Download III. Proposed controller design

Operation Analysis and Control of DFIG-Based Wind
Turbine under Harmonically Distorted Unbalanced
Grid Voltage Conditions
HAMID ARAB
ISLAMIC AZAD UNIVERSITY TEHRAN SOUTH BRANCH
TEHRAN, IRAN
HAMIDARAB85@GMAIL.COM
Abstract—Doubly Fed Induction Generators (DFIGs) for their
flexible control system and low price converters are taken into
consideration as a first choice for wind turbine’s generator, these
days.
In this paper, it’s proposed a control system which keeps wind
turbine connected to grid in Non-ideal condition like
harmonically distorted and unbalanced grid voltage condition.
Vector control method is used for designing the proposed control
system. The proposed voltage sequence decomposer makes it
possible to control both of unbalanced and harmonically
distorted grid voltage conditions at the same time. Here, the aim
of control system is to reduce pulsations of electromagnetic
torque and total active output power of DFIG.
For proving the accurate operation of proposed control system in
such a kind of condition, Simulations of the proposed control
strategy for a DFIG-based wind power generation system are
carried out using MATLAB/Simulink software.
Keywords- Wind Turbine – DFIG – Harmonically Distorted
Unbalanced conditions – PI-R controller – Vectorcontrol
I.
INTRODUCTION
A
ccording to the fact that doubly fed induction
generators (DFIGs) are widely used these days, the main
drawback of them, sensitivity to grid voltage properties, has got
more importance. Effects of balanced and unbalanced voltage
sags were studied in [1]. Depend on the amplitude of voltage
sag, system could be controllable or not. This problem for
DFIGs' operation under unbalanced grid voltage conditions
was well investigated in [2].
Also, operation and control of grid connected DFIG-based
wind turbines under harmonically grid voltage conditions have
been interested for many researchers during the last few years
[3-4]. Harmonically distortion of stator voltage could bring
some problems such as resonant pulsations in electromagnetic
torque and active/reactive output power. Plenty of control
methods are proposed for solving these problems. PI
controllers are one of them [1]. This controller is not suitable
for encountering Non-Ideal voltage conditions. Recently,
control methods based on PI-R controller were widely used in
DFIG system for operating in harmonically distorted or
unbalanced stator voltage conditions.
In this paper, a new control system is proposed for keeping
DFIG-based wind turbine connected to the grid in worst NonIdeal grid voltage conditions that is existence of harmonically
distortion and unbalanced grid voltage conditions at the same
time.
This paper is organized as follows. Section II studies
behaviors of DFIG and describes operation of Grid-Side and
Rotor-Side converters under harmonically distorted unbalanced
grid voltage conditions. Section III discusses the proposed PI-R
current controllers in detail whereas simulations results are
presented in section IV. Finally, section V draws the
conclusion.
II.
ACTIVE AND REACTIVE OUTPUT POWER OF DFIG UNDER
HARMONICALLY DISTORTED UNBALANCED GRID VOLTAGE
CONDITIONS
Under distorted unbalanced grid voltage conditions, there



are eight stator voltage components, viz., V sdq
 , V sdq  , V sdq 5

and V sdq
7 .
Stator active and reactive power can be calculated as
follows [10]
3  ˆ
Ps  JQs   V sdq
I sdq
2

Fig. 2 shows the spatial relationships between the stator
stationary  s  s reference frame, rotor  r  r frame rotating at
the angular speed of r , dq  and dq  reference frames
rotating at the respective angular speed of s and s , finally
dq 5  and dq 7  reference frames rotating at the angular speed of
5s and 7s , respectively.
Electromagnetic power ( Pe ) could be written in matrix form as
follows
 I rd  
  
 I rq  
 I rd  
  
3L 
I 
Pe  m r C   5rq  
I
2Ls s
 rd55 
 I rq 5 
I 7 
 rd 7  
 I rq7 7  
Figure 1. Spatial relationships between the stationary αβ reference frame, the
rotor
 r  r reference frame, dq  , dq  , dq 5 
and
dq 7 
Under harmonically distorted unbalanced conditions, if
vector F is assumed to be a parameter like voltage, current or
flux, it contains both positive and negative sequence
components plus 5th and 7th harmonic components. So, F could
be expressed as
Fdq  Fdq   Fdq 5  Fdq 7 
 Fdq   Fdq e  j 2s t  Fdq55e  j 6s t  Fdq7 7 e  j 6s t

By substituting (2) in (1), the stator active and reactive
power are given, respectively, by
Ps  Ps 0  Ps sin 2 sin(2s t )  Ps cos 2 cos(2s t )
 Ps sin 6 sin(6s t )  Ps cos 6 cos(6s t )
Q s  Q s 0  Q s sin 2 sin(2s t )  Q s cos 2 cos(2s t )
Q s sin 6 sin(6s t )  Q s cos 6 cos(6s t )

According to simplification process used in [7-8], stator
active and reactive power could be expressed in matrix form as
follows
Ps 0
Qs 0 Ps sin 2 Qs sin 2 Ps cos 2 Qs cos 2 Ps sin 6 Qs sin 6 Ps cos6 Qs cos6 
 I rd  
V sq  
  
  
 I rq  
V sd  
 I rd  
V sq  
  
  
I
V sd   3L m
3


 A   5  
 B   I 5rq 
2s Ls
2L s
V
 rd55 
 sq55 
 I rq 5 
V sd 5 
I 7 
V 7  
 rd 7  
 sq 7  
 I rq7 7  
V sd7 7  
Where [C] is given in the appendix, too.
Also, active and reactive power transferred to grid through
GSC contains dc component, sin 2s , cos 2s , sin 6s and
cos 6s . Here, the first three above components are just taken
into account, for simplification.
 V sd 
 Pg 0 
 
Q 
 V sq 
 g0 
 Pg cos 2  3  V sd 

  
 Pg sin 2  2  V sq 
V 
Q g cos 2 
 sq


 V sd 
Q g sin 2 
III.


V sq 
V sd 
V sd 
V sq 
V sq 
V sd 
V sd 
V sq 
V sd 
V sq 
V sq 
V sd 
V sq  

V sd    I gd  


V sq    I gq  

V sd    I gd  


V sd    I gq  

V sq  

PROPOSED CONTROLLER DESIGN
A. Phase angle of fundamental voltage and sequential
decomposition of stator voltage
When the network voltage is unbalanced or harmonically
distorted, the traditional PLL approach is not capable of
tracking the input voltage accurately because the PI controller
used in PLL is only effective to regulate dc components [10].
In [5] a sequence decomposer has been proposed that was
suitable just for harmonically distorted conditions, but this
section is going to design a new software decomposition
method and an improved PLL scheme, suitable for
harmonically distorted unbalanced grid voltage conditions.
As Fig. 3 shows, firstly, fundamental stator voltage
component is extracted in  reference frame and then its
phase angle will be computed.

Where [A] and [B] are given in the appendix.
The electromagnetic torque of DFIG is calculated as
P
Te  e
where p is the number of pole pairs.
r
p
Figure 2. Block diagrom of the improved PLL, suitable for harmonically
distorted unbalanced conditions
In  reference frame and with taking into account 5th and
7th harmnic components, stator voltage is as follows
V  V  cos(s   ) V  cos(s   ) V 5 cos(5s  5 )

V 7 cos(7s  7 ) V   V   V  5 V  7
V V sin(  ) V sin(  ) V sin(5  )

s


s

5
s
5
 
V 7 sin(7s  7 ) V   V   V  5 V  7


Where s  s t and   ,   ,  5 and  7 are referred to the
initial angle shifts of the corresponding voltage components.
After computing the first- and second- and third-order
differentials of V  and V  in (8) with respect to  s and
gathering V  , V ' , V '' and V ''' together into matrix
form, it could be written as follows
V   
 V 
V 
V ' 
  
 
V  5 
V '' 




V '''   K V  7 


V   
V 




V   
V ' 
V 
V '' 
 5 
 
V  7 
V ''' 
V   
 V 
V 
V ' 
  
 
V  5 
V '' 




V  7   K 1 V ''' 


V   
V 




V   
V ' 
V 
V '' 
 5 
 
V  7 
V ''' 
Where T s is sample time.
Differential components could be calculated for V  from
the similar way. Thus, the positive and negative sequence and
also harmonic components of stator voltage can be calculated
by instituting results of (12) for corresponding component in
(11).
Ⅰ Electromagnetic torque resonant pulse mitigation.

0
0
0 
0
0
0 
0
0
0 

0
0
0 
1
1
1 

1
5
7 
1 25 49  

1 125 343 
Consequently, inversing the coefficient matrix can make it
simplified and result will be as follows
1 1
1
1 5
7
1 25 49
1 125 343
0 0
0
0 0
0
0 0
0
0 0
0

dV  V  (t ) V  (t T s )

V ' 
d s
sT s


dV ' V  (t )  2V  (t T s ) V  (t  2T s )

V '' 
d s
(sT s )2


dV '' V  (t )  3V  (t T s )  3V  (t  2T s ) V  (t  3T s )

V ''' 
d s
(sT s )2


B. control targets determination and current references
The control targets in designed control system are as
follows
Where [K] is the coefficient matrix
1
1

 1

1
 K   
0

0
0

 0
Meanwhile, the first- and second- and third- order
differentials of V  whit respect to  s could also be calculated
in the discrete forms as
0
0
0
0
1
1
1
1
Ⅱ Reducing resonant pulses of wind turbines total active
power.
So, according to control targets listed above, current
references are supposed to be calculated. For first target
satisfaction (13) must be satisfied, which is possible via RSC as
follows:
Pe cos 2  0

Pe sin 2  0

Pe cos 6  0
Pe sin 6  0

As a result, according to (6), current references could be
obtained.
For next control target, based on (3) and (7), the total active
power generated by the system can be represented as
Ptotal  Ps  Pg  (Ps 0  Pg 0 )  (Ps sin 2  Pg sin 2 )sin 2s t
(Ps cos 2  Pg cos 2 ) cos 2s t  Ps cos 6 cos 6s t  Ps sin 6s t 

In (21) stator voltage components are obtained in terms of
stator voltage differentials. So, if stator voltage differentials
could be computed, stator voltage component will be obtained.
Thus, to mitigate the oscillation of the total active power
output, it is necessary to control the GSC such that with
making change in Pg sin 2 and Pg cos 2 oscillating terms with
twice the grid frequency should be equal to zero, i.e.

Ps sin 2  Pg sin 2  0


Ps cos 2  Pg cos 2  0

Thus, for the GSC, the required reference values for the
positive sequence currents can be obtained according to Pg*0
Figure 3. Schematic diagram of the proposed control syestem under harmonically distorted unbalanced grid voltage conditions
(or V dc* ) and Q g* 0 . The important matters for different control
targets under unbalanced conditions are negative sequence
current references [7] that could be obtained by substituting
(15) to (7).
C. Proposed control system
Fig.3 shows the proposed control system. As it is shown,
the measured stator voltage is decomposed sequences are used
for current references calculation. Also, fundamental
component is used for stator voltage phase-angle calculation.
Finally, after current references are calculated, all of them will
be transferred to the dq  reference frame, to avoid the current
from decomposing that makes a slow and inaccurate control
system.
PI-R controller is a reciprocal regulator. It means, if it is
regulated for 6ωs, it will work properly for -6ωs. It is
composed by two parts. PI part is responsible for dc component
of power and the resonant part is in charge of control the
resonant power oscillations.[8]
In this paper, PI-R controller is used for both of RSC and
GSC. Control blocks are shown in Fig. 4 and Fig. 5,
respectively.
As it’s shown in Fig. 4, PI-R controller in RSC is regulated
at ±6ωs for encountering harmonic distortion in grid voltage
and at ±2ωs for facing unbalanced stator voltage conditions.
According to the fact that GSC plays just a control role for
supplying active and reactive power, it is regulated just for
mitigating resonant oscillations caused by unbalanced
conditions in total output active power.
Figure 4. PI-R controller for RSC suitabla for harmonically distorted
unbalanced conditions
Figure 5. PI-R controller for GSC suitable for unbalanced conditions
In this paper, by calculating the unbalance factor [2] and
harmonic distortion, in unbalanced or harnomically distorted
grid conditions, just needed parts of control system are getting
to work.
IV.
SIMULATION RESULTS
Simulations of the proposed control strategies for a DFIGbased wind-power-generation system are conducted by using
Matlab/Simulink. The DFIG is rated at 1.5 MW. This rated
power is considered as 1 P.u and reference reactive power is
assumed to be 0 P.u.
Fig. 6 shows the schematic diagram of the tested system.
Discrete models are used with a simulation time step of 5 μs.
The nominal converter dc link voltage is set at 1100 V.
An AC programmable source is used for generating 4 and 3
percent 5th and 7th harmonic components, respectively, in
stator voltage during 3-3.2 sec. also, 10% single phase voltage
sag occurs to the grid at the same time period.
Simulation results for rotor currents that are the main
control parameters in proposed control system are shown in
Fig. 7.
Figure 6. Scheme of the simulated system
system to dynamic variations in electrical domain is too much
lower than the mechanical one. As a result of this fact,
fluctuations in output power and electromagnetic torque caused
by changing in wind speed or wind turbulence are negligible.
Figure 7. Rotor currents in abs reference frame
a.
Fig. 10 shows total output active power, stator output active
and active power transferred through GSC between DFIG and
grid. Since, the size of converters are partial scaled ( about 30%
of DFIG rating ), GSC is just responsible for supplying a small
portion of needed power and it is obvious in fig10 that the main
part of output active power is generated by stator.

d -axis component of RSC's current reference and
response
a.
b.
stator output active power
q  -axis component of RSC's current reference and
response
b.
c.
active power transferred through GSC
d  -axis component of GSC's current reference and
response
c.
d.
total output active power
q  -axis component of GSC's current reference and
response
Figure 8. simulation results for RSC and GSC currents in dq reference frame
in addition to their current references
d.
Fig. 9 shows how rotor current components track rotor current
references. Also it’s observable that GSC’s components have
the same behaviour.
In carried out simulation in this paper, it is assumed that the
rotor speed is fixed at 1.2 P.u. it should be paid attention to this
point that because of large inertia of wind turbine and
generator, mechanical time constant is very larger than
electrical time constant.in other words, the response time of
electromagnetic torque
Figure 9. Simulation results of output active powers and electrmagnetic
torque of DFIG
As Fig. 9 shows, the active power transferred through GSC
is regulated to produce resonant pulsations in opposite of stator
active power resonances to mitigate total output active power
resonant pulsations.
TABLE I.
COMPARISON OF VARIOUS DFIG'S CONTROL SYSTEMS OPERATION UNDER DIFFEREN GRID CONDITIONS
Control parameter
P-R controller
[7]
PI-R controller
[8]
PI controller
[8]
Proposed controller
Grid condition
unbalanced
Harmonically
distorted
Harmonically
distorted
Harmonically distorted
unbalanced
%
I s5th
-
2.48
4.87
1.53
%
I s7th
-
1.96
3.85
1.19
%
I r29th
-
2.08
4.18
3.02
%
I r31th
-
1.93
3.06
2.81
%
I r31th
4.3
-
-
1.92
P total Pulsation%
0.5
-
-
4.31
T e Pulsation%
-
0.35
5.69
3.24
Fig. 9.d shows the electromagnetic torque. As control
system in this paper was designed to eliminate resonant
components whit 2ws and 6ws angular frequencies in
electromagnetic torque, it is observable from Fig. 9.d that
electromagnetic torque has a few pulsations under
harmonically distorted unbalanced conditions.
Table. I is prepared for a better comparison between
proposed control system and other related control systems
under non-ideal grid conditions.
There are some differences between obtained results of this
paper and other researches results. These discrepancies derived
from different decomposition methods and inequality of grid
conditions.
According to the table. I the current components in this
paper have less harmonic pollutions than the corresponded
components in other listed researches. This feature comes from
mathematical inheritance of this paper’s decomposition
method, whereas other decomposition methods are mostly
based on filtering methods. Also, the amplitudes of resonant
pulsations of active power and electromagnetic torque resulted
from proposed control system are larger than control systems
designed in [7] and [8] because the grid condition in this paper
assumed to be harmonically distorted and unbalanced at the
same time whereas those articles studied just one of these
conditions.
V.
CONCLUSION
The fact that DFIG’s rotor windings are connected directly
to the grid has been made them very sensitive to disturbances.
This paper, made it possible to control operation of DFIG
under such a non-ideal conditions by proposing a novel method
for stator voltage sequence decomposition and phase angle
computation, under harmonically distorted unbalanced grid
voltage conditions.
At first control targets that are base of current references
definition, were determined and then by using PI-R controllers
in both of RSC and GSC resonant pulsations of total output
active power and electromagnetic torque were mitigated.
Superiority of this paper to the other similar researches
could be a comprehensive considered condition that is
harmonically
distortion
and
unbalance
conditions
simultaneously.
Finally, the obtained results according to the non-ideal
conditions of tested system were satisfaction.
APPENDIX
 V sd 
V sq 
0
0




V sd 
V sq  V sd 
 V sq 



V sd 
V sq  V sd 
 V sq 

 V 
V sq 
V sd  V sq 
sd 


0
0
0
0
A
0
0
0
0

V 5  V 7  V 5  V 7 
0
0
sd 5 
sd 7 
sq 5 
sq 7 

V sq5 5  V sq7 7  V sd7 7  V sd5 5 
0
0
 5
7
5
7
V

V

V

V
0
0
 sq 5  sq 7 
sd 5 
sd 7 
 7
5
7
5
0
0
V sd 7  V sd 5  V sq 7  V sq 5 
V sd5 5 V sq5 5 V sd7 7  V sq7 7  

V sq55  V sd55  V sq7 7  V sd7 7  

0
0
0
0 
0
0
0
0 

0
0
0
0 

0
0
0
0 



 
V sd  V sq  V sd  V sq 

V sq  V sd  V sq  V sd  

V sq  V sd  V sq  V sd  

V sd  V sq  V sd  V sq  
 V sd 


 V sq 
 V sq 


 V sd 
 V 
sd 
B 

 V sq 
V 5 V 7 
sd 7 
 sd 5
V sq55 V sq7 7 
 5
7
V sq 5 V sq 7 
V 7  V 5
sd
7

sd
5

V sq 
V sd 

sd 

sd 

sq 

sq 

sd 

sq 

sq 

sd 

sd 

sq 
V sq 

sd 

sd 

sq 

sq 

sd 
V
V
V
V
V
V
V
V
V
V
V
V
V
V sq55 V sq7 7 
V sd7 7  V sd55
V sd5 5 V sd7 7 
V sq7 7  V sq5 5 
V
V sd55
V
5
sq 5 
V sq55
V
5
sd 5 
V sd7 7 
V
7
sq 7 
0
0
0
0
0
0
0
0
0
0
V
0
0
V sd 
0
V sq 
0
V sd 
0
0
0
0
0
0
V sq 
V sq 
V sd 
V sd 
V sd 
V sq 
V sq 
V sq 
V sd 
V sq7 7  

V sd7 7  
0 

0 
0 

0 
V sq  
V sd  

V sd  
 
V sq  

V sd 
V sq 
V sd  V sq  V sq55 V sd55 V sq7 7  V sd7 7  




V sd 
V sq  V sd 
0
0
0
0 
 V sq 





C 
V
V sq 
V sd  V sq 
0
0
0
0 
 5 sd  7 

5
7





V

V
V

V
0
0

V
V

V
V
 sq 5 sq 7  sd 5 sd 7 
sq 
sd 
sq 
sd  
5

7

5

7





V
0
0
V sd  V sq  V sd  V sq  
 sd 5 V sd 7  V sq 5 V sq 7 
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