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CHAPTER 4
PITCH CONTROL OF WIND TURBINE GENERATORS
4.1
INTRODUCTION
The use of wind power has in the last decade increased in the
central parts of Europe and at the west coast of the U.S. The rest of the world
is following these and today this is the fastest growing energy source on a
world basis. India has one of the fifth largest wind power installed capacity in
the world.
This chapter describes the modeling of the various components in a
pitch controlled wind energy system. It also describes the design of the pitch
controller and discusses the response of the pitch-controlled system to wind
velocity variations. The pitch control system is found to have a large output
power variation and a large settling time.
The pitch function gives full control over the mechanical power and
if the most common method is used for the variable speed wind turbines. At
wind speeds below the rated power of the generator, the pitch angle is at its
maximum though it can be lower to help the turbine accelerate faster. Above
the rated wind speed, the pitch angle is controlled to keep the generator power
at rated power by reducing the angle of blades.
The pitch control system is one of the most widely used control
techniques to regulate the output power of a wind turbine generator. The
method relies on the variation in the power captured by the turbine as the
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pitch angle of the blades is changed. Hydraulic actuators are used to vary the
pitch angle. The wind turbine generator describes the design of the pitch
controller and discusses the performance of the system in the presence of
disturbances.
The control system consists of two controllers are inverter
controller that keeps the load voltage constant and the pitch controller acting
on the blades angle by using simulation.
The variable speed induction generator using Volts/Hertz control
enables efficient wind energy capture and is shown in Figure 4.1. The output
of the generator-side converter can be varied to control the speed of the
induction generator (Schians 2007). The grid-side converter can be controlled
to inject the desired power and reactive power into the grid. Thus, the wind
system is capable of providing reactive power support, if required. The
disadvantage of this configuration is the large cost associated with the power
converter, since the converter has to be rated for the maximum power output
of the generator.
Figure 4.1 Volts / Hertz controlled induction generator
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For fixed speed turbines, the active stall can be used to limit the
power, not by reducing the pitch angle as in pitch controlled, but by
increasing the pitch angle to a point where the blade stalls and in that way
reduces the force on the turbine. By regulating, the angle to be on the limit of
stalling, fast torque changes from the wind will be neutralized (Schinas et al
2007; Nayar and Bundell 1987).
4.2
PRINCIPLE OF CONTROL
4.2.1
Aerodynamic Power Control for Wind Turbines
When a generator reaches rated power, the turbines must limit the
mechanical power delivered to the generator. This is valid because the
generator reaches the rated power at for instance 15 m/s while the maximum
speed is typically 25 m/s for a wind turbine. Control is done by three different
methods called stall, pitch and a combination called active stall.
There are no moving parts in the stall-controlled blades and the
challenge is in the construction of the blades to avoid vibration and make
them stall gradually.
The pitch angle is controlled to keep the generator power at rated
power by reducing the angle of the blades. By regulating, the angle to be on
the of stalling, fast torque changes from the wind will be reutilized (Nayar and
Bundell 1987).
The power captured by the turbine is given by
Pm = Pw × C p
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Figure 4.2 Airstreams around a turbine
The mass flow rate is a constant for upstream (0), the rotor (1) and
down stream (2) mass flow rate mass as shown in Figure 4.2.
m = pA0V0 = pAV
1 1 = pA2V2
(4.1)
The turbine model represents the power captured by the turbine.
The power in the wind (Pw) in an area A is given by,
Pw =
1
ρ AVw3
2
(4.2)
where ρ is the density of air and Vw is the wind speed.
However, the turbine captures only a fraction of this power. The
power captured by the turbine (Pm) previously expressed as Pm = Pw × C p ,
where Cp is a fraction called the power coefficient. The power coefficient
represents the fraction of the power in the wind captured by the turbine and
has a theoretical maximum of 0.55. The power coefficient can be expressed
by a typical empirical formula as,
Cp =
1
γ − 0.022β 2 − 5.6 ) e −0.17γ
(
2
(4.3)
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The variation of CP with the pitch angle β for various values of the
tip speed ratio γ. Thus, by varying the pitch angle, the power coefficient can
be changed and the power captured by the turbine can be controlled. If the
Cp-γ performance characteristic is available, the turbine parameters can also
be modeled from data fields containing the group of curves derived from
measurement or from calculation or analytical function. The groups of power
coefficient and tip speed ratio curves obtained by measurement or by
computation can also be approximated in closed form by non-linear functions
as shown in Figure 4.3.
Figure 4.3
Power Coefficient vs tip speed ratio for various values of
pitch angle
Normal operation, blade pitch adjustments with rotational speeds
are approximately expected at βn = 5 to 10 °/ S = 0.09 to 0.17 rad/sec
(Siegfried 2006).
4.2.2
Wind Turbine Controller
The name of the controller for the wind turbine is the multi
processor controller, which is an abbreviation of multi processor controller.
The controller monitors and controls all functions in the turbine, in order to
ensure that the performance of the turbine is optimal at any wind speed.
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The control will stop the turbine if supervision detects an error. At
an operator panel, data of current operation is displayed.
The multi processor controller is divided in to two parts:
1.
Ground controller and
2.
Top-controller.
Ground processor takes care of cut in and cutout of the generator
and the capacitors and of current and voltage measurement. Top processor
takes care of the tasks in the nacelle, example: Speed, pitch and power control
yawing and internal temperature control (www.awea.org).
4.2.3
Data Collection
The multi processor controller collects continuously data about the
performance of the turbine example:
¾
Rotor and generator speed,
¾
Wind speed,
¾
Hydraulic pressure,
¾
Temperature,
¾
Power and energy production and
¾
Pitch.
If some irregularities or errors arise, the data is stored in a LOG
and/or an ALARM LOG, making it possible to analyze errors in the turbine.
4.2.4
System of Parameters
The software to the MP-controller system is basically constructed
so that all variables can be initialized. Examples of parameters are power
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reference, various alarm limits, calibration values for anemometer etc. To
every type of turbine and variants, a set of parameters is present, which is
selected by start-up of the turbine.
4.2.5
Turbine Control with OptiTip
When the turbine is stopped (PAUSE, STOP or EMERGENCY
STOP), the blades will be present in a pitch angle of 90ْ (out of the wind), as
shown in Figure 4.5. When the turbine is in RUN-mode, it is able to produce
electrical energy, but the momentary wind conditions are determining for how
much. This is controlled by the OptiTip control system of the multi processor
controller.
The momentary wind conditions can be divided into four
categories, shown by the power curve in Figure 4.4,
Figure 4.4 Power Curve
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1.
Low wind, the generator is not connected to grid.
2.
Medium wind, the generator is connected, but does not
produce nominal power.
3.
Higher wind, the generator is connected and produces nominal
power.
4.
Stop wind, the generator is disconnected and the turbine is
stopped.
When the wind is very low and the rotor does not rotate with a very
low speed, the pitch angle will be approximately 450. This will give maximum
start moment to rotor, which gives a quicker start, when the wind increases.
The MP-controller will then pitch the blades to 0ْ (into the wind).
The rotating speed for the rotor and the generator will increase towards the
nominal, which the multi processor controllers will try to keep (speed
control).
The same situation occurs with connected generator. When the
wind decreases and the produced power become negative, the generator will
be disconnected from the grid and the MP controller will control the speed. If
the wind decreases even more then the rotating speed will decrease below
nominal value and the rotor will run freely.
At medium wind speed, the rotating speed is regulating to the
nominal value and if the pitch angle can be kept at 50 (which says that there
would be enough energy in the wind), the generator is connected to the grid.
With the generator connected and but enough energy in the wind to
produce nominal power, the pitch angle is regulated as a function of the wind
speed.
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This function is calculated with precision, simulated and evaluated
by measurements. It is called OptiTip. This is implemented in turbines to
optimize the aerodynamics of the blades, which will optimize the energy
production as shown in Figure 4.5.
Figure 4.5 Pitch setting at different operating states
When the generator is producing power, it causes a torque, in
opposition to the mechanical torque of the rotor.
The MP-controller based fully automatic systems controls the
produced powers, so the rotor speed is kept constant within a narrow band,
which is called slip, which is the procentual relation between actual and
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synchronous rotating speed and optimal adjustment of the angle of the blade
in relation to the prevailing wind, thus generating maximum power.
Such processes are currently used by machines in 30 KW to MW
range that employ power electronics to convert the frequency to that required
with their design in the limits, such models permit.
4.2.6
Power Factor Correction
An asynchronous generator contains no permanent magnet and is
not separately excited. That means, that an asynchronous generator has to get
exciting current from the grid and the magnetic field is only established, when
generator is connected to the grid.
When the generator excites current from the grid, the generator
consumes reactive power from the grid. The current in the cable to the
generator will consist of two parts,
1.
Active current corresponding to the active power production
(KW) and
2.
Reactive current corresponding to the reactive power
consumption (KVAr).
Because of the exciting current, there is a phase shift between the
current and the voltage. The current delayed compared to the voltage by an
angle (θ). A term of the phase shift is the power factor (cos θ).
A part of the generator’s exciting current / reactive power is
delivered from the capacitors, which are called power factor correction. The
capacitors are connected to the grid a little later than the generators are
disconnected, before the generator is disconnected from the grid.
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The advantage of the power factor correction is that the loss in the
grid decreases, because the grid current decreases. At no-load the grid current
is about zero Amp, because the generator’s no-load current (only reactive
current) is delivered from the capacitors.
4.3
PITCH CONTROL SYSTEM DESIGN
Pitch control means that the blades can pivot upon their own
longitudinal axis. The pitch control used for speed control, optimization of
power production and to start and step the turbine.
The control system structure used to generate the pitch angle
reference is given in Figure 4.6 (Murdoch et al 1982). The pitch controller
consists of two paths a nonlinear feed forward path, which generates β0 and a
linear feedback path, which generates ∆β.
Figure 4.6 Pitch angle reference generator
The feed forward path uses the information about the desired power
output, wind velocity and the turbine speed to determine the pitch angle
required. Equation (4.4) gives the pitch angle as a function of the measured
variables.
2 Pref e
1 ⎡
β0 =
⎢γ − 5.6 −
0.022 ⎣⎢
Pw
0.17 γ
⎤
⎥
⎦⎥
(4.4)
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However, the feed forward term assumes that all the components
are ideal and does not account for the losses in the system. The feedback path
compensates for the losses by decreasing the pitch angle, if the output power
is less than the desired power, to increase the power captured. The P-I
controller (Proportional integration) for the system is designed using the
Zeigler-Nicholas rules for tuning PID (Proportional integration and
differentiation) controllers.
4.3.1
Zeigler - Nicholas Rules
The method used here is the first method applicable for plants
without integrators or dominant complex conjugate poles, as the plant
response for the wind system is found to correspond to these requirements of
the Zeigler-Nicholas rules.
For a plant response to a unit step input as given in Figure 4.7, the
intersection of the tangent line at the inflection point with the start and end
values of the curve gives the delay time (L) and the time constant (T).
Figure 4.7
Obtaining the time constant and delay time for a response to
a unit step
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For a controller of the type
KP (1+1/Ti s)
The values of KP and Ti are given as
KP =0.9(T/L); Ti =L/0.3
4.3.2
P-I Controller Design
In order to use the Zeigler-Nicholas rules for designing the P-I
controller, the step response of the plant is required. The block diagram
showing the plant and controller used for generating the step response is
shown in Figure 4.8. The actuator is modeled as an integrator in a feedback
loop, as shown in Figure 4.9.
The rate limiter limits the rate of change of the pitch angle, as most
pitch actuators cannot change the pitch angle more than a particular degrees /
sec. The value used for the rate limiter in the simulations is 50 / sec.
Figure 4.8 Plant and controller definition
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Figure 4.9 Hydraulic actuator model used in the simulation
The unit-step response of the plant, obtained by applying a onedegree step input is shown in Figure 4.10 (Pena et al 1996). The measured
values of the time delay L and the time constant T are,
L = 0.03s and T = 0.155s.
Thus, the values of the proportional and integral constants are,
KP = 4.65 and Ki = 46.5.
Figure 4.10 Plant response to a unit step input
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The SIMULINK block diagram of the pitch controlled wind energy
system is shown in Appendix A3.
4.4
ANALYSIS OF FIELD TEST RESULTS
4.4.1
Wind Shear Correction
No correction needs to be applied to the wind speed-reading for
anemometer heights different from hub height.
4.4.2
Correction of Power for Air Density Variations
Before data analysis using the method of bins is carried out,
corrections to the data sets for air density variations must be applied. In this
procedure, the wind speed range of operation of the wind turbine is divided
into a series of intervals (bins).
The aim of the corrections is to bring the power curve and the
calculated mean power as close as possible to the values which would be
obtained if the measurements were all carried out at a standard air density at
sea level of 1.225 Kg / m3 (1013.3 mbar, dry air, 15.15 degree Celsius or
288.15 degrees Kelvin).
For a stall-controlled wind turbine, each 10 min average net power
values shall be corrected by applying the following formula:
Ps = PT [1.225 ρT ]
where,
Ps = Power corrected to standard conditions,
PT = Uncorrected average power,
ρT = Test air density and
(4.5)
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PT is calculated from 288.15 degrees Kelvin.
ρT = 1.225 [ 288.15 T ][ B 1013.3]
(4.6)
where,
B
= Barometric pressure, (mbar)
T
= t + 273.15 and
t
= Air temperature in degrees Celsius.
For a pitch-regulated WTG, the correction is the same as for a stall
controlled WTG as long as the measured power levels are below 70 % of
rated power. For measured power levels above 70 % of rated power, the
correction applies instead to wind speed (and not to power) according to the
following expression.
Vs = Vt [ ρT 1.225]
1/3
(4.7)
where Vt is the measured, uncorrected wind speed (m / s) and Vs is the wind
speed corrected to standard conditions.
ni
Pi = 1 ni ∑ Pij
(4.8)
j =1
where,
Vij = jth 10 minute average of wind speed in the ith bin,
Pij = jth 10 minute average of net power in the jth ith bin and
ni = Number of data sets in the ith bin.
The ensemble averages (Vi, Pi) are then plotted and a curve fitted
through the plotted points. This curve is the WT power curve. The minimum
conditions of shorter pre-averaging time does not reduce the total time, as the
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number of data sets per bin multiplied by the pre averaging time shall be
constant and must be met before the curve is established.
The power curve is a linearly scaled Cartesian coordinate system
graph of WT net power corrected for air density variations (ordinate) versus
wind speed (abscissa) as shown in Figure 4.11. Both scales start at zero. The
ordinate scale should extend to at least 110 % of the WT maximum power.
The abscissa should extend to a wind speed of at least 20 meters / second.
The power curve is to be displayed graphically as indicated in
Figure 4.11 and in form of a table as shown in Table 4.1. Care should be
taken not to apply air density corrections to fractions of the power, which are
not dependent on air density, such as gearbox and generator losses.
Figure 4.11 Output power profile of the pitch controlled wind turbine
generator
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Table 4.1 The results of the method of bins analysis
Bin no
Bin
interval
Number
of
datasets
Bin averages
m/s
n1
1
3.0-3.5
12
Wind
speed V2
(m/s)
3.27
2
3.5-4.0
10
3.73
-7.34
3
4.0-4.5
26
4.20
7.36
4
4.5-5.0
19
4.76
5.63
5
5.0-5.5
33
5.24
11.01
-
-
-
-
-
Nominally
-
-
-
-
-
fixed speed
-
-
-
-
-
02.6
21
13.0-13.5
18
13.22
119.7
22
13.5-15.0
22
13.76
120.4
23
15.0-16.0
11
15.07
116.5
24
16.0-18.0
5
16.93
111.8
25
18.0-70.0
6
18.87
113.1
Net
speed
P1 (kw)
-6.22
Rotor speed
(rpm)
If, for instance, the relation between net power P and rotor power PR is of the
form
P = α PR − β
(4.9)
with α and β constant, then the correction of power for air density variations
should be
Ps = 1.225 ρT (α PR − β )
(4.10)
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This will be the case with grid-connected, constant speed WTG,
where the electric losses normally will be proportional to the power produced,
while the mechanical losses in the drive train will be rotor speed dependent
and hence constant for a constant speed WTG.
4.5
RESULTS OF THE SIMULATION
The power output of the pitch-controlled wind turbine generator to
the wind velocity variation of Figure 4.12, is shown in Figure 4.13. The
desired output power is 12 KW. The output power variation is large (12 %)
and the settling time of the system is about 15 sec. The pitch angle reference
generated by the pitch controller and the actual pitch angle of the blades
(output of the actuator) are plotted in Figure 4.14.
The response of the pitch actuator is slow (the time constant is
1 second) and this limits the performance of the system. The plot of the rotor
speed is shown in Figure 4.15. The rotor speed is always above 1.0 p.u,
indicating that the generator is operating at super-synchronous speeds and has
pitch regulated rotor blades for high performance and for highly effective start
and break.
Figure 4.12 Wind speed profile used for simulation
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Figure 4.13 Output power profile of the pitch controlled wind turbine
generator
Figure 4.14 Plots of the pitch angle reference and the output of the pitch
actuator
Figure 4.15 Rotor speed of the induction generator
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4.6
THE MERITS OF PITCH REGULATED WIND ENERGY
GENERATORS
The two basic types of wind energy generators that have been
installed in India are “Pitch-regulated and stall-regulated.”
Pitch-regulated Wind Energy Generator (WEG) is manifold. In
Stall-regulated WEG’s as the blades are firmly connected to the rotor the flow
over the profile of the blade is lost and less torque is produced on the rotor
shaft thereby limiting the power output.
From the Figure 4.16 can be seen that a “Pitch Regulated WEG” is
preferable to a “Stall-Regulated WEG.” For a Pitch-Regulated WEG the
generation even after reaching maximum remains constant when speed
increases whereas in the Stall-Regulated WEG it starts to drop down.
Figure 4.16 Comparison of Power Curves of “Pitch-Regulated and StallRegulated WEG”
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The Pitch Regulated WEG has the following additional merits.
¾
Stopping of Rotor: The Pitch system makes it possible to
rotate the blades to a position, which stops and starts the rotor
at any wind speed.
¾
Active Control: The Pitch system is useful for active
regulation by which nominal power can always be reached.
However, in stall regulated, power curve can be changed only
by effecting a permanent change in blade angle.
¾
Speed: The Speed can be controlled prior to connecting the
WEG to the grid. That is, the pitch control system facilitates
rotation at proper speed for a longer period of time before
connecting to the grid.
¾
Lower wind speeds: Even at lesser winds in Pitch-Regulated
WEG’s maximum torque is obtained and the rotor starts
whereas in Stall Regulated WEG’s higher wind speed is
required, as the design is such. This in turn may lead to
decrease in the lifetime of the electrical components.
¾
Power: The power can be limited at locations with a weak
grid. The WEG can easily be regulated by the Pitch control
system and there is no need to change the WEG design to
produce less nominal power.
¾
Pitch Control System: The pitch control system is not
significantly affected by the change in air density and change
in temperature, about placement of the WEG’s at certain
heights above sea level. Maximum power production will be
always be attained in a pitch controlled WEG while in a stall
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controlled WEG it is poor when there is change in temperature
or and when the blades are dirty.
¾
Calculation of Blade and Rotor Loads: In the case of PitchRegulated WEG’s the blades always experience laminar flow
across the profile and turbulent, chaotic flow has no influence.
This means that WEG loads in a Pitch Controlled WEG are
determined in a more correct manner.
¾
Greater Flexibility: The Pitch-Regulated WEG can readily
be transformed to other turbine by changing the Pitch control
strategy and programming a different blade angle.
¾
Better test facilities: As the blade angle can be turned to, a
well-defined position is easier; it is simulation of specific
production or testing condition.
¾
Power optimization below nominal Power: The power is
optimized by rotating the blade to an angle, which results in a
better and optimized power production. This is done by the
pitch control system, which could compare the power
measured as a certain wind speed with a master curve and
change the pitch angle accordingly.
¾
Blade geometry: It is possible to optimize blade geometry
without worrying about power regulation and the same can
only be done by a Pitch system and not by Stall.
¾
Greater Capacity Factor: It is easy to get a greater capacity
factor for a Pitch Regulated WEG, since only a new pitch
control strategy (Software) and a smaller generator at same
speed is needed.
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¾
Reduced loading on the tower and foundation: The bending
load on the tower and foundation from the rotor is relatively
small as horizontal forces becomes smaller due to reduced
drags across the blade profile at high wind speeds.
¾
Less Noise at large wind speed: At large wind speeds, the
blade angle are greater and this in turn results in less noise
from the blade tip.
¾
Blade as one Structural Element: Each blade is one
structural
element
without
hydraulic
system
and/or
mechanical systems to rotate the blade tip as an aerodynamic
brake. For Pitch-Regulated WEG’s, the total blade is an
aerodynamic brake. As such, even at low wind velocity, the
Pitch regulated blade has a large surface area against the wind
and as the wind-velocity increases this surface area decreases
gradually resulting in optimum production at all times.
4.7
SCOPE FOR THE FUTURE
For adapting the usage of the pitch angle mechanism of the stepper
motor as shown in Figure 4.17 in place of the hydraulic actuator, following
mechanism is involved given below:
1.
Stepper motor – 10 Kg torque, 60 RPM, 24 V and 2 amps, 10
degree.
2.
Single axis travel mechanism.
3.
Piston inside the shaft.
4.
Converter for linear movement to circular movement. Based
on the RPM sense, the stepper motor will rotate clockwise or
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anti-clockwise of travel mechanism. The travel mechanism
will move the piston to front and back (that is some linear
movement). The linear movement of the piston gets converted
to circular movement of the blade axis by reciprocating links
and it is an easy mechanism. This converts linear moment to
circular moment, there by making the blade rotate circularly.
Figure 4.17 Pitch angle mechanism of the stepper motor
The cost is very low comparing to hydraulic actuator mechanism.
This mechanism can be used up to 30 KW wind turbine.
4.8
SUMMARY
The pitch control system is easy to implement, but the response is
slow and output power variation is large. The aerodynamic power control for
the variable speed wind turbine can limit the power into the turbine by
reducing the angle of the blades. The pitch control has a large response time.
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Therefore, fast torque changes caused by wind gusts will affect the
generator. The speed range of the generator is depending on the converter
voltage and the load situation. A higher voltage available for the converter in
the rotor circuit, will give a higher range of speed. A speed was chosen to
make the generator choose the mechanical speed, which gives the best power
output related to the wind speed. A rate limiter was chosen to avoid fast
changes in the mechanical speed.
The scaling of the converter could be investigated and compared
with the winding ratio of the machine, to find the optimal winding ratio
compared with bus voltage in the converter. The response time is mainly
dictated by the hydraulic actuator, which limits the performance of the
system. The controller should be used in conjunction with the pitch control
system to avoid large losses during steady state operation. The pitch angle
mechanism of the steeper motor is also discussed.