Gasch R., Twele J. (Eds.) Wind Power Plants: Fundamentals, Design, Construction and Operation
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422 Annex I
Individual or coupled blade pitching by the propeller moment is part of this group,
too. Fig. 12-21 shows the principle and performance characteristics of such a ro-
tor. Fig. 12-22 gives the block diagram for such designs. The proportional control
keeps the rotational speed almost fixed, but there is a small proportional offset.
The synchronization of the individual actuators assures a smooth start of the con-
trol, and moreover avoids aerodynamic unbalances. Fig. 12-23 shows such a syn-
chronized rotor.
Turbine
M = M (˖, v,
J
)
Driving
torque M
R
Load torque
-M
L
+
Angular speed
˖
Inertia 4
dt
M
³
4
'
':
Wind
v (t)
Regulator and actuator
Pitch
angle
˖
Turbine
M = M (˖, v,
J
)
Driving
torque M
R
Load torque
-M
L
++
Angular speed
˖
Inertia 4
dt
M
³
4
'
':
Wind
v (t)
Regulator and actuator
Pitch
angle
˖
Fig. 12-22 Block diagram of the control system with a centrifugal governor
˖
Normal operation Pitching Storm position
Pre-stressed spring Fly weight
˖
Normal operation Pitching Storm position
Pre-stressed spring Fly weight
Fig. 12-23 Hub of a pitch rotor with centrifugal mechanism (see Fig. 12-21)
Passive control by aerodynamic forces
According to aerodynamics, the point of action of lift and drag forces is found at
about 25% of blade chord length for a wide range of angles of attack. If a profile is
not aligned on the radial line with its “c/4 point”, a torque is generated. Depending
12 Supervisory and control systems for wind turbines 423
on the chosen alignment of the chord, this torque tries to turn the profile into or
out of the inflow. This torque is
Treg
FxM
, (12.12)
where x is the distance between the radial pitch axis and the point of action of the
thrust F
T
. The thrust on one rotor blade is
T
2
T
32
cv
A
F
U
. (12.13)
Rotor shaft
Hub
Hub
Blade bearing
Anschlag
End stop
Rotation
Rotor shaft
Belt
Tension
spring
Blade pitch axis
Profile
Resulting pressure point
F
S
F
u
F
R
M
v
x
Resulting
pressure point
Effective
lever arm x
Blade
pitch axis
Pressure line
Section
view
Section
view
Cam disk
Rotor shaft
Hub
Hub
Blade bearing
Anschlag
End stop
Rotation
Rotor shaft
Belt
Tension
spring
Blade pitch axis
Profile
Resulting pressure point
F
S
F
u
F
R
M
v
x
Resulting
pressure point
Effective
lever arm x
Blade
pitch axis
Pressure line
Section
view
Section
view
Cam disk
Fig. 12-24 Principle and design of a passive control by aerodynamic forces [7]
Similar to the aerodynamic forces, this torque is proportional to the square of the
wind speed. It is, therefore, well suited as input of the control. For the common
pitching towards feather, the point of action of the aerodynamic forces on the
chord has to lie behind the radial line. Similar to the centrifugal pitch, a spring de-
termines the start of the control action and the control characteristics as well. The
blades should be synchronized in order to avoid aerodynamic unbalances. Com-
bined with a synchronous generator, this mechanism provides a simple and easy
system that operates independent of external energy.
424 Annex II
Annex II
The differential equation for the control behavior of wind turbines and its
linearization around the operating point
If pitch control is used, the control action has to be sufficiently fast to assure con-
stant rotational speed for instance during gusts. In addition, it has to be stable and
must not generate any unstable oscillations. Therefore, the differential equation
describing this dynamic behavior has to be analyzed. Fig. 12-7 has already pre-
sented a simplified block diagram of a wind turbine. In the following, the corre-
sponding differential equation of motion are presented:
4
:
M
L
(:, P
el
) – M
T
(:, v,
D
) = 0 (12.14)
with
4 moment of inertia of the rotor
M
L
counteracting torque of the load which opposes the rotation
M
T
accelerating torque of the turbine
: angular velocity of the turbine
:
angular acceleration
P
el
electrical power output (in stand-alone operation)
v wind speed
D
blade pitch angle (denoted
J
in Fig. 12-7)
In a pitch control the pitch angle
D will be manipulated in order to control the
torque of the turbine, which is the main objective. This torque is also dependent on
wind speed and rotational speed, cf. Figs. 6-15 and 6-16. For a closer analysis of
the control dynamics, it is useful to linearize the above differential equation
around a fixed operating point. M
T
is therefore expanded in a Taylor’s series. M
T
can be calculated from the moment coefficient c
M
which depends on the tip speed
ratio and the blade pitch angle.
M
T
=
2
U
A
R
c
M
(
O
D
) v
2
R =
2
U
A
R
c
M
¸
¹
·
¨
©
§
D
O
,
v
R
v
2
R (12.15)
where
U
air density
R rotor radius,
A
R
swept rotor area,
O
tip speed ratio.
12 Supervisory and control systems for wind turbines 425
For the Taylor series, the partial differentials of M
T
are required:
),2(
2
2
2
2
,
M
MR
R
2
M
rotorM
T
R
c
vcRA
RAv
v
c
AvRc
v
M
:
w
w
w
w
w
w
w
w
O
DO
U
U
O
O
U
DO
(12.16)
Rv
c
A
M
2
M
R
T
2
D
U
D
w
w
w
w
(12.17)
vR
c
A
Rv
c
A
M
2
M
R
2
M
R
T
2
2
O
U
O
O
U
w
w
:w
w
w
w
:w
w
(12.18)
The partial derivatives of M
T
can be graphically interpreted. The common repre-
sentation of the moment coefficients depending on the tip speed ratio with
D
as a
parameter shows clearly
O
w
w /
M
c
as the tangent of the corresponding c
M
(
O
)-
curve at the operating point
O
=
O
op
. If the moment coefficients are plotted in the
(
O
,
D
)-plane, Fig. 12-25, it becomes clear that
O
w
w
/
M
c
corresponds to the slope of
the tangent in direction of
D
at the operating point
D
=
D
op
and
O
=
O
op
.
D
D
O
,
M
c
OP
O
O
D
D
D
O
,
M
c
OP
O
O
D
Fig. 12-25 Interpretation of the partial derivatives of c
M
at the operating point as linear tangents,
blade pitch angle D
426 Annex II
From the Taylor expansion of the performance characteristics c
M
= c
M
(
O
D
) we
obtain a linearized representation of the curve of the turbine torque
M
T
= M
T
(
D
:
, v) in the neighborhood of an operating point which is given by
O
op
and
D
op
:
':
»
»
¼
º
«
«
¬
ª
w
w
'
»
»
¼
º
«
«
¬
ª
w
w
'
»
»
¼
º
«
«
¬
ª
:
w
w
':
:w
w
'
w
w
'
w
w
'
0
ȜȜ
ĮĮ
M
2
R
2
0
ȜȜ
ĮĮ
M
R
0
ȜȜ
ĮĮ
M
0opopMR
ȜȜ
ĮĮ
T
ȜȜ
ĮĮ
T
ȜȜ
ĮĮ
T
T
op
op
op
op
op
op
op
op
op
op
op
op
|
2
|
2
|,2
2
|||
v
c
RAv
c
RA
vR
c
vcRA
MM
v
v
M
M
O
U
D
D
U
O
DO
U
D
D
(12.19)
If we assume that the consumer load also changes only in a linear way with the ro-
tational speed, we obtain for the speed
:
=
:
0
and for a wind speed v
0
the lin-
earized differential equation:
D
D
U
O
DO
U
O
U
'
»
»
¼
º
«
«
¬
ª
w
w
'
»
»
¼
º
«
«
¬
ª
:
w
w
':
:w
w
':
w
w
:4
2
0
ȜȜ
ĮĮ
M
R
0
ȜȜ
ĮĮ
M
0opopMR
L
0
2
ȜȜ
ĮĮ
M
R
op
op
op
op
op
op
|
2
|,2
2
|
2
v
c
RA
vR
c
vcRA
M
vR
c
A
(12.20)
The change of the torque is caused by the change of rotational speed (through the
load and turbine curve), changes in wind speed, and changes in the blade pitch
angle. Only the latter is manipulated by the control. The design must assure that
the change in the rotational speed
'
:
is translated rapidly enough into a change of
the angle of attack
'
D
, without causing any oscillations in the control loop.
Fig. 12-26 shows how equation (12.20) may be represented in a block diagram
using the common symbols of control engineering for proportional, integral and
delay time terms.
12 Supervisory and control systems for wind turbines 427
Inertia
˂v ˂˖
+
-
˂M˂˞
':
:w
w
T
M
v
v
M
T
'
w
w
D
D
'
w
w
T
M
Measurement
rot. speed
Controller
Ĭ
Inertia
˂v ˂˖
++
--
˂M˂˞
':
:w
w
T
M
v
v
M
T
'
w
w
D
D
'
w
w
T
M
Measurement
rot. speed
Controller
Ĭ
Fig. 12-26 Block diagram for the linearization of the turbine characteristics
References
[1] Föllinger, O.: Regelungstechnik (Control Engineering), 6th edition 1990, Hüthig
Buch Verlag, Heidelberg
[2] Manwell, J.F. et al.: Wind Energy Explained, J. Wiley & Sons, UK 2002
[3] Burton, T. et al.: Wind Energy Handbook, J. Wiley & Sons, Chichester, UK 2001
[4] Heier, S., Windkraftanlagen (Wind Energy Converters): 3rd edition, Teubner Verlag
Stuttgart, 2003
[5] Schörner, J. et al.: Stand und Entwicklungsrichtung des Antriebsstranges von Wind-
kraftanlagen (State of art and development tendencies of wind turbine drive trains),
Windkraftjournal, Vol. 6/2001, p. 38-48
[6] Franquesa, M.: Kleine Windräder (Small wind turbines), Pfriemer Verlag, München,
1988
[7] Frieden, P.: WENUS: Innovative Konzepte zur Pitchregelung (WENUS: Innovative
concepts for pitch control), DEWEK 1994, Tagungsband
[8] Bossanyi, E. A.: Individual Blade Pitch Control for Load Reduction, Wind Energy, 6,
2, p. 119 – 128, 2002
[9] Bossanyi E. A.: Further load reductions with individual pitch control, Wind Energy 8,
4, p. 481 – 485, 2005
[10] Bianchi, F. D., De Battista H., Mantz, R. J.: Wind Turbine Control Systems, Springer –
Verlag London, 2007
R. Gasch and J. Twele (eds.), Wind Power Plants: Fundamentals, Design, Construction 428
and Operation, DOI 10.1007/978-3-642-22938-1_13, © Springer-Verlag Berlin Heidelberg 2012
13 Concepts of electricity generation by wind
turbines
Wind turbines for power generation may be characterized according to their type
of application
- Grid-connected wind turbines
- Wind turbines for stand-alone operation and
- Wind turbines for hybrid systems, e.g. wind-diesel or wind-photovoltaic
systems.
Grid-connected wind turbines, section 13.1, have the advantage that their pro-
duced power can be fed into the grid at all times. The storage problem for excess
electrical energy, e.g. at night, is transferred to the grid and is solved there often
by using hydro power plants with pump storage facilities. These have in Germany
an installed capacity of approx. 6000 MW. Not only wind turbines produce some-
times excess electricity. Nuclear power plants which operate as base load plants
also have times, e.g. at night, when they cannot deliver all the produced power
directly to the consumer. Their excess “black” electricity is used to pump water
“uphill” at night, and during the day to satisfy peak demands it flows “downhill”
again, now delivering “green” electricity.
The problem of deficits in power generation from wind during periods of calm is
passed on to the grid as well. The grid then depends on steam powered or gas
powered generators which can be brought on-line within minutes. Thus, grid-
connected wind turbines have it easy as far as mismatches between supply and
demand for electricity are concerned. However after start-up, they have to be con-
nected smoothly to a grid which operates with firm values of voltage, phase and
frequency and tolerates only modest levels of harmonics. This demands substan-
tial outlays for the control of the power electronics in the interface to the grid (see
chapter 14).
Wind turbines in stand-alone operation or small insular grids can usually func-
tion with more relaxed rules, see section 13.2. For many devices it does not matter
if they are run at 47 Hz or 52 Hz. The key issues are here: What to do with the
electrical energy if no one needs it? Quite often, “dead loads” are turned on, which
turn the excess power into heat. Even more problematic is a lack of power produc-
tion: less important loads, e.g. the washing machine, are switched off by a priority
control, and energy storage systems and accumulators are used where they are
available. If the storage systems are empty and there is still no wind, one is on the
safe side only with a hybrid system, e.g. a wind-diesel system, section 13.3.
13 Concepts of electricity generation by wind turbines 429
13.1 Grid-connected wind turbines
The diameter of the rotor was around 10 m in 1980; today it exceeds 100 m for
machines rated at 3 MW – an this is not the only significant change! The truly
revolutionary development took place on the electrical side of the system. Ini-
tially, the rotational speed of the wind turbine was coupled rigidly to the grid fre-
quency for both, the synchronous (SG) and the asynchronous generator (ASG, i.e.
induction generator).
However, the discussion of aerodynamics in chapter 5 showed that optimal opera-
tion of a wind turbine requires that it must be running with the design tip speed
ratio O
opt
. The turbine can deliver the largest possible amount of power only, if its
rotational speed adapts to the varying velocities of the wind in such a way, that it
remains at O
opt
. This is to say: double wind velocity requires double rotational
speed.
Thanks to developments in power electronics during the 1980s and 1990s we
now build variable-speed, “wind speed governed” wind turbines even for the MW
class. Turbine and generator initially produce a “wild” three-phase current of vari-
able frequency and voltage. This current is rectified and then converted back into
three-phase current – but now of 50 or 60 Hz. Miraculously, for a whole decade
the ratings of affordable AC-DC-AC converters increased in parallel with similar
increases in the power ratings of the wind turbines.
The company Enercon pioneered the concept of variable-speed, “wind speed
governed” operation. In 1993, this new wind turbine concept entered the market
with their wind turbine E-40, which has no gears and uses an annular synchronous
generator that feeds into the grid via a converter. This concept was and still is eco-
nomically quite successful, cf. section 13.1.3.
In the beginning of the 1990s, the asynchronous machine had become quite
flexible with regard to the rotational speed due to the Opti-Slip concept of Vestas:
an adjustable resistance in the rotor circuit allows the machine brief increases in
the rotational speed of up to 20% during wind gusts, cf. section 13.1.2.
The asynchronous machine eventually gained complete variability of speeds
thanks to the introduction of a guided converter in the rotor circuit (doubly-
feeding AS machine with a current converter cascade that may work above or be-
low synchronous frequency), cf. section 13.1.4. The advantage of this concept,
which entered the market approx. 1996 (Loher-SEG), is that not the entire gener-
ated power has to be converted as for the synchronous machine, but only that part
of it which is required or produced in the rotor. Moreover, the asynchronous
machine loses its disadvantage of reactive power consumption from the grid. Due
to the converter in the rotor circuit it is able to provide controllable reactive power
to the grid – like the synchronous machine with converter.
430 13.1 Grid-connected wind turbines
Asynchrongenerator Synchrongenerator
Über Umrichter ins Netz Direkt ins Netz
drehzahlvariabel drehzahlsteif
n
max
/n
min
¡ 2:1
Blindleistung regelbar Blindleistungsbedarf
dynamische Stall-
Schlupfregelung gesteuert
mit Pitchverstellung mit/ohne Pitchen kein Pitchen
n
Gear
box
f
ASG
n
Gear box
DC
=
~
=
~
f
SG
with/without
n
Gear box
f
ASG
n
Gear box
f
DC
=
~
~
=
ASG
As above but permanent magnetic excitation
n
max
/n
sync
= 1 : 1,05
n
max
/n
sync
= 1 : (1,10 - 1,20)
n
Rotor
Substation
÷
Synchronous generator
Asynchronous generator
Direct to the grid, need of
reactive power,
nearly constant speed
Stall control
Without pitch
Dynamic slip
control, with/
without pitch
with pitch
AC-DC-AC conversion
reactive power adjustable
variable speed n
max
/n
min
§ 2:1
÷
Asynchrongenerator Synchrongenerator
Über Umrichter ins Netz Direkt ins Netz
drehzahlvariabel drehzahlsteif
n
max
/n
min
¡ 2:1
Blindleistung regelbar Blindleistungsbedarf
dynamische Stall-
Schlupfregelung gesteuert
mit Pitchverstellung mit/ohne Pitchen kein Pitchen
n
Gear
box
f
ASG
n
Gear box
DC
=
~
=
~
f
SG
with/without
n
Gear box
f
ASG
n
Gear box
f
DC
=
~
~
=
ASG
As above but permanent magnetic excitation
n
max
/n
sync
= 1 : 1,05
n
max
/n
sync
= 1 : (1,10 - 1,20)
n
Rotor
Substation
÷
Synchronous generator
Asynchronous generator
Direct to the grid, need of
reactive power,
nearly constant speed
Stall control
Without pitch
Dynamic slip
control, with/
without pitch
with pitch
AC-DC-AC conversion
reactive power adjustable
variable speed n
max
/n
min
§ 2:1
÷
Fig. 13-1 Types of grid-connected wind turbines
13 Concepts of electricity generation by wind turbines 431
Fig. 13-1 gives an overview of these four wind turbine types for grid-connected
power generation:
- wind turbine with asynchronous generator feeding directly into the grid
(Danish concept),
- its improvement with dynamic slip control,
- the variable-speed wind turbine with synchronous generator feeding the
entire power via a converter into the grid and
- the variable-speed wind turbine with asynchronous generator and a con-
verter in the rotor circuit feeding only a part of the power via a converter
into the grid.
Each type will be discussed briefly below. The number of types of available ma-
chines was enlarged in 2005 by wind turbines which use permanent magnets to
supply the excitation in a synchronous generator and provide AC-DC-AC conver-
sion of the entire produced power [9].
13.1.1 The Danish concept: Directly grid-connected asynchronous
generators
In the 1980s, the asynchronous generator (induction generator with a squirrel-cage
rotor) that is directly connected to the grid dominated the market for wind turbines
completely. This is known as the ‘Danish concept’, which was developed in the
1950s by the engineer Johannes Juul and tested at the Gedser wind turbine (1957-
1967), cf. chapter 2.
The Danish wind turbines with a capacity of 30 to 450 kW (D = 12 to 35 m)
were typically equipped with one small and one large asynchronous generator. In
today’s machines, only pole changing is used. If the wind speed is sufficiently
high, the small asynchronous machine is connected to the grid. At first the turbine
accelerates in the motor mode, but when it exceeds the synchronous speed it
changes automatically to the generator mode. If the wind speed increases, the
small generator is switched off and the large generator switched on. Its operating
point lies at a higher rotational speed, to the right in the performance characteris-
tics diagram, Fig. 13-2. Therefore, it follows the increasing supply of power by the
turbine rotor and reaches once again the turbine optimum. This generator operates
up to wind speeds of 25 m/s where the turbine cuts out because of severe storm
conditions. The generator keeps the rotor close to the (gear transmitted) synchro-
nous speed, if it was designed robust enough to prevent a ‘pulling out’ (M > M
p
),
cf. section 11.2.2. The power of the turbine is limited in a quite “natural” way, by
flow separation at the rotor blades. Therefore, no pitching is necessary to control
and limit speed and power. Only in case of a power failure in the grid, spoilers or
tip brakes are deployed by centrifugal mechanisms. They serve to prevent over-
speeding, cf. section 12.1.1.