TEMPUS ENERGY: WIND TURBINE CONTROL
1: Introduction
When using wind energy to generate electrical power, it is not sufficient to have a wind
turbine containing reliable components. It is also important to have appropriate control
systems, management systems and safety systems.
Figure 1 visualizes a wind turbine without any control system. There is no pitch control and
the generator (it can be an asynchronous generator or a synchronous generator) is
connected with the grid without using any power electronic converters. The power injected
into the grid is time-varying and weather dependent i.e. it is not possible to control this
power. When the power of such a wind turbine is small in comparison with the total grid
power, no problems occur. Other power generating units will be controlled in such a way the
power balance of the grid is maintained.
Figure 1: Wind turbine injecting an uncontrolled supply (source Heier)
In case the power generated by the wind turbine (or by a number of wind turbines) is a
significant part of the total power consumed by the loads in the grid, power balance
problems will occur in the grid. In such a situation, it is not possible to use wind turbines
injecting such an uncontrolled supply.
Figure 2 visualizes a thermal power station injecting power into the grid. The power balance
has its impact on the grid frequency and the grid voltage level. For instance using droop
control, it is possible to control the generated power which is injected into the grid. By
adjusting the fossil fuel consumption, by controlling the amount of steam sent to the
turbine, by controlling the excitation of the synchronous generator the generated active and
reactive power can be controlled.
Figure 2: Thermal power station injecting a controlled supply (source Heier)
Figure 3 visualizes a controlled wind turbine injecting its power into the grid. The power
balance has its impact on the grid frequency and the grid voltage level. For instance using
droop control (or another control mechanism), it is possible to control the generated power
which is injected into the grid. Indeed, by controlling for instance the pitch angle of the rotor
blades, the generated active power can be controlled. In case the wind turbine contains a
generator in combination with power electronic converters, the injected power can also be
controlled by controlling the speed of rotation.
Figure 3: Wind turbine injecting a controlled supply (source Heier)
When considering the wind turbine of Figure 3, the power supplied by the wind is timevarying i.e. it depends on the wind speed. This means the maximum power which can be
injected into the grid depends on the time-varying wind speed. The control mechanism is not
only needed to change the power which is injected into the grid according to the needs of
the grid, the control mechanism is also needed to inject a constant power into the grid as
the wind speed is changing.
When considering the thermal power station of Figure 2, the fuel consumption and the
steam flow is controlled which controls the primary available power. When considering the
wind turbine of Figure 3, the situation is totally different. Notice that the control mechanism
is not able the change the power of the oncoming wind. The control mechanism only
controls what part of the power of the oncoming wind is converted into electrical power.
This electrical power can be maximized but in other situations this power can be limited. A
limitation of the electrical power can be useful
-
to avoid an excess of power injected into the grid (to maintain the power balance),
to limit the electrical power to the rated value in order to protect the mechanical and
electrical installation of the wind turbine (in case of wind speeds which are higher
than the rated wind speed).
Notice control mechanisms are not only needed to control the power which is injected into
the grid. Control mechanisms are also needed to start the wind turbine, to shut down the
wind turbine, to protect the wind turbine against damage (e.g. by performing an emergency
shut-down). In general, there are two levels of control system operation: the dynamic
control systems and the supervisory control system (also called management system).
2: The dynamic control system and the supervisory control system
From a hierarchical point of view, the supervisory control system operates at a higher level
than the dynamic control systems. Based on measurements (measuring internal conditions
like temperature, accelerations, pitch angle,… and measuring external conditions like wind
speed, consumer desires, grid frequency,…) the behavior of the wind turbine (or the wind
turbine farm) can be controlled.
The supervisory control system takes decisions on logical connections and determines the
set points for the dynamic control (for instance it determines the desired pitch angle for the
blades, the desired speed of the wind turbine, the required power). Moreover, the
supervisory control system is responsible for
-
the automatic start-up and shut-down of the wind turbine depending on wind and
turbine conditions,
safety monitoring of the turbine components (based on measurements, faults can be
detected implying the need for a shut-down to protect the installation).
A distinction is needed between
-
wind turbines operating in island mode where the wind turbine feeds a smaller local
grid without other generating units,
grid connected wind turbines.
3: Wind turbines operating in island mode
3.1: Wind turbines without a control system
In general, a small wind turbine installation must be inexpensive which implies a control
system (including a pitch control system of the rotor blades) is often omitted. In case such a
single wind turbine is feeding an electrical load in island mode, it is difficult to maintain the
power balance. Figure 4 visualizes such a small wind turbine equipped with fixed rotor
blades (no pitch control) and a self-excited synchronous generator.
Figure 4: Wind turbine without a control system feeding loads in island mode (source Heier)
Figure 5: Typical power production of a wind turbine
A typical relationship between the generated power 𝑃 and the speed of rotation 𝑛 of the
rotor is visualized in Figure 5 for different wind speeds. In case the generator feeds a load
consuming a constant electrical power, the wind turbine will operate in working point 1
when the wind speed equals 8 𝑚/𝑠. Working point 1 is a stable working point. As the speed
of rotation increases (while the wind speed remains constant), the generated power
decreases which implies the consumed electrical power is larger than the generated power.
Kinetic energy will be consumed implying a decrease of the speed of rotation and working
point 1 is regained. A similar transient occurs when the speed of rotation temporarily
decreases which implies working point 1 is a stable working point.
When the wind speed increases (for instance from 8 𝑚/𝑠 to 10 𝑚/𝑠) starting from working
point 1, more power will be extracted from the wind. The excess of power will be used to
increase the speed (since the consumed electrical power remains constant) and arrive in
working point 2 . In working point 2, the speed of rotation is higher implying the
synchronous generator generates a higher frequency. As visualized in Figure 4, in case the
wind turbine contains no control system the frequency (and also the amplitude) of the
generated voltage will change as the wind speed changes.
Suppose the wind speed increases from 8 𝑚/𝑠 (working point 1) to 10 𝑚/𝑠. In order to
avoid working point 2 and the changing frequency of the supply voltage, working point 3 can
be obtained by increasing the consumed power. Since the speed of the synchronous
generator is the same when comparing working points 1 and 3, the generated frequency
remains the same.
The consumed power can be increased by adding additional loads or by adding a bypass
controlled by the speed of rotation as visualized in Figure 6. This bypass is a so-called dump
load, the higher the wind speed and the lower the other useful loads the more power is
consumed by this dump load. For instance this energy can be stored in batteries to be used
in case there is no wind in order to supply the loads.
Figure 6: Wind turbine having a controllable load (source Heier)
3.2: Wind turbines with a control system
Figure 7 visualizes a wind turbine feeding a number of loads in an island configuration. When
feeding sensitive electrical loads, the supplied voltage level and the frequency should be
kept almost constant. To achieve this property, the consumed electrical power must always
be smaller than the power which can be generated by the wind turbine (and equal to the
actually generated power). In case of low wind speeds, the consumed power must be
reduced which is performed by the “consumer control” in Figure 7.
In case of higher wind speeds, the generated power of the wind turbine tends to be higher
than the consumed load. In order to maintain the power balance, using pitch control (i.e. an
appropriate adjustment of the rotor blades) the generated power can be adapted to the
consumed power.
Figure 7: Wind turbine having a pitch control system (source: Heier)
Figure 8: Rotor efficiency as function of the tip speed ratio (source: Heier)
Figure 8 visualizes the rotor efficiency 𝐶𝑃 of a wind turbine as a function of the tip speed
ratio 𝜆. Suppose the wind speed remains constant and also the speed of rotation of the wind
turbine must remain constant implying the tip speed ratio is constant. As visualized in Figure
8, by changing the pitch angle the rotor efficiency changes implying the generated power
changes and can be adapted to the consumed/needed power.
4: Wind turbines operating in grid connected mode
In case wind turbines inject their power in a strong grid, the grid and its loads are able to
absorb this power. This allows the operator of the wind turbine to maximize the power
output which will depend on the time-varying wind speed. Control systems are needed in
order to maximize this power output as the wind speed changes (changing the pitch angle of
the rotor blades and/or change the speed of the rotor blades and the generator). Especially
for low wind speeds, the power output is maximized. When the wind speed is larger than the
rated wind speed, the power must be limited to the rated power of the wind turbine.
In case a large number of large wind turbines inject their power in the public grid and the
total installed power of these wind turbines is a significant part of the grid capacity, a
different situation occurs. The generated power must be adapted to the loads in order to
maintain the power balance in the grid. This means the control systems reduce the
generated power when the power consumption in the grid is limited.
A large number of control strategies exist and the chosen control strategy depends on the
components of the wind turbine. A distinction can be made between stall controlled or pitch
controlled rotor blades. The used generator type (asynchronous generator, doubly-fed
induction generator, synchronous generator) and the power electronic converters also have
a major impact on the control strategies. An entire overview of the existing control
strategies is not possible, a number of approaches are given in order to sketch some
possibilities.
4.1: Constant speed operating schemes
4.1.1: Stall regulated turbines
A stall regulated turbine has fixed-pitch rotor blades which operate near the optimal tip
speed ratio at low wind speeds implying a maximum rotor efficiency. When the wind speed
increases, the angle of attack increases which implies the stall effect occurs. This reduces the
efficiency and limits the generated power to the rated power.
The most common stall-regulated turbines operating at fixed speed have an induction
generator which is connected with the grid without using any power electronic converters.
This implies the design only requires and allows a control mechanism (management system)
when starting and stopping the wind turbine based on wind speed and possibly other power
criteria. Once the brake is disengaged, the turbine may freewheel up to operating speed
before the generator is connected with the grid. Alternatively, the generator may be used as
a motor to reach the operating speed.
4.1.2: Stall regulated turbines with two speeds
Figure 9: Rotor efficiency of a wind turbine with different speeds
When considering stall regulated wind turbines, the overall efficiency can be increased by
operating at different wind speeds. In case of low wind speeds, the rotor efficiency is higher
when the speed of rotation is lower. In case of high wind speeds, the rotor efficiency is
higher when the speed of rotation is higher (Figure 9 considering three speeds of rotation:
20 𝑟𝑝𝑚, 30 𝑟𝑝𝑚, 40 𝑟𝑝𝑚 ).
The most common stall-regulated turbines operating at for instance two fixed speeds have
an induction generator which allows to change the number of pole pairs. This induction
machine is connected with the grid without using any power electronic converters. This
implies the design only requires and allows a control mechanism when starting and stopping
the wind turbine and when changing the number of pole pairs.
Alternatively, the speed of rotation can be changed by using two generators of different size.
The smaller generator has a larger number of pole pairs and is used for lower wind speeds.
Using two gear boxes having different gear ratios is also an option.
4.1.3: Pitch regulated turbines
Rotor blades with controlled pitch angle can be used in constant speed wind turbines. For
lower wind speeds, the pitch is controlled in order to maximize the power output. When the
wind speeds exceeds the rated wind speed, the pitch angle is controlled in order to limit the
rotor efficiency 𝐶𝑃 and the generated power (avoiding powers larger than the rated power).
This approach implies a continuously functioning control system is needed to adjust the
pitch angle to the measured wind speed. The control system must react sufficiently fast in
comparison with the changes in the wind speed. When considering wind gusts, problems can
occur. The faster the pitch mechanism reacts to gusts, the smoother the generated power.
However, the blade rotation velocities are limited by the strength of the pitching mechanism
and the rotor blade inertia. This implies the power is only controlled in the average and
power fluctuations still exist due to wind gusts.
4.2: Variable speed operating schemes
4.2.1: Stall regulated turbines
Figure 10: Controlling a variable speed stall regulated turbine (source: Manwell)
Figure 10 visualizes the control strategy of a variable speed stall regulated wind turbine.
Below the cut-in wind speed, no power is generated. When the wind speed exceeds the cutin wind speed, the generator speed in controlled in order to obtain a constant and maximum
rotor efficiency 𝐶𝑃 . Using power electronics the generator torque can be controlled which
regulates the rotor speed (the rotor accelerates when the generator torque is smaller than
the aerodynamic torque of the rotor). More precisely, for higher wind speeds a larger speed
of rotation is needed.
As the generator speed reaches the maximum design rotor speed, the turbine will operate in
a constant speed mode (actually, the turbine behaves as a stall regulated turbine with fixed
speed). As the wind speed increases, the generated power will increase but this increase will
be limited by the stall mechanism.
Above rated power, the turbine is operated in a constant-power mode. As the wind speed
increases, the speed of rotation is decreased which stimulates the stall effect (causing a
turbulent air flow instead of a laminar air flow) and reduces the rotor efficiency 𝐶𝑃 . This
approach limits the generated power.
This approach uses power electronics to control the rotor speed (but no pitch control of the
rotor blades occurs) in combination with the connection and disconnection logic which is
used for constant speed stall regulated operation.
4.2.2: Pitch regulated turbines
Variable speed pitch regulated wind turbines combine two approaches to affect the turbine
operation: speed changes and blade pitch changes. At lower wind speeds i.e. operating at
partial load conditions, the wind turbine generally operates at a fixed pitch angle but the
rotor speed is changed in order to maintain the optimal tip speed ratio. This maximizes the
rotor efficiency 𝐶𝑃 and the generated power. For higher wind speeds, the blade pitch will be
changed to reduce the rotor efficiency 𝐶𝑃 and limit the generator power to the rated power
of the wind turbine.
Since the rotor speed can vary, the additional energy due to wind gusts can be stored as
kinetic energy which reduces the fluctuations of the power injected into the grid. Since this
inertia reduces the impact of the wind gusts on the electrical power, the pitch control
mechanism can be slower in comparison with the fixed speed pitch regulated wind turbines.
5: Supervisory control system
The supervisory control system allows a number of operating states of a wind turbine. Figure
11 visualizes these main operating states where a distinction is made between transitional
states and stationary states. Often, the wind turbine remains in a stationary state for a long
period of time, the transitional states are only entered during a transition from one
stationary state to another. Depending on the turbine design, some of these states may be
absent, some states may be subdivided into multiple states and some states may be
combined onto one single state.
The first state visualized in Figure 11 is the “system check and initialization state” which is a
transitional state. This state includes all actions needed to make the turbine ready for
operation or the check whether the turbine is ready for operation. For instance, the rotor
and yaw position must be determined, sensors must be checked to be sure that the turbine
systems are operating correctly, actuators may be tested to be sure they are ready for
operation (e.g. sufficient pressure is needed in the hydraulic and pneumatic reservoirs).
Once the turbine is ready for operation due to the actions in the “system check and
initialization state”, the stationary “ready for operation” state is entered. In this state, the
rotor is still stationary and the parking brake is still engaged. By maintaining e.g. sufficient
pressure in the hydraulic and pneumatic reservoirs, by correcting the yaw position if the
direction of the wind speed changes … the wind turbine is kept ready for operation. In the
“ready for operation” state, the wind speed is measured. Averages and other statistical
parameters are calculated to verify whether the wind turbine can be started up with the
expectation that the turbine will continue to run for a while and will not be shut down
immediately due to a low wind speed. For instance in case of low wind speeds, the wind
turbine can remain in this “ready for operation” state for a long time.
Figure 11: Overview of wind turbine operation states (source: Manwell)
In case the averaged wind speed is sufficiently high, the wind turbine goes from the “ready
for operation” state to the “start and brake release” state which is a transitional state. In
this state, the brake is released. In case of a pitch-regulated turbine, by realizing a
sufficiently high pitch angle (as visualized in Figure 8) also at low speeds of rotation i.e. small
tip speed ratios 𝜆 power can be extracted from the wind. Due to the rotor efficiency 𝐶𝑃 a
torque is developed which allows to accelerate the rotor blades and the turbine. As the
speed of rotation increases, the tip speed ratio gradually increases implying the need to
decrease the pitch angle by the control system. This approach allows to increase 𝐶𝑃 and
extract power from the wind.
During the “start and brake release” state, the speed of rotation of the generator increases
and the wind turbine goes to the “grid connection state” which is also a transitional state. As
the rotor speed approaches operating speed, the generator contactor is closed. Power
production starts with the completion of the grid connection and the achievement of the
correct operation speed. During the “grid connection” state, the system and the grid faults
continue to be checked. Moreover, the turbine continues to be oriented into the wind
direction (yawing).
During the “power production” state, the generated power is injected into the grid. The
control mechanism depends on the turbine design. Essentially the pitch angle and/or the
speed of rotation can be controlled and the control mechanism also depends on the wind
speed (for instance maximizing the power production in case of low wind speeds and limiting
the power production to the rated value in case of a higher wind speed).
The “power production” state is a stationary state and not only the generated power is
controlled. The supervisory controller also detects system faults, controls the yaw
orientation, monitors the generated power and the rotor speed in order to identify
operating problems. Possibly, the set point for the generated power is adjusted (for instance
limited) in order to maintain the power balance in the grid.
In the “grid disconnection” state, the generator is disconnected from the grid. This is a
transition state towards the “freewheeling” state or the “shutdown” state. The
“freewheeling” state is a stationary state with the generator disconnected from the grid
implying no power is generated. During this “freewheeling state, the rotor rotates freely
based on a small wind speed. When the wind speed increases, a transition to the “grid
connection” state and the “power production state” is obtained.
When the wind turbine operates in the “freewheeling” state and the wind speed drops even
further, a transition to the “shutdown” state occurs (also a transition from the “grid
connected” state to the “shutdown” state can occur). The transitional “shutdown” state can
be needed in case the wind speed is too low to stay in the “freewheeling” state or in case
the wind speed is too high and a shutdown is needed to protect the installation against
damage. This rotation is stopped using aerodynamic drag devices or by pitching the blades.
The parking brake and the yaw brake are engaged. Once the shutdown procedure is finished,
the wind turbine is ready for a new operating cycle (as the wind speed increases or
decreases towards the useful range of speeds).
Finally, the transitional “emergency shutdown” state is entered when a normal shutdown in
not possible due to for instance component failures. The emergence shutdown is also
performed when the normal shutdown is too slow. An “emergency shutdown” results in a
rapid engagement of the brakes. Notice, further operation of the wind turbine is not possible
without an intervention of the operator.
6: The pitch control system
Consider a pitch regulated wind turbine and assume for simplicity the speed of the
generator and the rotor blades is fixed. Based on the measured wind speed and the desired
active power (e.g. this desired active power is obtained using droop control), the required
pitch angle 𝜃 is known. In order to obtain this required pitch angle, an open loop control
system or a closed loop control system can be used as visualized in Figure 12.
Figure 12: Open-loop and closed-loop control systems (source: Manwell)
6.1: Open-loop control system
Suppose the open-loop control system of Figure 12 is used to control the pitch angle of the
rotor blades. The pitch mechanism is driven by a servo motor with a spring return. The
control system is also subject to external pitching moments i.e. disturbances. The torque of
the servo motor can be modeled as a linear combination of the motor speed and the applied
voltage. The differential equation describing the dynamical behavior of the pitch mechanism
equals
𝐽 𝜃̈𝑃 (𝑡) + 𝐵 𝜃̇𝑃 (𝑡) + 𝐾 𝜃𝑃 (𝑡) = 𝑘 𝑣(𝑡) + 𝑚 𝜃̇𝑃 (𝑡) + 𝑄𝑃 (𝑡) .
Here, 𝜃𝑃 (𝑡) is the pitch angle, 𝐽 is the total inertia of the rotor blade and the pitch motor, 𝐵
is the coefficient of viscous friction of the pitch mechanism, 𝐾 is the pitch mechanism spring
constant (the pitch mechanism contains a spring return). Moreover, 𝑘 𝑣(𝑡) + 𝑚 𝜃̇𝑃 (𝑡)
models the driving torque of the servomotor and 𝑄𝑃 (𝑡) is a pitching torque due to dynamic
and aerodynamic forces which act as a disturbance to the pitch mechanism.
In steady state, the pitch angle is constant implying its first and its second derivatives with
respect to time equal zero. This implies the differential equation reduces (the disturbance
𝑄𝑃 and the voltage 𝑣 applied to the servo motor are assumed to be constant) to
𝜃𝑃 =
𝑘
𝑄𝑃
𝑣+
.
𝐾
𝐾
The steady state pitch angle depends on the voltage applied to the servo motor but it also
depends on the disturbance 𝜃𝑃 . The smaller the spring constant 𝐾, the larger the impact of
the disturbance on the pitch angle. In case the spring constant 𝐾 is larger, the impact of the
disturbance on the pitch angle deceases but a larger servo motor torque is needed.
In order to obtain the desired 𝜃𝑃,𝑟𝑒𝑔 , a voltage
𝑣 =
𝐾
𝜃
𝑘 𝑃,𝑟𝑒𝑓
is applied leading to a behavior described by the differential equation
𝐽 𝜃̈𝑃 (𝑡) + (𝐵 − 𝑚) 𝜃̇𝑃 (𝑡) + 𝐾 𝜃𝑃 (𝑡) = 𝐾 𝜃𝑃,𝑟𝑒𝑓 + 𝑄𝑃 (𝑡) .
Here, the pitch angle 𝜃𝑃 (𝑡) is the output. The voltage 𝑣(𝑡) applied to the servo motor and
the disturbance torque 𝑄𝑃 (𝑡) are the two inputs. A block diagram of the system described
by this differential equation is given in Figure 13.
Figure 13: Block diagram of the open loop pitch control system (source: Manwell)
By taking the Laplace transform of the differential equation (with a general 𝜃𝑃,𝑟𝑒𝑓 (𝑡)), one
obtains that
𝜃𝑃 (𝑠) =
𝐾 𝜃𝑃,𝑟𝑒𝑓 (𝑠)
𝑄𝑃 (𝑠)
+
.
𝐽 𝑠 2 + (𝐵 − 𝑚)𝑠 + 𝐾 𝐽 𝑠 2 + (𝐵 − 𝑚)𝑠 + 𝐾
In reality, all kind of disturbances 𝑄𝑃 (𝑡) (having a Laplace transform 𝑄𝑃 (𝑠)) are possible.
Here, the behavior of the pitch control system will be studied in case the disturbance is a
unit step i.e. 𝑄𝑃 (𝑡) = 𝜇(𝑡) (giving 𝑄𝑃 (𝑠) = 1/𝑠) starting from a steady state position of the
rotor blades. Assume 𝐽 = 1⁄16, 𝐵 − 𝑚 = 1⁄4 and 𝐾 = 1. By taking the inverse Laplace
transform of
𝜃𝑃 (𝑠) =
or equivalently
𝐽
𝑠2
1
1
16
1
1
𝑠+4
= 2
= − 2
+ (𝐵 − 𝑚)𝑠 + 𝐾 𝑠
𝑠 + 4𝑠 + 16 𝑠
𝑠 𝑠 + 4𝑠 + 16
𝜃𝑃 (𝑠) =
1
𝑠+2
2
√12
−
−
2
2
𝑠 (𝑠 + 2)2 + √12
√12 (𝑠 + 2)2 + √12
one obtains that
𝜃𝑃 (𝑡) = 𝜇(𝑡) − 𝑒 −2𝑡 𝑐𝑜𝑠(√12 𝑡) −
2
√12
𝑒 −2𝑡 𝑠𝑖𝑛(√12 𝑡) .
The evolution of 𝜃𝑃 (𝑡) due to the disturbance 𝑄𝑃 (𝑡) = 𝜇(𝑡) is visualized in Figure 14. Notice
the disturbance not only accounts for a steady state error in the pitch angle, there is also a
significant overshoot in the transient behavior.
Figure 14: Pitch angle due to a unity step disturbance (source: Manwell)
6.2: Closed-loop control system
In case of an open loop control system, due to a disturbance quite often a steady state error
in the pitch angle occurs. By using a closed loop system as visualized in Figure 15, the
performance of the pitch control system can be improved (for instance avoiding a steady
state error of the pitch angle) without significantly complicating the control system.
Figure 15 visualizes the closed loop pitch control system. When comparing the closed loop
system of Figure 15 with the open loop system of Figure 13,
-
the motor and blade dynamics remain the same,
the pitching moment acts as an external disturbance,
the voltage 𝑣(𝑡) applied to the servo motor gives the desired torque to adjust the
pitch angle,
there is a desired pitch angle 𝜃𝑃,𝑟𝑒𝑓 (𝑡) which can be constant or time-varying.
The closed loop system contains a feedback of the actual pitch angle (the pitch position)
𝜃𝑃 (𝑡) giving the error 𝑒(𝑡) = 𝜃𝑃,𝑟𝑒𝑓 (𝑡) − 𝜃𝑃 (𝑡) on the pitch angle. Using a controller, for
instance a PID controller, the voltage applied to the servo motor is obtained.
Figure 15: Block diagram of the closed loop pitch control system (source: Manwell)
The differential equation describing the behavior of the PID controller is given by
𝑣(𝑡) = 𝐾𝑃 𝑒(𝑡) + 𝐾𝐼 ∫ 𝑒(𝑡) 𝑑𝑡 + 𝐾𝐷 𝑒̇ (𝑡)
where 𝐾𝑃 , 𝐾𝐼 and 𝐾𝐷 are well chosen constants. In case 𝐾𝐷 = 0 i.e. a PI controller is used,
the behavior of the closed loop system is given by taking the derivative of
𝐽 𝜃̈𝑃 (𝑡) + 𝐵 𝜃̇𝑃 (𝑡) + 𝐾 𝜃𝑃 (𝑡) = 𝑘 𝑣(𝑡) + 𝑚 𝜃̇𝑃 (𝑡) + 𝑄𝑃 (𝑡) .
and using the 𝑣(𝑡) provided by the controller. More precisely,
𝐽 𝜃⃛𝑃 (𝑡) + (𝐵 − 𝑚) 𝜃̈𝑃 (𝑡) + (𝐾 + 𝑘𝐾𝑃 )𝜃̇𝑃 (𝑡) + 𝑘𝐾𝐼 𝜃𝑃 (𝑡)
= 𝑘𝐾𝑃 𝜃̇𝑃,𝑟𝑒𝑓 (𝑡) + 𝑘𝐾𝐼 𝜃𝑃,𝑟𝑒𝑓 + 𝑄̇𝑃 (𝑡) .
Also here, the dynamic response of the closed-loop system to a unit step disturbance
𝑄𝑃 (𝑡) = 𝜇(𝑡) can be calculated. In case 𝐾𝑃 = 𝐾𝐼 = 2, the evolution of the pitch angle due
to this unit step disturbance is visualized in Figure 16 and compared with the open-loop
control system. Notice due to the feedback and the I-action of the controller, no steady state
error of the pitch angle occurs which shows the superior behavior of the feedback system.
Indeed, by taking the Laplace transform of the differential equation, one obtains that
𝜃𝑃 (𝑠) =
𝐽𝑠 3
(𝑘𝐾𝑃 𝑠 + 𝑘𝐾𝐼 ) 𝜃𝑃,𝑟𝑒𝑓 (𝑠)
𝑠 𝑄𝑃 (𝑠)
+ 3
.
2
+ (𝐵 − 𝑚)𝑠 + (𝐾 + 𝑘𝐾𝑃 )𝑠 + 𝑘𝐾𝐼 𝐽𝑠 + (𝐵 − 𝑚)𝑠 2 + (𝐾 + 𝑘𝐾𝑃 )𝑠 + 𝑘𝐾𝐼
Here, the behavior of the pitch control system will be studied in case the disturbance is a
unit step i.e. 𝑄𝑃 (𝑡) = 𝜇(𝑡) (or equivalently 𝑄𝑃 (𝑠) = 1⁄𝑠 ) starting from a steady state
position of the rotor blades. This implies
𝜃𝑃 (𝑠) =
𝐽𝑠 3
+ (𝐵 −
𝑚)𝑠 2
1
.
+ (𝐾 + 𝑘𝐾𝑃 )𝑠 + 𝑘𝐾𝐼
Here, 𝐽 = 1⁄16, 𝐵 − 𝑚 = 1⁄4, 𝐾 = 1, 𝑘 = 1, 𝐾𝑃 = 2 and 𝐾𝐼 = 2 which gives
𝜃𝑃 (𝑠) =
𝑠3
+
4𝑠 2
16
.
+ 48𝑠 + 32
Using partial fraction decomposition,
𝜃𝑃 (𝑠) =
0.3647
0.3647𝑠 + 0.9482
− 2
𝑠 + 0.7004 𝑠 + 3.2996 𝑠 + 45.6886
or equivalently
𝜃𝑃 (𝑠) =
0.3647
0.3647(𝑠 + 1.6498)
6.5549
−
− 0.0529
.
2
(𝑠 + 1.6498)2 + 42.9668
𝑠 + 0.7004 (𝑠 + 1.6498) + 42.9668
Figure 16: Pitch angle due to a unity step disturbance (source: Manwell)
By taking the inverse Laplace transform, one obtains that
𝜃𝑃 (𝑡) = 0.3647 𝑒 −0.7004 𝑡 − 0.3647 𝑒 −1.6498 𝑡 𝑐𝑜𝑠(6.5549 𝑡)
− 0.0529 𝑒 −1.6498 𝑡 𝑠𝑖𝑛(6.5549 𝑡)
which is visualized in Figure 16. It is important the steady state error due to the disturbance
𝜃𝑃 (𝑡) = 𝜇(𝑡) goes to zero.
6.3: Resonances
The closed loop pitch control system gives a reasonable disturbance rejection to a step
input. However, in case of sinusoidal disturbances due to changing wind speeds attention is
needed. This is the case when the excitation frequency is close to the natural frequency of
the closed loop system. The response to a sinusoidal disturbance with a magnitude 1 and a
frequency of 1.04 Hz is visualized in Figure 17. The response magnitude of the pitch angle
depends on the damping of the system and the excitation frequency. In the present
example, this magnitude is large in comparison with the response to a unit step. A welldesigned control system will avoid these natural frequencies or provide additional damping
at these frequencies.
Figure 17: Response of the closed-loop pitch control system (source: Manwell)
7: Monitoring, faults and safety systems
Wind turbines contain a lot of sensors which allow to measure a large number of internal
and external parameters. These parameter values can be logged and they are used by the
control systems to optimize the behavior of the wind turbine. The measured parameter
values also trigger the supervisory control system (also called management system) to go
from one state to another state (see Figure 11). In case these parameters exceed a
predefined range, actions to protect the wind turbine can be taken e.g. an emergency
shutdown is initiated (due to the safety system).
For instance the pitch control system needs a measurement of the wind speed. The wind
turbine needs an anemometer covering a sufficiently large measurement range which must
cover the cut-in wind speed, the nominal wind speed and the shut-down wind speed. The
average wind speeds are determined over 1, 3, 5, 10 or 15 minute periods and also the
minimum and the maximum wind speed values are determined. This implies the
anemometer must be able to measure wind speeds up to 1.5 times the shut-down wind
speed.
Using accelerometers also vibrations in the wind turbine are monitored. When the vibrations
exceed a predefined threshold, the wind turbine is brought to a standstill. Especially when
resonances occur due to excitations close to a natural frequency, large vibrations can occur.
In order to prevent the need for a shut-down, it is important to pass the dangerous speed
range as fast as possible (e.g. when accelerating the speed of rotation of the rotor blades).
If the speed of rotation of the wind turbine exceeds the maximum permissible operating
speed (e.g. 10% above the nominal range), a shut-down is needed which can be initiated by
the management system. In case of a further increase of the wind speed even an emergency
shut-down is needed which can be initiated by the safety system.
Temperature measurements are also performed. When exceeding temperature thresholds,
it can be assumed the system is overloaded or a fault occurs. Also in such a situation, a shutdown is initiated.
To protect the generator and/or the power electronic converters in the wind turbine, the
wind turbine is disconnected from the grid in case grid faults occur. The installation must be
protected against overvoltages coming from the grid but also against voltage dips. Due to a
voltage dip, the wind turbine is not able to inject sufficient power into the grid which implies
the power coming from the wind is stored as kinetic energy in the wind turbine. The speed
of the wind turbine increases and overspeeds must be avoided. In order to maintain the
power balance in the grid, disconnecting the wind turbine from the grid must be avoided as
much as possible i.e. it is important to improve the ride-through capability of the wind
turbine.
References
Blaabjerg F. and Chen Z., Power Electronics for Modern Wind Turbines, Morgan & Claypool
Publishers, 2006.
Heier S., Grid Integration of Wind Energy Conversion Systems, Wiley and Sons, 2006.
Manwell J., Mc Gowan J. and Rogers A., Wind Energy Explained: Theory, Design and
Applications, Wiley and Sons, 2009.
Raven F., Automatic Control Engineering, Mc Graw-Hill, 1987.