Local

transforme r

Figure 7.32 Broad Range Variable Speed Generation

GENERATOR 441

arranged to operate at any power factor within the rating of the equipment with

very low harmonic distortion.

Figure 7.33 shows how narrow band variable speed control may be implemented.

A wound rotor induction generator is used and control is possible over all four

quadrants of speed and torque. The generator stator is connected directly to the

network with a frequency converter in the rotor circuit. This ‘doubly fed’ concept

was used in early large prototype wind turbines, e.g., the 3 MW Growian con-

structed in Germany in the early 1980s (Warneke, 1984) and the Boeing MOD 5B in

the USA at the same time. At that time, cyclo-converters were used to change the

frequency of the rotor circuit but modern practice is to use two voltage source

converters similar to the broad range variable -speed designs but having a lower

power rating. Again, control techniques vary but one approach is to use vector

control techniques on the machine side converter to adjust torque and the excitation

of the generator independently. The network side bridge maintains the DC link

voltage and supplies additional reactive power to maintain the power factor of the

wind turbine (Pena, Clare and Asher, 1996). Doubly-fed inducti on generators are

becoming increasingly common in large wind turbines where the beneﬁts of limited

variable-speed operation are required but at the reduced cost of controlling only a

fraction of the output power. A possible future development is the use of the

brushless doubly-fed generator where rather than use slip rings the rotor is excited

by a second controlled stator winding. This approach eliminates the requirement

for slip-rings and brushes but is not yet used commercially.

7.6 Mechanical Brake

7.6.1 Brake duty

As indicated in Sectio n 6.8.3, a mechanical brake can be called on to fulﬁl a variety

of roles, according to the braking philosophy adopted for the machine in question.

The minimum requirement is for the mechanical brake to act as a parking brake, so

that the machine can be stopped for maintenance purposes. The brak e will also be

Rotor

circuit

Stator

circuit

Local

transformer

Wound rotor

induction

machine

Figure 7.33 Narrow Range Variable Speed Generation

442

COMPONENT DESIGN

used to bring the rotor to a standstill during high wind shut-downs for the majority

of machine designs, and during low-speed shut-downs as well in some cases.

Aerodynamic braking is used to decelerate the rotor initially, so the mechanical

brake torque can be quite low. However, IEC 61400-1 requires that the mechanical

brake be capable of bringing the rotor to a complete stop from a hazardous idling

state in any wind speed less than the 1 year return period 3 s gust (see Table 5.1).

If the mechanical brake is required to arrest the rotor in the event of a complete

failure of the aerodynamic braking system, then there are two deployment options

to consider. Either the mechanical brake can be actuated when an overspeed

resulting from the failure of the aerodynamic system is detected, or actuated

simultaneously with the aerodynamic brake as part of the standard emergency

shut-down procedure. The advantage of the former strategy is that the mechanical

brake will rarely, if ever, have to be deployed in this way, so that some pad or even

disc damage can be tolerated when deployment actually occurs. In addition, fatigue

loading of the gearbox will be reduced if the brake is mounted on the high-speed

shaft. On the other hand, if the mechanical brake is actuated before signiﬁcant

overspeed has developed, then the aerodynamic torque to be overcome by the

mechanical brake in the event of aerodynamic braking failure will be less.

The most severe emergency braking case will arise following a grid loss during

generation in winds above rated. In the case of pitch-regulated machines, the

maximum overspeed will occur after grid loss at rated wind speed because the rate

of change of aerodynamic torque with rotational speed decreases and soon becomes

negative at higher wind speeds. Conversely, if the pitch mechanism should jam, the

braking duty becomes more severe at wind speeds at or above cut-out, because

much higher aerodynamic torques are developed as the rotor slows down and the

angle of attack increases. For stall-regulated machines the critical wind speed is

generally at an intermediate value between rated and cut-out.

7.6.2 Factors governing brake design

The braking torque provided by callipers gripping a brake disc (Figure 7.34) is

simply the product of twice the calliper force, the coefﬁcient of friction (typically

0.4), the number of callipers and the effective pad radius. Callipers providing

clamping forces of up to 500 KN are avai lable. However, the brake design is also

limited by:

• centrifugal stresses in the disc,

• pad rubbing speed,

• power dissipation per unit area of pad, and

• disc temperature rise.

The nature of these constraints is described below.

The critical stress generated by centrifugal stresses is in the tangen tial directio n at

MECHANICAL BRAKE 443

the inner radiu s of the brake disc, but it is governed principally by the disc rim

speed according to the following formula:



(a) ¼

3 þ 

rø

1 þ

1  

3 þ 



(7:58)

where a and b are the inner and outer disc radii respectively and ø is the disc

rotational speed. One brake manufacturer, Twiﬂex, quotes a maximum safe disc

rim speed of around 90 m/s for their discs manufactured in spheroidal graphite

cast iron.

Brake pads are generally made from sintered metal or a cheaper, resin-based

material. The former can accept rubbing speeds of up to 100 m/s, but some

manufacturers quote permitted rubbing speeds for the latter of only about 30 m/s.

However, Wilson (1990) reports satisfactory performance of resin-based pads at a

rubbing speed of up to 105 m/s if the power dissipation rate per unit area, Q,is

kept low enough. The criterion, ascribed to Fero do, is that Q ¼ PV <

11:6MW=m

, where  is the coefﬁcient of friction, P is the brake-pad pressure in

KN/m

and V is the rubbing speed in m/s. This requires the pad pressure to be

reduced to 275 KN/m

, assuming a friction coefﬁcient of 0.4.

During braking the kinetic energy of the rotor and drive train together with the

additional energy fed in by the aerodynamic torque are dissipated in the brake disc

and pads as heat, resulting in rapid initial temperature rise near the surface of the

Figure 7.34 High-speed Shaft Brake Disc and Calliper (Reprodued by permission of NEG-

Micon)

444

COMPONENT DESIGN