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APSAEM12 Journal of the Japan Society of Applied Electromagnetics and Mechanics Vol.21, No.3 (2013)
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Improving Stability for Independent Power Control of Wind-Turbine Doubly
Fed Induction Generator during Grid Unbalance With Pi-Fuzzy Controller
Truc Pham-Dinh *1
and Hai Nguyen-Thanh *2
This paper presents modified SFOC control of Doubly Fed Induction Generator (DFIG) wind turbine during grid
unbalance for improved stability by using hybrid PI-Fuzzy controllers and eliminating negative sequence components.
The system consists of a common induction generator with slip ring and power electronic converters at both stator
and rotor sides. The modifications are applied to rotor side converter for active and reactive power controls of wind
turbine. The turbine, generator and control units are also described. The investigation is based on
MATLAB/SIMULINK. Simulation results show improved stability of active and reactive powers delivered by DFIG.
Keywords: DFIG; grid unbalance; PI-Fuzzy; wind turbine.
(Received: 31 May 2012, Revised: 4 June 2013)
1. Introduction
Doubly fed induction generators have been the
popular choice in wind power generation due to the low
rating of power electronic circuit connected to the rotor
side of the generator and the grid [1]. The active and
reactive powers delivered by DFIG can be controlled
independently by Stator Flux oriented Control which is
designed for operation with balanced grid voltage [2].
However, most of the grids experience the problems of
voltage unbalance, which raise the winding temperature
and cause pulsation of torque and power [3]. This paper
will investigate the stabilities of active and reactive
powers during transient unbalance of grid voltage for
traditional and modified stator flux oriented controls of
DFIG. The modifications are hybrid PI-Fuzzy controller
and Sequence Component controller. The grid unbal-
ance is modelled with a reduction of 25 % of voltage in
one phase. Wind speed is varied randomly during the
process.
2. Mathematical Model of Wind Turbine
The model of wind turbine and its formula of shaft
torque, turbine torque, power transferred to generator
and related parameters are presented in this session. Fig.
1 illustrates the mechanical system of wind turbine
which is often used in large wind turbine systems.
Fig. 1. Mechanical model of wind turbine [9].
The power extracted from the wind is:
),(
2
1 3
��� pwturb CAvP � (1)
Where:
� = 31.22 (kg/m3
)� air density
A=R2
��(m2
) the cross-sectional area through
which the wind passes.
R(m): length of turbine’s blades.
vw (m/s):the wind speed normal to the cross-
session area A
Cp (����: the aerodynamic efficiency which depends on
the tip spe������������������������������������������������
to Betz’s efficiency, the maximum theoretical efficiency
is 59.3% [10].
i
eC
i
p
�
�
�
��
5.12
54.0
116
22.0),(
�
��
�
�
��
�
�
���
(2)
�������������������������������������������������������
the outer tip of the blade is moving divided by the wind
speed
w
turb
v
R�
� � (3)
_______________________
Correspondence: Truc Pham-Dinh, Faculty of Electrical and
Electronic Engineering, Ho Chi Minh City University of
Technology, 268 Ly Thuong Kiet Street, District 10, Ho Chi
Minh City, Vietnam
email: trucphamdinh@yahoo.co.uk
*1
Ho Chi Minh City University of Technology
*2
Le Hong Phong High School, Ho Chi Minh City
Regular Paper

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日本 AEM 学会誌 Vol. 21, No.3 (2013)
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�������turb (rad/s)�is the angular velocity of turbine.
The turbine efficiency Cp is the function of tip-speed
ratio �����������������
3. Control Methods and Modifications
Structure of control method for DFIG is shown in
Fig. 2, converters on grid side and rotor side of DFIG
are controlled by stator flux oriented control to achieve
the independent control of active and reactive powers.
Modification of the control system by using hybrid PI-
Fuzzy controller has provided better performance of the
generated powers [5]. However, this is only verified
with balanced grid voltage. To improve stability of the
powers, inclusion of sequence component controller
with Notch filter has been suggested by [6] and pre-
sented in Fig. 3 to eliminate negative sequence compo-
nents.
An investigation on DFIG model and system behav-
iour based on SFOC under unbalanced grid voltage
conditions has been provided in [7]. As indicated in [8],
in contrast to SFOC, stator voltage orientation (SVO)
results in the system stability and damping being inde-
pendent of the rotor current. Thus in this section a
modified DFIG model based on SVO is presented.
Fig. 2. ����������������������������������-connected
DFIG-based wind generator [4].
Fig. 3. The proposed current control scheme for the
RSC of a DFIG using PI+Fuzzy controller [6].
Fig. 4 shows the spatial relationships between the
����������������s reference ����������������������r refer-
�������������������������������������r, and the dq+ and
dq� ���������������������������������������������������s
������s, respectively. As shown, the d+
-axis of the dq+
reference frame is fixed to the positive sequence stator
voltage V+
sd+. According to Fig. 4, the transformations
�������������s�������r and dq+ and dq� reference frames
are given by the following equation [6;7;8].
I+
dq = I �������e�����
I�
dq = I �������e�����
��� (4)
I+
dq = I�
dq e������
I�
dq = I+
dq e�����
��� (5)
I+
dq = I������ e����������
I�
dq = I (����� e���������
. (6)
d
d
sdq
sdq s sdq s sdq
�
� � �
� � �
�
� �V R I j
�
(7)
I��
+
= I��
+
+ + I��
+
- = I��
+
+ + I��
-
- e-�����
. (8)
I��
+
= I��
+
+ + I��
+
- = I��
+
+ + I��
-
- e-�����
. (9)
Active and reactive power of stator:
P���
+
������������
+
+����
+
- V���
+
����
+
� (10)
Q���
+
������������
+
+����
+
- V���
+
����
+
� (11)
PI-Fuzzy controllers as shown in Fig. 5 are used to
control the errors between the required and actual values
of both the active power and reactive power delivered to
the grid by the generator. The parameters of the PI-
Fuzzy are adjusted by the fuzzy rules to obtain the best
output to drive the errors to zero. The outputs of these
controllers are commanded values of d-q components of
rotor current in the stator flux oriented reference frame.
These commanded values of currents are used to regu-
late the RSC for provision of the rotor phase voltage to
DFIG.
Fig. 4. Relationships between �����s�������r and dq+
and dq� reference frames.

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427(95)
Fig. 5. PI- Fuzzy Controller.
Table 1 Rule Base of Kp [5]
Table 2 Rule Base of Ti [5]
The fuzzy rules for parameters of PI-FUZZY con-
trollers are presented in table 1 and table 2. The rules
are developed by trial and error method. LN, SN, ZE,
SP, and LP represents large negative, small negative,
zero, small positive, large positive. S, M, H are for small,
medium, high.
The triangular membership functions of inputs and
outputs of PI-Fuzzy controller are shown in Figs. 6 and
7.
Fig. 6. Membership functions of two inputs of fuzzy
bloc.
Fig. 7. Membership functions of two outputs of fuzzy
bloc.
Table 3 Parameters of DFIG 2.3MW
Parameter Symbol Value
Stator inductance LS 159.2 (�H)
Rotor inductance Lr 159.2 (�H)
Magnetic inductance Lm 5.096 (mH)
Stator resistance RS 4 (��)
Rotor resistance Rr 4 (��)
Number of pole pairs P 2
Frequency of the
electric system �S 100���rad/s)
Inertia J 93.22 (kg.m2
)
Inertia of Rotor Jrot
4.17×106
(kg.m2
)
4. Simulation and Results
Simulation of proposed control method for a 2.3
MW DFIG is carried out, parameters of the generator
are shown in table 3. The grid voltage unbalance hap-
pens after 35 seconds, the commanded values of reac-
tive power and active power change at 50s and 60s
respectively. Comparisons of average values of the
powers in steady state with different controllers are
presented in table 4 and 5. Both actual values and
percentage of references are shown. The randomly
variable wind speed is shown in Fig. 8. DFIG’s rotor
speed is shown in Fig 9. Grid voltage unbalance which
happens after 35 s is shown in Fig. 10.

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Fig. 8. Random variation of wind speed.
0 10 20 30 40 50 60
-500
0
500
1000
1500
2000
Time [s]
Variationofrotorspeed(nr)
Fig. 9. Variation of rotor speed.
34.9 34.92 34.94 34.96 34.98 35 35.02 35.04 35.06 35.08 35.1
-800
-600
-400
-200
0
200
400
600
800
Time [s]
Vabcs[V]
Fig. 10. The grid voltage unbalance happens after 35
seconds.
Table 4 Average Value of Ps in Steady State for 3 Control-
lers
�����
�������
PI PI-FUZZY PI-
������������
MW %* MW %* MW %*
Balanced 0.976 2.38 0.976 2.41 0.975 2.53
Unbalanced 0.905 9.52 0.92 8.00 0.925 7.50
(*)%= 100
sref s
sref
P P
P
�
Table 5 Average Value of Qs In Steady State for 3 Controllers.
�����
�������
PI PI-FUZZY PI-������������
MVAR %** MVAR %** MVAR %**
Balance 0.491 1.71 0.502 -0.39 0.502 -0.37
Unbalance 0.440 12.1 0.481 3.7 0.482 3.62
(**)%= 100
sref s
sref
Q Q
Q
�
32 34 36 38
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
Time [s]
Iabcr[A]
With PI & Notch Filter
32 34 36 38
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
With PI-F & without Notch Filter
Time [s]
32 34 36 38
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
With PI & without Notch Filter
Time [s]
Fig. 11. Phase rotor current of DFIG.
20 40 60 80
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
PI-F & with Notch Filter
Time [s]
Ps[MW]
20 40 60 80
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
PI-F & without Notch Filter
Time [s]
20 40 60 80
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
PI & without Notch Filter
Time [s]
Fig. 12. Active output power of DFIG.
20 40 60 80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time [s]
Qs[MVAR]
PI-F & with Notch Filter
20 40 60 80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
PI-F & without Notch Filter
Time [s]
20 40 60 80
0
0.2
0.4
0.6
0.8
1
1.2
1.4
PI & without Notch Filter
Time [s]
Fig. 13. Reactive output power of DFIG.
The simulation results with different controllers are
shown in Figs. 11 to 14; for rotor currents, active and
reactive powers, and generator’s torque respectively.

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20 40 60 80
-20000
-15000
-10000
-5000
0
5000
PI-F & with Notch Filter
TIME [S]
Te
20 40 60 80
-20000
-15000
-10000
-5000
0
5000
PI-F & without Notch Filter
TIME [S]
20 40 60 80
-20000
-15000
-10000
-5000
0
5000
PI & without Notch Filter
TIME [S]
Fig. 14. Torque of DFIG.
5. Discussion
The generator’s rotor speed fluctuates significantly
when and after the voltage unbalance happens as shown
in Figs. 9 and 10. The phase rotor currents are slightly
distorted when grid unbalance happens as shown in Fig.
11. The inclusion of Notch filter for elimination of
negative phase sequence does not change significantly
the waveform of rotor phase current.
However, Notch filter causes significant effects on
active power delivered to the grid during unbalance as
shown in Fig. 12 and highlighted in table 4. After the
grid unbalance happens, the active power still follows
the commanded value, but with fluctuation. The combi-
nation of the PI-Fuzzy controller and Notch filter
improves the response of active power by reducing the
fluctuation. The steady state error of active power
during voltage unbalance is also cut down to 7.5 % of
reference value from 9.52 % when the filter and the
hybrid controller are not used.
Similarly, the combination also reduces fluctuation
in reactive power responses due to voltage unbalance as
shown in Fig. 13 and summarized in table 5. The steady
state error in reactive power response has been reduced
to 3.6 % of reference value with the incorporation of the
controller and the filter. The PI-Fuzzy controller and
Notch filter do not result in improvement of generator’s
torque responses as shown in Fig. 14.
6. Conclusion
The inclusion of hybrid PI-Fuzzy controller and
Notch filter for sequence component controlling have
improved the stability of active and reactive powers
delivered to the grid by DFIG during grid voltage
unbalance. High fluctuations are observed in both active
and reactive powers, discrepancies between the active
power and reactive power average values and reference
values have been significantly reduced. The further
improvement for reduction of power ripples and steady-
state discrepancy should be suggested.
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