Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
CONTROL OF A DOUBLY-FED INDUCTION MACHINE OPERATING AS A GENERATOR
IN A WIND POWER PLANT IN THE EVENT OF VOLTAGE DIPS
Krzysztof Blecharz / Gdańsk University of Technology
1. INTRODUCTION
Modern generator units used currently in wind power plants make it possible to supply power to the power
grid in a wide wind turbine changes range. The operation of a machine in a wide range of generator shaft rotational speed facilitates a decrease in mechanical stresses both on the shaft and mechanical transmission gear and
an increase in wind turbine operating efficiency. In high-power wind power plants, slip-ring induction machines
are used as generators where the rotor is powered by a power electronics converter facilitating a two-way flow
of energy; however, the stator is connected directly to the power grid (fig. 1). In the literature, such solutions
are referred to as generator units with a doubly-fed induction machine.
�
Power grid
Pss
Pr
Psr
is
u dc
~
-
Machine
converter
ips
~
Pm
ir
-
Ps
Grid
converter
Fig. 1. Wind power plant with a doubly-fed induction machine – propagation of energy with over-synchronous speed
The main advantage differentiating such solutions from others is the power of the converter supplying
the rotor being approximately 30% of the nominal power of the whole generator. This is crucial with regard to
the costs of constructing the converter in the rotor circumference, taking into account the constantly increasing
installed unit power in wind power plants.
The sensitivity to voltage interferences on the stator side is a significant disadvantage of generator units
with a doubly-fed induction machine.
The rotor and stator are magnetically coupled, which results in voltage interferences originating in the
power system being directly transformed to the rotor side. The voltage interferences have a significant influence
on the operation of the converter supplying the generator’s rotor and may result in its being damaged.
Summary
The paper presents the problems related to the methods of regulating the power of a doubly-fed induction
machine operating as a generator in a wind power plant.
It touches upon the problem of generator operation when
voltage interferences appear on the power system side in
the form of a voltage dip. The paper presents power regulation systems based on asynchronous machine multi-scalar models enabling to extend the range of the generator’s
continuous operation in the event of a voltage dip on the
wind power plant terminal connecting it to the system.
5
Krzysztof Blecharz / Gdańsk University of Technology
6
A short-circuit is the most common disturbance in the operation of a power system. It directly results in
voltage drops on the transmission grid elements and voltage dips in the system nodes.
The characteristic feature of a doubly-fed induction machine is the poorly attenuated flux oscillation resulting from the voltage dip on the stator side. Flux oscillations result directly in the oscillation of power transmitted to the system. This is a disadvantageous phenomenon.
The goal of a generator control system in standard operating conditions is to be able to independently
regulate the active and reactive power constantly maintaining the generated energy quality parameters [1].
If there is voltage interference on the power grid side, the generator control system should function
properly within the range of the construction limits of a converter in the rotor circumference and attenuate the
oscillations of the output power transmitted to the system. This facilitates the active operation of a wind power
plant in the direction of voltage stabilisation on the terminal connecting it to the power grid through supplying
the reactive power.
The regulations provided by transmission grid operators in different countries [2, 3] include guidelines
for continuous wind power plant operation when a voltage dip is present.
The fulfilment of conditions imposed by regulations provided by individual operators makes it possible
to maintain a relatively large number of wind turbines in the system. Thus, the risk of generating an additional
disturbance or system destabilisation is lower.
The power regulation unit structures presented in the literature may be divided according to the type of
control methods used. The largest group of regulation systems includes the solutions based on the Field Oriented Control (FOC) technique and systems using the direct torque control (DTC) method.
The smaller group of regulation systems comprises solutions using the non-linear control technique with
doubly-fed induction machine multi-scalar models developed at the Gdańsk University of Technology [4].
2. MATHEMATICAL MODEL OF A WIND POWER PLANT SYSTEM
In order to examine the dynamics doubly-fed induction machine control system operation and the generator unit reaction to symmetrical voltage dips on the power system side, a mathematical model of a wind power
plant has been developed.
�
is
L net
G
unet
Rnet
i net
Cf
idg
Lg
Rg
Cd
ig
model of the power grid and filter
on the wind power plant output
idr
Pgsc
two-way
converter model
DFIM
Pr
DFIM model
Fig. 2 Wind power plant model diagram
The mathematical model comprises several elements: a simplified model of the power grid, filter model,
functional model of a two-way converter in the rotor circumference and the model of a doubly-fed induction
machine. In order to describe the dynamics of a doubly-fed induction machine model, vector equations for
a mono-harmonic machine have been used – see below [4]:
�
dS
u S  R S iS 
 ja  S
d
(1)
Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
�
d r
u R  R R iR 
 j(a  m ) r
d
*
� dm
J
 Im  S iS  m o
d
(2)
(3)
�  L iS  L i R
S
S
m
(4)
�  L i R  L iS
R
R
m
(5)
where:
– stator and rotor voltage space vectors, �u S , u R – stator and rotor current space vectors current,
�u S , u R – stator and rotor voltage space vectors, R , R – stator and rotor windings resistance,
S
R
τ – relative time; ωm – rotor angular velocity; ωu – angular speed of reference system rotations
J – rotor moment of inertia; m0 – driving torque on the machine shaft.
A detailed description of the remaining elements of the mathematical model has been presented, in the
form of differential equations, in paper [5].
� S ,  R
3. DOUBLY-FED INDUCTION MACHINE MULTI-SCALAR MODEL
For the purposes of a generator power control system, it is beneficial to use the slip-ring asynchronous
machine multi-scalar model described in paper [6].
The type “z” multi-scalar model of a doubly-fed induction machine is obtained as a result of adopting the variables of state depending on the values of the stator stream and rotor current vectors and the angle between these
vectors; the variables of state are, however, independent from the co-ordinate system. The variables look as follows:
�z11  r
(6)
�z12   sx i ry   syi rx
(7)
�z 21   S2
(8)
�z 22   sx i rx   syi ry
(9)
By determining the multi-scalar variable derivatives using the equations of the machine vector mathematical
model equations (1)-(5), a non-linear differential equations system of the multi-scalar model is obtained [6]:
�dz11 L m
1

z12  m 0
d JLS
J
(10)
�dz12
(11)
d

1
L
L
L
z12  z11z 22  m z11z 21  s u r1  m u sf 1  u si1
TV
w
w
w
�dz 21
R
R L
 2 S z 21  2 S m z 22  2u sf 2
d
LS
LS
(12)
�dz 22
(13)
d

2
1
R L
R L z 2  z 22
L
L
z 22  S m z 21  S m 12
 z11z12  S u r 2  m u sf 2  u si2
TV
LS w 
LS
z 21
w
w
where:
�u r1  u ry  sx  u rx  sy
(14)
7
Krzysztof Blecharz / Gdańsk University of Technology
8
�u r 2  u rx  sx  u ry  sy
�u sf 1  u sy  sx  u sx  sy
�u sf 2  u sx  sx  u sy  sy
�u si1  u syi rx  u sx i ry
�u si2  u sx i rx  u syi ry
�
TV 
LS w 
L2S R r  L2m R S  w  R S
(15)
(16)
(17)
(18)
(19)
(20)
where:
�
L
PS   m z12
Ls
(21)
�
1 Lm
QS 

z 22
Ls Ls
(22)
The active and reactive power of a doubly-fed induction machine on the stator side in the generator’s fixed
condition may be expressed as follows by means of adopted multi-scalar variables [6]:
4. DOUBLY-FED INDUCTION MACHINE POWER REGULATION SYSTEMS
For the purposes of control system synthesis, the type “z” multi-scalar model of a doubly-fed induction
machine has been used. Different types of controllers may be used in the generator power regulation system. In
paper [4], the active and reactive power control has been achieved by means of four cascade-connected PI type
controllers, two of which operate the active and reactive power control lane. If PI type controllers are used, it is
necessary to ensure the linearization of the machine equations by using the decoupling block [4]. Unfortunately,
this control system does not ensure attenuation of the oscillation of power transmitted to the system caused by
the voltage dip on the power grid side [5].
In order to improve the control system operation, it has been suggested to provide, on the control loop,
a non-linear sliding controller based on the sliding control technique. The control structure diagram is shown in
fig. 3 [7]. Using the sliding controller results in low-amplitude and high-frequency oscillations in the regulated
values ranges and it is likely that there will be a constant average error value present. This is a characteristic
feature of systems featuring sliding controllers caused by the effect of rapid switchovers within the controller
structure.
One of the solutions making it possible to limit this phenomenon is to force a sliding movement in an additional auxiliary feedback loop whose operating rage includes the controlled variables observer. The generator
power control system structure based on this algorithmic approach has been presented in fig. 4. The mathematical description of the multi-scalar variables dynamics observer has been presented in paper [9].
The synthesis method and the sliding controller internal structure have been shown in paper [7]. In both
suggested control systems, the generator shaft speed has been estimated on the basis of the rotor current measurement in the rotor co-ordinate system, and next on the basis of the calculations related to the same current
in the stator co-ordinate system [4].
Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
�
power grid
u r1
ur2
Sliding controller
Grid
control
system
Transformation
u r�S
u r�S
u r�R
(+)
(+)
Transformation
� RSestK
Correction
(+)
Pzad
Qzad
Correction
u r�R
� RSes t
�s ��S
z11, z12, z21, z22
(+)
(-)
usf 1, u sf2, u si1, u si2
(-)
Vector
controller
Estimation of:
rotor angle
location,
stator flux,
multi-scalar
model variables,
power P and Q
ir��R
DFIM
is ��S
u s�� S
ps
qs
Fig. 3. Diagram of the power control system structure for a doubly-fed induction machine with a sliding controller based on type “z” multi-scalar model dependencies
�
power grid
ur1
ur2
Sliding controller
u r�S
z12
Pzad
(-)
Qzad
(+)
Multi-scalar
variables
observer
(+)
(-)
u r �S
u r�R
Transformation,
correction
z22
z11, z12, z21, z22
Power grid
inverter
regulation
system
Transformation,
correction
ur�R
� s��S
Vector
controller
Estimation of:
rotor angle
location,
stator flux,
multi-scalar
u sf1, u sf2, u si1, u si2 model variables,
power P and Q
ps
qs
ir��R
DFIM
i s�� S
u s��S
Fig. 4. Diagram of the power regulation system structure for a doubly-fed induction machine with a sliding controller and multi-scalar variables
observer based on type “z” multi-scalar model dependencies
9
Krzysztof Blecharz / Gdańsk University of Technology
10
5. DFIM ACTIVE AND REACTIVE POWER CONTROL
In the standard condition of a power grid operation where all its parameters are maintained within permissible ranges [10], the active power in a wind power plant which is transferred to the system is determined
on the output of a supervisory power regulation system.
The value of this power depends on the wind power and wind turbine parameters. From the point of view
of wind power plant operation efficiency, maximisation of the power obtained from wind is significantly relevant.
This issue is discussed in numerous publications [12, 13].
In order to ensure correct and stable operation of the power system, the transmission system operators
(in the case of large generating units) require forecasting the active power value which may be transferred from
a wind power plant to the system [3].
The Grid Code [10] contains also guidelines referring to the active power change speed on the power
plant terminal. The Polish transmission system operator demands that the average active power change gradient
during 1 minute does not exceed 30% of the wind farm nominal power and the regulation systems of individual
generator units must ensure the active power decreases to the level of at least 20% of the nominal power in less
than 2 seconds. As far as smaller generating units are concerned, these requirements are provided individually
in connection agreements.
The reactive power regulation on the stator side in the nominal power grid condition may be achieved
using two different strategies.
The first strategy entails the machine being magnetised by the rotor current magnetising component and
the reactive power being generated by a machine inverter. A machine supplied in this way does not draw the
inductive reactive power from the power grid. The generator operates with a power factor equal to unity. The
reactive power value set in the regulation system is zero.
The second strategy requires that the generator can operate by any power factor that is possible to obtain.
The reactive power value on the wind power plant generator output is defined by the wind farm operator taking
into account the present value of generated active power and the required voltage level at the point of connecting the wind power plant to the system, according to the following dependency [11]:
�Q zad  min Q max , Q 
S
S
PCC
(23)
where: ΔQPCC means the reactive power value on the generator terminal connecting it to the system in
order to ensure the required voltage level. However, QSmax is the maximum reactive power value taking into
account the nominal apparent power of the generator and the active power supplied to the system. It is determined as follows:
� max
QS 
S   P 
max 2
MDZ
zad 2
S
(24)
According to the transmission power grid operators’ requirements, in standard operating conditions, the
wind power plant generator connected to the power system must be able to operate with a power factor in the
range from 0.975 of the inductive type to 0.975 of the capacitive type [10], within the full load range.
The change of active and reactive power on the generator output in the broad range of the cos(φ) power
factor is related with changes of the generator’s rotor supply voltage. The voltage generated by the converter
supplying the machine rotor is the function of active and reactive power set values and the generator shaft slip.
The value of this voltage may be expressed by the dependency determined in the vector equation below:
�
 R R  jsL R R S  jLS   sL2m 
 R R  jsL R 
uR  
 iS
 uS  
jL m
jL m




(25)
The dependency (25) has been obtained on the basis of a generator’s vector equations (1) - (5) in the
steady state for the synchronously rotating co-ordinate system. Fig. 5 and 6 show the rotor voltage amplitude
value depending on the shaft rotational speed and generator’s operating point. The presented diagrams have
been obtained on the basis of dependencies and expressions for active and reactive power on the stator side
Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
11
while properly parametrizing the active and reactive power values set in the power control system. The active
power value Ps = –0,5 is equal to the generator’s nominal power. However, the reactive power value Qs = 0,7 is
equal to the inductive reactive power drawn by the generator’s stator in the condition when the machine rotor
is not powered.
�
�
0.5
0.5
Qs =-0.3
0.4
0.4
0.3
0.3
Ps= -0.2
|ur |
|ur |
0.2
0.2
0.1
0.1
Qs=0.7
Qs =0.7
0
0.7
0.8
Ps = -0.5
Ps= -0.5
0.9
1
��
1.1
1.2
1.3
Fig. 5. Amplitude of rotor voltage in the function of shaft rotational speed and active power Ps with the constant reactive power
value Qs
0
0.7
0.8
0.9
1
��
1.1
1.2
1.3
Fig. 6. Amplitude of rotor voltage in the function of shaft rotational speed and reactive power Qs with the constant active power
value Ps
The diagrams in fig. 5 and 6 show that it is possible to estimate the reserve of the rotor supply voltage
value that can be generated by the machine converter depending on the generator operation point. This is particularly relevant taking into account the possibility of continuing constant generator operation during a power
grid voltage dip.
Reactive power control on the stator side is important taking into account the method of operation of
a doubly-fed induction machine with power grid voltage fluctuations and in case a voltage dip on the power plant
terminal occurs. Together with the decrease in the power grid voltage value, the area of the active and reactive
power to be generated by the generator [8] also decreases.
6. RESULTS OF SIMULATIONS AND EXPERIMENTS
In order to check the correct operation of suggested control systems and feasibility of the assumed mathematical model of a wind power plant system, simulations and experiments have been carried out.
Simulations for operation of individual control systems and generator’s reaction to the symmetrical voltage dip on the power grid side have been carried out by a computer program written in C++, in the Borland
C++ 4.5 programming package. In order to solve the differential equation, the fourth-order Runge–Kutta method has been used. The simulation program has taken into account the digital character of the control systems
operation and the impulse width modulation algorithm, both on the machine and power grid inverter side. All
values have been expressed in relative units [4].
The experiments on the wind power plant model have been carried out in a laboratory station whose
structure is shown in fig. 7. The examinations included a 2 kW doubly-fed induction machine and a synchronous
generator (apparent power 20 kVA). The power grid voltage dips have been forced by short-term activation of a
symmetrical 3-phase rectifier little R3 resistance. This solution allowed achieving voltage dips in a broad range
of depth and duration. During the tests, the constancy of the wind power plant shaft rotational speed was assumed.
Krzysztof Blecharz / Gdańsk University of Technology
12
�
R2
G
M
DFIM
M
thyristor
controller
R1
operator’s
console
R3
Fig. 7. Laboratory station
structure
The operation in the system shown in fig. 7 where the energy is exchanged between the doubly-fed induction machine transmitting the energy obtained on the shaft to a synchronous generator is not favourable, taking
into account high power oscillations in the system. Thus, the synchronous generator was loaded with an external
R1 3-phase receiver with resistance characteristics. This enabled equalizing the power balance in the system.
The tests for the operation dynamics of the presented regulation systems consisted in forcing step changes of values set in active and reactive power control sloops. The influence of the operation of individual control
sloops on each other and the speed of reaction to power spikes was also assessed. In order to compare the
dynamic properties of the tested control systems, all systems underwent the same sequence of changes of setpoints. The simulation results are shown in fig. 8 and 9. The short duration of the active and reactive power step
change sequence resulted from the small time constants of the generator.
The examination of the reactor system reaction to a voltage dip consisted in forcing symmetrical voltage
dips (of different depth and duration) on the machine stator side. The ability of the following control systems
to attenuate oscillations of the power transmitted to the system and the range of the regulation system correct
operation was assessed.
The results of the experiments for dips lasting 200 ms are shown in fig. 10 and 11.
a)
simulation
� 0
b)
0
ps
ps
-0.5
-0.5
0
0
qs
qs
-1
-1
2
z11
2
z 11
0
0
0
z 12
0
z12
-0.5
-0.5
1.5
1.5
z21
z 21
1.0
1.0
1
z22
1
z 22
0
0
0
50
100
time [ms]
0
50
100
time [ms]
Fig. 8. Active
power ps and
reactive power
qs runs on the
DFIM stator side
and multi-scalar
variable runs
for a controller
model based on
type “z” model
dependencies
with a sliding
controller a) and
a sliding control
and observer b)
Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
� 0
z 12
-0.5
2
z21
0
1
z22
0
0
50
100
time [ms]
Fig. 9. Runs of multi-scalar variables recreated in the observer; runs as for the event shown in fig. 8b
�
0.5
0
-0.5
ps
qs
ωr
1
0
-1
1
0
0.5
z 12 0
-0.5
uab 2
ubc 0
uca
-2
isa 0.5
isb
0
isc -0.5
ira
irb
irc
2
0
-2
0
200
400
time [ms ]
Fig. 10. DFIM reaction to a voltage dip (duration 200 ms and depth 70%) for a control system based on the type “z” model dependencies with
a sliding controller (EXPERIMENT)
13
Krzysztof Blecharz / Gdańsk University of Technology
14
�
1
ps 0
-1
1
qs 0
-1
1
z12 0
-1
ωr
2
0
uab 2
ubc 0
uca -2
isa
isb
isc
1
0
-1
ira
irb
irc
2
0
-2
0
200
400
time [ ms]
Fig. 11. DFIM reaction to a voltage dip (duration 200 ms and depth 60%) for a control system based on the type “z” model dependencies with
a sliding controller and observer (EXPERIMENT)
7. SUMMARY
On the basis of the conducted tests, it may be concluded that the developed regulation systems enable
independent active and reactive power control on the doubly-fed induction machine stator side. The control
systems are have high operation dynamics and the reaction of the control systems to step changes of the set
power values, in individual control loop, is very fast. In the event of network voltage dips occurring, the control
system ensures the generator’s continuous operation. The range of the generator’s correct operation depends
on the maximum permissible voltage on the rotor side which can be generated by the machine converter. Among
the examined control systems, the system with a sliding controller and observer has the best properties related
to attenuation of active power oscillations.
Control of a Doubly-fed Induction Machine Operating as a Generator
in a Wind Power Plant in the Event of Voltage Dips
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nowych wymagań. Modelowanie i Symulacja, Kościelisko, 2004.
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2002.
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