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

Подождите немного. Документ загружается.

8.2 Closed-loop Control: Issues and Objectives

8.2.1 Pitch control (see also Sections 4.2.4 and 6.7.3)

Pitch contro l 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. However, for ﬁxed-

speed turbines, the optimum pitch angle for aerodynamic efﬁciency varies slightly

with wind speed. Therefore, on some turbines, the pitch angle is varied slowly by a

few degrees below rated in response to a heavily averaged anemometer or power

output signal.

Above rated wind speed, pitch control provides a very effective means of regulat-

ing the aerodynamic power and loads produced by the rotor so that design limits are

not exceeded. In order to achieve good regulation, however, the pitch control needs

to respond very rapidly to changing conditions. This highly active control action

needs very careful design as it interacts strongly with the turbine dynamics.

One of the strongest interactions is with the tower dynamics. As the blades pitch

to regulat e the aerodynamic torque, the aerodynamic thrust on the rotor also

changes substantially, and this feeds into the tower vibration. As the wind in-

creases, the pitch angle increases to maintain constant torque, but the rotor thrust

decreases. This allows the downwind tower deﬂection to decrease, and as the tower

top moves upwind the relative wind speed seen by the rotor increases. The

aerodynamic torque increases further, causing more pitch action. Clearly if the

pitch-controller gain is too high this positive feedback can result in instability. It is

therefore vital to take the tower dynamics into account when designing a pitch

controller.

Below rated wind speed, the pitch setting should be at its optimum value to give

maximum power. It follows that when the wind speed rises above rated, either an

increase or a decrease in pitch angle will result in a reduction in torque. An increase

in pitch angle, deﬁned as tu rning the leading edge into wind, reduces the torque by

decreasing the angle of attack and henc e the lift. This is known as pitching towards

feather. A decrease in pitch, i.e., turning the leading edge downwind, reduces the

torque by increasing the angle of attack towards stall, where the lift start s to

decrease and the drag increases. This is known as pitching towards stall.

Although pitching towards feather is the more common strategy, some turbines

pitch towards stall. This is commonly known as active stall or assisted stall (see

Section 6.7.4). Pitching to feather requires much more dynam ic pitch activity than

pitching to stall: once a large part of the blade is in stall, very small pitch move-

ments sufﬁce to control the torque . Pitching to stall results in signiﬁcantly gre ater

thrust loads because of the increased drag . On the other hand, the thrust is much

more co nstant once the blade is stalled, so thrust-driven fatigue loads may well be

smaller.

CLOSED-LOOP CONTROL: ISSUES AND OBJECTIVES 475

A further problem with pitching to stall is that the lift curve slope at the start of

the stalled region is negative, i.e., the lift coefﬁcient decreases with increasing angle

of attack. This results in negative aerodynamic damping, which can result in

instability of the blade bending modes, both in-plane and out of plane. This can be a

problem also with ﬁxed pitch stall-regulated turbines.

Most pitch controlled turbines use full-span pitch control, in which the pitch

bearing is close to the hub. It is also possible, though not common, to achieve

aerodynamic control by pitching only the blade tips, or by using ailerons, ﬂaps, air-

jets or other devices to modify the aerodynamic properties. These strategies will

result in most of the blade being stalled in high winds. If only the blade tips are

pitched, it may be difﬁcult to ﬁt a suitable actuator into the outboard portion of the

blade; accessibility for maintenance is also difﬁcult.

8.2.2 Stall control

Many turbines are stall-regulated, which means that the blades are designed to stall

in high winds without any pitch action being required. This means that pitch

actuators are not required, although some means of aerodynamic braking is likely

to be required, if only for emergencies (see Section 6.8.2).

In order to achieve stall-regulation at reasonable wind speeds , the turbine must

operate closer to stall than its pitch-regulated counterpart, resulting in lower

aerodynamic efﬁciency below rated. This disadvantage may be mitigated in a

variable-speed turbine, when the rotor speed can be varied below rated in order to

maintain peak power coefﬁcient.

In order for the turbine to stall rather than accelerate in high winds, the rotor

speed must be restrained. In a ﬁxed speed turbine the rotor speed is restrained by

the generator, which is governed by the network frequency, as long as the torque

remains below the pull-out torque. In a variable speed turbine, the speed is

maintained by ensuring that the generator torque is varied to match the aerody-

namic torque. A variable-speed turbine offers the possibility to slow the rotor down

in high winds in order to bring it into stall. This means that the turbine can operate

further from the stall point in low winds, resulting in higher aerodynamic

efﬁciency. However, this strategy means that when a gust hits the turbine, the load

torque not only has to rise to match the wind torque but also has to increase further

in order to slow the rotor down into stall. This removes one of the main advantages

of variable-speed operation, namely that it allows very smooth control of torque

and power above rated.

8.2.3 Generator torque control (see also Sections 6.9 and 7.5)

The torque developed by a ﬁxed-speed (i.e., directly-connected) induction generator

is determined purely by the slip speed. As the aerodynamic torque varies, the rotor

speed varies by a very small amount suc h that the generator torque changes to

match the aerodynamic torque. The generator torque cannot therefore be actively

controlled.

476 THE CONTROLLER

However, if a frequency converter is interposed between the generator and the

network, the generator speed will be able to vary. The frequency converter can be

actively controlled to maintain constant generator torque or power output above

rated wind speed. Below rated, the torque can be controlled to any desired value,

for example with the aim of varying the rotor speed to maintain maximum

aerodynamic efﬁciency.

There are several means of achieving variable-speed operation. One is to connect

the generator stator to the network through a frequency converter, which must then

be rated for the full power output of the turbine. Alternative arrangements include

a wound rotor induction generator with its stator connected directly to the network,

and with its rotor connected to the network through slip rings and a frequency

converter. This means that the frequency converter need only be rated to handle a

fraction of the total power, although the larger this fraction, the larger the a chiev-

able speed range will be.

A special case is the variable slip induction generator, where active control of the

resistance in series with the rotor windings allows the torque/speed relationship to

be modiﬁed. By means of closed-loop control ba sed on measured currents, it is

possible to maintain constant torque above rated, effectively allowing variable-

speed operation in this region. Below rated it behaves just like a normal induction

generator (Bossanyi and Gamble, 1991, Pedersen, 1995).

8.2.4 Yaw control

Turbines whether upwind or downwind, are generally stable in yaw (Section 3.10)

in the sense that if the nacelle is free to yaw, the turbine will naturally remain

pointing into the wind. However, it may not point exactly into wind, in which case

some active control of the nacelle angle may be needed to maximize the energy

capture. Since a yaw drive is usually required anyway, e.g. for start-up and for

unwinding the pendant cable, it may as well be used for active yaw tracking. Free

yaw has the advantage that it does not generate any yaw moments at the yaw

bearing. However, it is usually necessary to have at least some yaw damping, in

which case there will be a yaw moment at the bearing.

In pra ctice, most turbines do use active yaw control. A yaw error signal from the

nacelle-mounted wind vane is then used to calculate a demand signal for the yaw

actuator. Frequently the demand signal will simply be a command to yaw at a slow

ﬁxed rate in one or the other direction. The yaw vane signal must be heavily

averaged, especially for upwind turbines where the vane is behind the rotor.

Because of the slow response of the yaw control system, a simple dead-band

controller is often sufﬁcient. The yaw motor is switched on when the averaged yaw

error exceeds a certain value, and switched off again after a certain time or when

the nacelle has moved through a certain angle.

More complex control algorithms are sometimes used, but the control is always

slow-acting, and does not demand any special design considerations. One exception

is the case of active yaw control to regulate aerodynamic power in high winds, as

used on the variable speed Gamma 60 turbine referred to in Section 6.7.5. This

clearly requires very rapid yaw rates, and results in larg e yaw loads and gyroscopic

CLOSED-LOOP CONTROL: ISSUES AND OBJECTIVES 477

and asymmetric aerodynam ic loads on the rotor. This method of power regulation

would be too slow for a ﬁxed-speed tu rbine, and even on the Gamma 60 the speed

excursions during above-rated operation were quite large.

8.2.5 Inﬂuence of the controller on loads

As well as regulating the turbine power in high winds, and perhaps optimizing it in

low winds, it is clear that the action of the control system can have a major impact

on the loads experienced by the turbine. The design of the controller must take into

account the effect on loads, and at least ensure that excessive loads will not result

from the control action. It is possible to go further than this, and explicitly design

the controller with the reduction of certain loads as an additional objective.

The reduction of certain loads is clearly compatible with the primary objective of

limiting power in high winds. For example, the limitation of power output is clearly

compatible with reduction of gearbox torque. In other cases, however, there may be

a conﬂict in which case the controller design is bound to be a compromise involving

a trade-off between competing goals. For example, there is a clear trade-off between

good control of power output and pitch actuator loads. The more actuator activity

can be tolerated, the better the power control can be.

The interaction between pitch control and tower vibration referred to in Se ction

8.2.1 is another importan t example, since the amount of tower vibration has a major

effect on tower base loads. Blade, hub and other structural loads will also be

inﬂuenced by pitch control activity. Generator torque control can have a major

impact on gearbox loads, as described below.

8.2.6 Deﬁning controller objectives

The primary objective of the closed-loop controller can usually be stated fairly

simply. For example, the primary objective of the pitch controller may be to limit

power or rotor speed in high winds. There may be more than one ‘primary’

objective, as in the case where the pitch or torque controller is also used to optimize

energy capture in low winds.

However, since the controller can also have a major effect on structural loads and

vibrations, it is vital to consider these when designing the control algorithm. Thus a

fuller description of the pitch controller objective s might be:

• to regulate aerodynamic torque in above-rated wind speeds;

• to minimize peaks in gearbox torque;

• to avoid excessive pitch activity;

• to minimize tower base loads as far as possible by controlling tower vibration,

and

• to avoid exacerbating hub and blade root loads.

478 THE CONTROLLER

Clearly some of these objectives conﬂict with others, so the contr ol design process

will inevitably involve some degree of trade-off or optimization. In order to do this,

it is necessary to be able to quantify the different objectives. It is usually almost

impossible to do this with any precision, because the various loads may affect not

only the costs of different components (some times in complex ways) but also their

reliability. Even the trade-off between energy capture and component cost is not

straightforward, as it will depend on the wind regime, the discount rate, and

knowledge of future prices for the sale of electr icity. Therefore, some degree of

judgement will always be required in arriving at an acceptable controller design.

8.2.7 PI and PID controllers

A brief general description is given here of PI and PID controllers, since they will be

referred to a number of times in the subsequent sections. The proportional and

integral (PI) controller is an algorithm which is very widely used for controlling all

kinds of equipment and processes. The control action is calculated as the sum of

two terms, one proportional to the control error, which is the difference between

the desired and actual values of the quantity to be controlled, and one proportional

to the integral of the control error. The integral term ensures that in the steady state

the control error tends to zero – if it did not, the integral term would make the

control action continue to increase. The proportional term makes the algorithm

more responsive to rapid changes in the quantity being controlled.

A differential term is often added, which gives a contribution to the control action

proportional to the rate of change of the control error. This is then known as a PID

controller. In terms of the Laplace operator s, which can usefully be thought of as a

differentiation operator, the PID controller from measured signal x to control signal

y can be written as follows:

y ¼ K

1 þ sT



x (8:1)

where K

, K

and K

are the proportional, integral and derivative gains respec-

tively. The denominator of the differential term is essentially a low-pass ﬁlter, and

is needed to ensure that the gain of the algorithm does not increase indeﬁnitely with

frequency, which would make the algorithm very sensitive to signal noise. Setting

¼ 0 results in a PI controller.

It is often the case that the control action is subject to limits. For example, if the

control action represents the blade pitch used to control power abov e rated, then

when the power drops below rated the pitch will be limited to the ﬁne pitch setting,

and will not be allowed to drop further. In this situation the integral term of the PI

or PID controller will grow more and more negative as the power remains below

rated. Then when the wind spee d rises again and the power rises above rated, the

integral term will start to grow again towards zero, but until it gets close to zero it

will more than compensate for the proportional and derivative terms. Therefore the

pitch may remain ‘stuck’ at ﬁne pitch for a considerable time, dependi ng on how

long the power has been below rated, until the integral term has come back close to

CLOSED-LOOP CONTROL: ISSUES AND OBJECTIVES 479

zero. This is known as integrator wind-up, and clearly it must be prevented. This is

done in effect by disabling the integrator when the pitch is on the limit. This is

known as ‘integrator desaturation’, which is described more fully in Section 8.6.

The design of PI and PID controllers, inclu ding the choice of gains, is described in

more detail in Section 8.4.

8.3 Closed-loop Control: General Techniques

This section outlines the pri nciples behind many of the types of closed-loop

controllers to be found in wind-turbines. Mathematical methods for designing the

closed-loop algorithms are covered in Section 8.4.

8.3.1 Control of ﬁxed-speed, pitch-regulated turbines

A ﬁxed-speed pitch-regulated turbine usually means a turbine that has an induction

generator connected directl y to the AC network, and which therefore rotates at a

nearly constant speed. As the wind speed varies, the power produced will vary

roughly as the cube of the wind speed. At rated wind speed, the electrical power

generated becomes equal to the rating of the turbine, and the blades are then

pitched in order to reduce the aerodynamic efﬁciency of the rotor and limit the

power to the rated value. The usual strategy is to pitch the blades in response to the

power error, deﬁned as the difference between the rated power and the actual

power being generated, as measured by a power transducer. The primary objective

is then to devise a dynamic pitch control algorithm that minimizes the power error,

although as explained above, this may not be the only objective.

The main elements of the control loop are shown in Figure 8.2. A PI or PID

algorithm is ofte n used for the controller.

When the power falls below rated, the pitch demand saturates at the ﬁne pitch

limit, maximizing the aerodynamic efﬁciency of the rotor. Since the optimum pitch

angle depends on the tip speed ratio, it is possible to increase energy capture below

rated by a small percentage if the ﬁne pitch limit is varied in response to the wind

speed. The measured power itself is the best available measure of wind speed over

Turbine

Pitch

actuator

Controller

Power

transducer

Wind

Electric

power

Measured

power

Pitch

demand

Blade pitch

Power

set-point

Figure 8.2 Main Control Loop for a Fixed-speed Pitch-regulated Turbine

480

THE CONTROLLER

the whole turbine. However , the ﬁne pitch limit should be varied relatively slowly

compared to the control-loop dynamics. Satisfactory performance can be obtained

by changing the ﬁne pitch limit in response to a moving average of the measured

power. The moving average time constant should be signiﬁcantly longer than the

blade-passing frequency to avoid unnecessary pitch activity below rated.

8.3.2 Control of variable-speed pitch-regulated turbines

With a variable-speed generator, it becomes possible to control the load torque at

the generator directly, so that the speed of the turbine rotor can be allowed to vary

between certain limits. An often-quoted advantage of variable-speed operation is

that below rated wind speed, the rotor speed can be adjusted in proportion to the

wind speed so that the optimum tip speed ratio is maintained. At this tip speed

ratio the power coefﬁcient, C

, is a maximum, which means that the aerody namic

power captured by the rotor is maximized. This is often used to suggest that a

variable-speed turbine can capture much more energy than a ﬁxed-speed turbine of

the same diameter. In practice, however, it may not be possible to realize as much

gain as this simple argument would suggest.

Maximum aerodynamic efﬁciency is achieved at the optimum tip speed ratio

º ¼ º

opt

, at which the power coefﬁcient C

has its maximum value C

P(max)

. Since the

rotor speed  is then proportional to wind speed U, the power increases with U

and 

, and the torque with U

and 

. The aerodynamic torque is given by

rAC

R ¼

rR

(8:2)

Since U ¼  R=º we have

rR



(8:3)

In the steady state therefore, the optimum tip speed ratio can be maintained by

setting the load torque at the generator, Q

, to balance the aerodynamic torque, i.e.,

rR

 Q

(8:4)

Here Q

represents the mechanical torque loss in the drive train (which may itself

be a function of rotational speed and torque), referred to the high-speed shaft. The

generator speed is ø

¼ G, where G is the gearbox ratio.

This torque–speed relationship is shown schematically in Figure 8.3 as line BC.

Although it represents the steady-state solution for optimum C

, it can also be used

dynamically to control generator torque demand as a function of measured

generator speed. In many cases, this is a very benign and satisfactory way of

controlling generator torque below rated wind speed.

For tracking peak C

below rated in a variable-speed turbine, the quadratic

CLOSED-LOOP CONTROL: GENERAL TECHNIQUES 481

algorithm of Equation (8.4) works well and gives smooth, stable control. However,

in turbul ent winds, the large rotor inertia prevents it from changing speed fast

enough to follow the wind, so rather than staying on the peak of the C

curve it will

constantly fall off either side, resulting in a lower mean C

. This problem is clearly

worse for heavy rotors, and also if the C

–º curve has a sharp peak. Thus in

optimizing a blade design fo r variable-speed operation, it is not only important to

try to maximize the peak C

, but also to ensure that the C

–º curve is reasonably

ﬂat-topped.

It is possible to manipulate the generator torque to cause the rotor speed to

change faster when required, so staying closer to the peak of the C

curve. One way

to do this is to modify the torque demand by a term proportional to rotor

acceleration (Bossanyi, 1994):

rR

 Q

 B

øø

(8:5)

For a stiff drive train, and ignoring frequency converter dynamics, the torque

balance gives:

 ¼ Q

 GQ

(8:6)

where I is the total inertia (of rotor, drive train and generator) and  is the

rotational speed of the rotor. Hence

(I  G

 ¼ Q



rR

þ GQ

(8:7)

100

120

140

160

180

0.00 200. 0 0 40 0. 00 600.0 0 800. 0 0 1000 . 00 1200 . 00 1400. 00 1600 .00 1800 .00 2000 . 00

Generator speed

Generator torque

A A1

4 m/s

6 m/s

8 m/s

10 m/s

12 m/s

14 m/s

16 m/s

18 m/s

Opt imum C

(fine pitch)

Increasing

pitch

Figure 8.3 Schematic Torque–Speed Curve for a Variable-speed Pitch-regulated Turbine

482

THE CONTROLLER

The effective inertia is reduced from I to I  G

B, allowing the rotor speed to

respond more rapidly to change s in wind speed.

Another possible method is to use available measurements to make an estimate

of the wind speed, calculate the rotor speed required for optimum C

, and then use

the generator torque to achieve that speed as rapidly as possible. The aerodynamic

torque can be expressed as

rAC

rR



=º

(8:8)

where R is the turbine radius,  the rotational speed, and C

the torque coefﬁcient.

If drive train torsional ﬂexibility is ignored, a simple estimator for the aerodynamic

torque is



¼ GQ

þ I

 ¼ GQ

þ IG

øø

(8:9)

where I is the total inertia. A more sophisticated estimator could take into account

drive train torsion, etc. From this it is possible to estimate the value of the function

F(º) ¼ C

(º)=º



(º) ¼



rR

(Gø

)

(8:10)

Knowing the function F(º) from steady-state aerodynamic analysis, one can then

deduce the current estimated tip speed ratio º



. The desired generator speed for

optimum tip speed ratio can then be calculated as

¼ ø

ºº=º



(8:11)

where

ºº is the optimum tip speed ratio to be tracked. A simple PI controller can

then be used, acting on the speed error ø

 ø

, to calculate a generator torque

demand which will track ø

. The higher the gain of PI controller, the better the C

tracking, but at the expense of larger power variations. Simulations for a particular

turbine showed that a below-rated energy gain of almost 1 percent could be

achieved, with large but not unacceptable power variations.

Holley, Rock and Chaney (1999) demonstrated similar results with a more

sophisticated scheme, and also showed that a perfect C

tracker would capture 3

percent more energy below rated by demanding huge power swings of plus and

minus three to four times rated power, which is totally unacceptable.

As turbine diameters increase in relation to the lateral and vertical length scales

of turbulence, it becomes more difﬁcult to achieve peak C

anyway because of the

non-uniformity of the wind speed over the rotor. Thus if one part of a blade is at its

optimum angle of attack at some instant, other parts will not be.

In most cases, it is actually not practical to maintain peak C

from cut-in all the

way to rated wind speed. Although some variable-speed systems can operate all

the way down to zero rotational speed, this is not the case with limited range

variable-speed systems based on wound rotor induction generators, which are

CLOSED-LOOP CONTROL: GENERAL TECHNIQUES 483

popular especially on larger turbines. These systems only need a power converter

rated to handle a fraction of the turbine pow er, which is a major cost saving. This

means that in low wind speeds, just above cut-in, it may be necessary to operate at

an essentially constant rotational speed, with the tip speed ratio above the optimum

value.

At the other end of the range, it is usual to limit the rotational speed to some

level, usually determined by aerodynamic noise constraints, which is reached at a

wind speed which is still some way below rated. It is then cost-effective to increase

the torque demand further, at essentially constant rotational speed, until rated

power is reached. Figu re 8.3 illustrates some typical torque–speed trajectories,

which are explained in more detail below. Turbines designed for noise-insensitive

sites may be designed to operate along the optimum-C

trajectory all the way until

rated power is reached. The higher rotational speed implies lower torque and in-

plane loads, but higher out-of-plane loads, for the same rated power. This strategy

might be of interest for offshore wind-turbines.

8.3.3 Pitch control for variable-speed turbines

Once the rated torque has been reached, no further increase in load torque can

occur, so the turbine will start to speed up. Pitch control is then used to regulate the

rotor speed, with the load torque held constant. A PI or PID controller is often

satisfactory for this application. In some situations it may be useful to include notch

ﬁlters on the speed error to prevent excessive pitch action at, for example, the

blade-passing frequency or the drive train resonant frequency (see Section 8.3.5).

Rather than maintain a constant torque demand while the pitch control is

regulating the rotational speed, it is possible to vary the torque demand in inverse

proportion to the measured speed in order to keep the power output, rath er than

the torque, at a constant level. Provided the pitc h controller is able to mai ntain the

speed close to the set point, there will be little difference between these two

approaches. The reduction of load torque with increasing speed has a slight

destabilizing effect on the pitch controller, but this is often not serious, and

provided the gearbox torque and rotor speed variations are not greatly affected, the

constant pow er approach is attractive from the perspective of power quality and

ﬂicker.

8.3.4 Switching between torque and pitch control

In practice, acoustic noise, loads or other design constraints usually mean that the

maximum allowable rotor speed is reached at a relatively low wind speed. As the

wind speed increases further, it is desirable to increase the torque and power

without any further speed increase, in order to capture more energy from the wind.

The simplest strategy is to implement a torque–speed ramp: line CD in Figure 8.3

Once rated power or torque is reached, pitch control is used to maintain the rotor

speed at its rated value. In order to prevent the torque and pitch controllers from

interfering with one another, the speed set-point for the pitch controller is set a little

484 THE CONTROLLER