ipec_hai

Improving Stability For Independent Power Control
Of Wind-Turbine Doubly Fed Induction Generator
with SFOC and DPC During Grid Unbalance
Truc Pham-Dinh, Nam Anh Nguyen
Faculty of Electrical and Electronic Engineering
Ho Chi Minh City University of Technology
Ho Chi Minh City, Vietnam
pdtruc@hcmut.edu.vn, trucphamdinh@yahoo.co.uk
Hai Nguyen-Thanh
Technology Department
Le Hong Phong High School
Ho Chi Minh City, Vietnam
hoc_vien@yahoo.com.vn
Abstract - This paper presents modified SFOC of Doubly Fed
Induction Generator (DFIG) in wind turbines during grid
unbalance for improved stability by using Notch filter to
eliminate second order harmonic components. Comparison of the
proposed controller with DPC using Notch filters for
improvement during grid voltage unbalance is also included. The
system consists of an induction generator with slip ring and
power electronic converters at both rotor and grid 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,
SFOC, DPC.
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 and Direct Power Control which are
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 control and direct power control of DFIG. The
modifications are hybrid PI-Fuzzy controller and Sequence
Component controller. The grid unbalance is modeled 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. Figure
1illustrates the mechanical system of wind turbine which is
often used in large wind turbine systems.
Figure 1: Model of the mechanical part of Wind Turbine [9].
The power extracted from the wind is:
),(
2
1 3
βλρ pwturb CAvP = (1)
Where:
ȡ = 31.22 (kg/m3
) air density
A=R2
π (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 (λ,β): the aerodynamic efficiency which depends on the
tip speed ratio Ȝ, and blade pitch angle ȕ . According to Betz’s
efficiency, the maximum theoretical efficiency is 59.3%[10].
The tip speed ratio Ȝ is defined as the speed at which the
outer tip of the blade is moving divided by the wind speed
w
turb
v
Rω
λ = (2)
Where Ȧturb (rad/s) is the angular velocity of turbine. The
turbine efficiency Cp is the function of tip-speed ratio λ, pitch
angle and ȕ
978-1-4673-4584-2/12/$31.00 ©2012 IEEE IPEC 2012155

i
eC
i
p
λ
β
λ
βλ
5.12
54.0
116
22.0),(
−
¸¸
¹
·
¨¨
©
§
−−= (3)
3. DIRECT POWER CONTROL AND STATOR FLUX
ORIENTED CONTROL OF DFIG
Structure of control method with DPC for DFIG is
shown in figure 2 and 3. The proposed control structure with
SFOC is shown in figure 4. Appropriate voltage vectors for
rotor side converter are selected to control generated active and
reactive power in DPC. Converters on 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 during voltage
unbalance, inclusion of Notch filter has been suggested by [6,
11] and presented in figure 3 and 4 to eliminate second
harmonic components.
In both control scheme in figure 3, Notch filters are
used to eliminate second order harmonic components in
positive and negative sequences of stator voltage. In figure 4,
Notch filters are used with positive sequences of stator voltage
and rotor current.
Figure 2: The con¿guration of DPC for grid-connected DFIG-based wind
generator without Notch filter. [11]
Figure 3: The typical con¿guration of a grid-connected DFIG-DPC with
Notch Filter [11].
Fig. 5 shows the spatial relationships between the
stationary (Į,ȕ)s reference frame, the rotor(Į,ȕ)r reference
frame rotating at the speed of Ȧr, and the dq+ and dqí
reference frames rotating at the angular speed of Ȧs and íȦs,
respectively. As shown, the d+
-axis of
the dq+
reference frame is fixed to the positive sequence stator
voltage V+
sd+.
Figure 4: The proposed control scheme for the RSC of a DFIG using PI+F
controller and Notch filters.
According to Fig. 5, the transformations between
(Į,ȕ)s, (Į,ȕ)r and dq+ and dqí reference frames are given by
I+
dq = I (Į,ȕ)s eíjȦst
Ií
dq = I (Į,ȕ)s ejȦst
, (6)
I+
dq = Ií
dq eí2jȦst
Ií
dq = I+
dq e2jȦst
, (7)
I+
dq = I(Į,ȕ)r eíj2Ȧslip+t
Ií
dq = F Į,ȕ)r ej2Ȧslip_t
. (8)
156

+
+
++
++= sdqs
sdq
sdqssdq j
dt
d
IRV ψω
ψ
(9)
Idr
+
= Idr
+
+ + Idr
+
- = Idr
+
+ + Idr
-
- e-j2Ȧst
. [6;7;8] (10)
Iqr
+
= Iqr
+
+ + Iqr
+
- = Iqr
+
+ + Iqr
-
- e-j2Ȧst
. [6;7;8] (11)
Active and reactive power of stator:
Ps +
+
= (3/2).(Vds
+
+ids+
+
- Vqs+
+
iqs+
+
) (12)
Qs +
+
= (3/2).(Vds
+
+iqs+
+
- Vqs+
+
ids+
+
) (13)
Figure 5. Relationships between (Į,ȕ)s, (Į,ȕ)r and dq+ and dqí reference
frames [6].
PI-Fuzzy controllers as shown in figure 6 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 variable parameters of the controllers, which are
fixed in traditional PI controllers, will help to achieve the best
performance of the system. 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 regulate the RSC for provision
of the rotor phase voltage to DFIG.
Figure 6: PI-Fuzzy controller.
The fuzzy rules for parameters of PI-FUZZY
controllers 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.
TABLE I: RULE BASE OF KP [5]
TABLE II: RULE BASE OF TI [5]
The triangular membership functions of inputs and
outputs of PI-Fuzzy controller are shown in figures 7 and 8:
Figure 7: Membership functions of two inputs of fuzzy block.
Figure 8: Membership functions of two outputs of fuzzy block.
157

4. SIMULATION AND RESULTS
Simulation of proposed control method’s
implementation for 2.3 MW DFIG is carried out, table 3. The
grid voltage unbalance happens after 35 seconds, the
commanded values of reactive power and active power change
at 50s and 60s respectively. Comparisons of average values of
active and reactive powers in steady state with different
controllers are presented in table 4 and 5. Both actual values
and percentage of references are shown. Average
electromagnetic torque of the generator is shown in table 6.
TABLE III : PARAMETERS OF DFIG 2.3MW
The randomly variable wind speed is shown in figure
9 and figure 10 is grid unbalance at 35s.
Figure 9: Random variation of wind speed.
29.95 29.96 29.97 29.98 29.99 30 30.01 30.02 30.03 30.04 30.05
-800
-600
-400
-200
0
200
400
600
800
Time [s]
Vabcs[V]
Figure 10: The grid voltage unbalance happens after 35 seconds.
TABLE IV: AVERAGE VALUE OF PS IN STEADY STATE FOR 3
CONTROLLERS.
%)(%)(
Psref
PsrefP
Deviation
−
=
During unbalanced voltage
Lowest value of PMax: DPC with Notch Filter (5%)
Highest value of PMin: DPC with Notch Filter (-4,2%)
TABLE V: AVERAGE VALUE OF QS IN STEADY
STATE FOR 3 CONTROLLER.
%)(%)(
Qsref
QsrefQ
Deviation
−
=
Lowest value of QMax : DPC with Notch Filter (5.7%)
Highest value of QMin : DPC with Notch Filter (-10.9%)
TABLE VI: AVERAGE VALUE OF GENERATOR’S TORQUE IN
STEADY STATE FOR THE 3 CONTROLLERS.
Lowest value of TeMax: SFOC with Notch Filter (15899 N.m)
Highest value of TeMin: SFOC with Notch Filter (10195 N.m)
The simulation results with different controllers are
shown in figures 11 to 16 for active and reactive output power
respectively. These figures demonstrate the power responses
when voltage unbalance happens and when the commanded
158

values of powers change under voltage unbalance. Torque
response of the generator is shown in figure 17.
20 30 40
1.8
2
2.2
2.3
DPC WITHOUT NOTCH FILTER
Time [s]
20 30 40
1.8
2
2.2
2.3
SFOC WITH PI+F& NOTCH FILTER
Time [s]
20 30 40
1.8
2
2.2
2.3
Time [s]
Ps[MW]
DPC WITH NOTCH FILTER
Figure 11: Active output power of DFIG when voltage unbalances happen.
20 40 60
0.8
1.1
1.4
1.7
2
2.3
Time [s]
20 40 60
0.8
1.1
1.4
1.7
2
2.3
Time [s]
20 40 60
0.8
1.1
1.4
1.7
2
2.3
Time [s]
Ps[MW]
Figure 12: Active output power of DFIG during the transient states.
49.5 50 50.5
0.8
1.1
1.4
1.7
2
2.3
Time [s]
49.5 50 50.5
0.8
1.1
1.4
1.7
2
2.3
Time [s]
49.5 50 50.5
0.8
1.1
1.4
1.7
2
2.3
Time [s]
Ps[MW]
Figure 13: Dynamic responses of DFIG’s active output power during the
change of commanded value.
20 30 40
0.8
0.9
1
1.1
1.2
Time [s]
Qs[MVAR]
20 30 40
0.8
0.9
1
1.1
1.2
Time [s]
20 30 40
0.8
0.9
1
1.1
1.2
SFOC WITH PI+F&NOTCH FILTER
Time [s]
Figure 14: Reactive output power of DFIG when voltage unbalances happen.
20 40 60
.7
1
1.3
1.6
1.9
2.2
Time [s]
Qs[MVAR]
20 40 60
0.7
1
1.3
1.6
1.9
2.2
Time [s]
20 40 60
.07
1
1.2
1.6
1.9
2.2
Time [s]
Figure 15: Reactive output power of DFIG during transient states.
49.5 50 50.5
.7
1
1.3
1.6
1.9
2.2
Time [s]
Qs[MVAR]
49.5 50 50.5
0.7
1
1.3
1.6
1.9
2.2
Time [s]
49.5 50 50.5
.07
1
1.2
1.6
1.9
2.2
Time [s]
Figure 16: Dynamic responses of DFIG’s reactive power during the change of
commanded value.
20 40 60 80
0
3
6
9
12
15
18
20
Time [s]
Te[KN.m]
20 40 60 80
0
3
6
9
12
15
18
20
Time [s]
20 40 60 80
0
3
6
9
12
15
18
20
FOC WITH PI+F& NOTCH FILTER
Time [s]
Figure 17: Torque of DFIG
5. DISCUSSION
DPC has shown good steady state active power responses
during the voltage balance and unbalance as shown in table 4. The
deviation of the mean value of active power from the reference value
is almost zero percent with the inclusion of Notch filter. SFOC is also
giving good performance with small deviation (about 1%). The
fluctuation of active power is smallest for DPC with Notch filter
during the unbalance.
Steady state responses of reactive power are also very good
when Notch filters are included. The deviations are 0% and 0.3%
respectively for DPC and SFOC. The deviation is much higher
without Notch filter during the voltage unbalance as shown in table 5.
159

There is no significant difference observed between the responses
during the voltage balance, with or without Notch filters. The
fluctuation is observed to be smallest for DPC with Notch filter.
SFOC however gives smallest torque variation during voltage
unbalance as shown in table 6.
The results obtained in table 4 are further demonstrated in
figure 11. SFOC’s active power response when voltage unbalance
happens has higher ripples while the responses obtained with the two
DPC schemes are not significantly distorted. The responses to change
in the commanded values during the unbalance are good for the three
control scheme as shown in figure 12. DPC schemes give faster
responses as shown in figure 13.
Higher ripples are also observed in reactive power
responses of SFOC when voltage unbalance occurs as shown in
figure 14. The observation is consistent with statistics presented in
table 5. Reactive powers in the three control scheme follow the
commanded values under the condition of voltage unbalance as
shown in figure 15. Time responses of reactive power in DPC control
schemes are also less than SFOC’s one as shown in figure 16.
Torque responses observed in figure 17 are also consistent
with the statistics shown in table 6.
6. CONCLUSION
The proposed SFOC scheme for DFIG with the inclusion of
PI-Fuzzy controllers and Notch filters has improved the stability of
independent control of active and reactive power during grid voltage
unbalance. The responses of active and reactive power are compared
with a traditional DPC and modified DPC using Notch filters to
increase the stability. The observations are made during the
occurrence of voltage dip in one phase, transient states as well steady
states of the powers under unbalanced condition. In all the
observations, the independent control of the powers are maintained
for the proposed scheme.
However, high fluctuations in active and reactive powers
are present in the responses obtained with the proposed scheme.
Although lower ripples are observed for generator’s torque.
Experimental verification of the new control scheme should
be carried out to validate the results obtained with simulation.
7. REFERENCES
[1] Ackermann, T. (2003), Wind power in power systems, John Wiley and
Sons, USA.
[2] Leonhard, W. (2001), Control of electric drives, Springer-Verlag, 3rd
edition, USA.
[3] Muljadi, E., Yildirim, D., Batan, T., and Butterfield, C.P. (1999),
“Understand the unbalanced-voltage problem in wind turbine generation”,
Proceeding of IEEE Industry Application Conference, Phoenix, USA,
pp.1359-1365.
[4]. Baggu, M. M. (2009); “Advanced control techniques for doubly fed
induction generator – based wind turbine converters to improve low voltage
ride- throught during system imbalances”, PhD Thesis, Missouri University of
Science and Technology.
[5]. Pham-Dinh, T., Pham-Trung, H., Le-Thanh, H. (2011), “PI-Fuzzy
Controller for Doubly Fed Induction Generator Wind Turbine”, Proceedings
of ASEAN Symposium on Automatic Control ASAC 2011, Vietnam, pp.79 –
81.
[6] Phan, V. T., Lee, H. H., Chun, T. W. (2010); “An Effective rotor current
controller for unbalanced stand – alone DFIG systems in the rotor reference
frame”, Journal of Power electrionics, Vol.10, No.6, pp194-202.
[7]. L. Xu, Y. Wang, “Dynamic modeling and control of DFIG based wind
turbines under unbalanced network conditions”, IEEE Trans. Power Syst. 22
(1) (2007) 314–323.
[8]. A. Peterson, L. Harnefors, T. Thiringer, “Comparison between stator-flux
and grid flux oriented rotor current control of doubly-fed induction
generators”, in: The 35th Annual IEEE Power Electronics Specialist
Conference, vol. 1, 20–25 June,2004, pp. 482–486.
[9] Sorensen, P.; Hansen, D.A.; Christensen, P.; Mieritz, M.; Bech, J.; Bak-
Jensen, B.; Nielsen, H. (2003); “Simulation and Verification of Transient
Events in Large Wind Power Installation”, Project Report, Risø National
Laboratory, Roskilde, Norway.
[10] Masters, M. G. (2004), Renewable and Efficient Electric Power Systems,
John Wiley and Sons, Inc., Publication.
[11] Jia-bing HU, Yi-kang HE, Lie XU (2008) ; “Dynamic modeling and
direct power control of wind turbine driven DFIG under unbalanced network
voltage conditions”, Journal of Zhejiang University SCIENCE
160

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