A Novel Robust Low Voltage and Fault Ride Through For Wind Turbine
Application Operating in Weak Grids
Manoj R Rathi,
marathi@ece.umn.edu,
Ned Mohan
mohan@ece.umn.edu
Department of Electrical and Computer Engineering
University of Minnesota
Low Voltage Ride Through Requirement
Abstract— Wind turbines are very susceptible to any disturbance, faults and low grid voltages. They are disconnected from
the grid whenever these conditions arise and reconnected once the
grid is healthy. Maintaining the wind turbine connected to grid
is real challenge. Future grid codes will require wind turbines
connected to grid even during the fault condition and have Low
Voltage Ride Through (LVRT) feature installed. LVRT feature is
not available in most of the present wind turbine and few do with
addition circuitry and control increasing the cost of the system. In
this paper, a novel control strategy and LVRT for wind turbines
with doubly fed induction generators is presented to maintain the
turbine connected to grid during fault and post fault condition
without addition circuitry. The controller is designed using H∞
technique and µ-analysis based robust control technique to take
into account various adverse conditions. The controller is tested
on low power hardware prototype and the results are presented.
1.2
Fault Condition
Voltage (pu)
1
0.8
0.6
Wind Turbines may be disconnected
0.4
0.2
0
−1
Fig. 1.
0
1
2
Time (sec)
3
4
5
Low Voltage Ride Through Requirement For Wind Generation
1. I NTRODUCTION
Wind energy is clean, renewable and abundant source
of energy. The total installed capacity in United States is
6,350 MW [1] and it is projected that by 2020 total installed
capacity will touch 100,000 MW. Present day technology
doesn’t support maintaining the wind turbine connected to
the grid during the fault and post fault conditions and if so
with an additional circuitry and cost, resulting in disconnection
of turbine during the fault conditions. Disconnection of such
a large power in future can severely affect power system
operation during the fault and post-fault conditions. Future
grid codes will require wind turbines to have Low Voltage
Ride Through (LVRT) [2] feature installed as shown in Fig. 1.
Due the variable nature of wind, doubly fed induction
generators (DFIG) are preferred for wind turbine application to
harnessing wind power. DFIGs can be operated at wide speed
range and ideally at any power factor using power electronic
converter in the rotor circuit. The rating of power electronics
converter depends on the operating speed range and generally
in the range of 10-40% of the machine rating. The stator of
induction machine is directly connected to grid while the rotor
is connected through back-to-back connected 3-phase voltage
source converters (VSCs) which on the other end is connected
to grid as shown in Fig. 2. The LVRT feature is provide
0-7803-9252-3/05/$20.00 ©2005 IEEE
by few wind turbine manufacturers and is implemented by
using pitch angle control and shorting the rotor circuit [3]
instead of using the rotor control to improve the performance
and supply the reactive power during and especially in the
post fault conditions. Shorting the rotor terminals will result
in drawing a very high reactive power during the post fault
condition and may lead to another disturbance affecting the
post fault operating condition of power system.
The grid side converter has to handle grid
faults/disturbances and maintain the DC-link voltage and
stator terminal voltages constant, while the rotor side converter
has to control the stator active and reactive power over a wide
voltage range including fault and low voltage conditions.
Also it’s desirable to maintain a good performance despite
known variations in the grid voltages, system parameters and
variations in the wind power. A procedure based on H∞
control synthesis and µ-analysis technique is used to design
the controller. The control scheme is tested by doing the
simulation studies and hardware verification on low power
laboratory prototype.
2. S YSTEM M ODELING
The variable speed wind turbine consisting of DFIG is
shown in Fig. 2. The stator of the DFIG is directly connected
2481
to grid while the rotor is connected to grid through a backto-back connected voltage source converter [4] as shown in
Fig 2. The per-phase equivalent circuit of the DFIG model is
shown in Fig. 3
DFIG
Lg
ωd = ωdA + ωm
Vs
is
ig
Vg
ic
where subscripts ’d’, ’q’, ’s’, ’r’ are used for d-axis component, q-axis component, stator and rotor respectively and ωd
is the synchronous speed (rad/s) and ωdA is the frequency of
the rotor voltages and currents. ωd and ωdA are related to the
rotor speed (ωm ) in electrical radians by
Pw
Lc
C
Vc
Lls
ir
+
Vdc
_
The relation between stator power and rotor power is given
by
Wind
Turbine
Vr
Ps
Rotor Side
Converter
Grid Side
Converter
Fig. 2.
Gear
Box
Rr
is
Llr
ir
Vs
im
Fig. 3.
Lm
= −
Pr
s
(12)
Qr
(13)
s
where Qmag is the magnetizing reactive power required by
DFIG and can be approximated by
Qs
Variable Speed Wind Turbine System
Rs
(11)
Qmag ≈
Vr
s
= Qmag −
2
(vsq (isd + ird ) − vsd (isq + irq ))
3
(14)
From the above equation 13 and equation 14, ideally
generator can be made to operate at any power factor by
injecting relatively small reactive power in the rotor circuit.
DFIG Model
The equations at the grid connection point are
The complete system is modeled in d− q reference frame.
The current direction chosen for developing the system model
is as shown in Fig. 2 and Fig. 3. Transformation [T ]abc→dq
is used to convert voltages and currents from ‘a − b − c’ to
‘d − q’ frame.
cos(θ) cos(θ − 23 pi) cos(θ − 43 pi)
[T ]abc→dq =
(1)
sin(θ) sin(θ − 23 pi) sin(θ − 43 pi)
The equations for the DFIG [5] is given by
vsd
=
vsq
=
vrd
=
vrq
=
Tem
=
Ps
=
Qs
=
Pr
=
Qr
=
d
d
isd + Lm ird + Rs isd − ωd Ls isq (2)
dt
dt
−ωd Lm irq
d
d
Ls isq + Lm irq + Rs isq + ωd Ls isd (3)
dt
dt
+ωd Lm ird
d
d
Lm isd + Lr ird + Rr ird − ωdA Lm isq (4)
dt
dt
−ωdA Lr irq
d
d
Lm isq + Lr irq + Rr irq + ωdA Lm isd (5)
dt
dt
+ωdA Lr ird
p
Lm (isq ird − isd ird )
(6)
3
2
(vsd isd + vsq isq )
(7)
3
2
(vsq isd − vsd isq )
(8)
3
2
(vrd ird + vrq irq )
(9)
3
2
(vrq ird − vrd irq )
(10)
3
Ls
d
(15)
igd + Rg igd − ωd Lg igq + vsd
dt
d
(16)
vgq = Lg igq + Rg igq + ωd Lg igd + vsq
dt
where subscript ’g’ represents grid side quantities. For the
grid-side converter, the voltage equations are
vgd
= Lg
d
icd + Rc icd − ωd Lc icq + vcd
(17)
dt
d
vsq = Lc icq + Rc icq + ωd Lc icd + vcq
(18)
dt
2
(vcd icd + vcq icq )
Pc =
(19)
3
where subscript ’c’ is used for grid side converter quantities.
The relationship between the grid currents, stator currents and
grid side converter currents is given by
vsd
=
Lc
igd = isd + icd
(20)
igq = isq + icq
(21)
The difference in the active power drawn from the grid and
that supplied to the DFIG rotor circuit charges the dc-link
capacitor. This can be expressed as
dvcap
1
(vdc − vcap )2
=
Perr −
(22)
dt
Cvcap
Resr
2 + 4R
vcap + vcap
esr (Pc − Pr )
(23)
vdc =
2
and vcap is the voltage across the capacitance, Resr is the
equivalent series resistance of the capacitor and vdc is the dclink voltage. Here, the losses in the grid-side and rotor-side
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ic_ref
converters are neglected.
Fig. 5.
ir_ref
Current
Controller
Fig. 6.
(24)
Ps = −Pc
Modeling Uncertainty
Wc
W Lg
Wf
+
(25)
nom
C
+
+
V
Disturbances
d
g_0
+
+
1
WVg_dist
d
W ir_dist
I
2
r_0
+
+
W ic
WVs
Fig. 4.
GSC and DFIG
System Model
V
Disturbances
s_0
Vdc_perf
Performance
Outputs
V s_mag
W
Vs_perf
y
K grid
+
+
f
+
+
+
+
v
g
WVs_dist
T
+
w_0
+
+
+
d
1
y
2
T
DFIG
and
GSC
Model
w
z
1
z
2
z
3
z
4
Performance
Outputs
W
Tem
Tem_perf
Ps
W
Qs
W
Ps_perf
WTw_dist
+
+
i
Qs_perf
r
u
Vdc
Vs_mag
Ps
Qs
vr
System Block Diagram
c
W
+
+
Pwind
vc
ir
i
V dc
Wf
W ir
Qs
r
5
Modeling Uncertainty
WTw
2
Ps
i
3
4
GSC H∞ Controller Design Model
Fig. 7.
The complete system with H∞ controllers is shown in
Fig. 4.
Current
ir_ref Controller
g
u
1
Rotor Hinf
Controller
+
+
v
z
z
WVdc_dist
d
Ps_ref
Qs_ref
DFIG
and
GSC
Model
2
3
3. H∞ C ONTROLLER D ESIGN
Current
Controller
z
1
d
nom
ic_ref
C
+
f
GSC Hinf
Controller
z
z
WVg
The rotor side control has to be operational during the
fault or low voltage conditions. Once the grid voltages are
restored back to normal, generator tries to draw large reactive
power which may lead to another disturbance disconnecting
the turbine from the grid. Thus a robust controller is synthesized for the grid side converter and rotor side converter
modeled by the system equations (2) through (23) to maintain
the turbine connected to grid. The fault condition may last up
to 150 msec or even more. The grid side controller senses the
DC link voltage error and stator terminal voltage magnitude
error and develops the current commands to compensate them
while the rotor side control senses the stator active and reactive
power errors and generates the rotor current command to
compensate them.
Vdc_ref
L
f
g
+
+
nom
Vg
+
+
f
maintaining the system in running condition.
Vsmag_ref
ir
Plant
Rotor Side Converter Current Control System Block Diagram
g_nom
ic
vr
ir
L
Vs_mag
ic
Plant
Grid Side Converter Current Control System Block Diagram
During the low voltage conditions, grid can’t absorb or
supply power and hence the wind power reference for the
generator has to be made zero. Thus the stator power becomes
Vdc
vc
ic
The grid side converter operates as a STATCOM maintaining the stator terminal voltage to the require value and
supplying the required power to the rotor circuit maintaining
the DC link voltage constant. The rotor side converter controls
the stator active and reactive power by injecting active and
reactive power in the rotor circuit governed by equations (12)
and (13). If losses in the system are neglected, then power
extracted from the wind should flow into the grid. Thus the
stator power can be written as
Ps = −Pwind − Pc
Current
Controller
Fig. 8.
y
K rotor
3
y
4
Rotor H∞ Controller Design Model
Pc
To synthesize H∞ controllers [6] for grid side converter
and rotor circuit, faster inner current control loops are desirable. The system block diagram for grid side converter current
controller design and rotor side current controller design is
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TABLE II
shown in Fig. 5 and Fig. 6 respectively. System modeled by
equations equation (17) and equation (18) is used to design the
grid side converter current controller and equations (2) through
(5) for the rotor side current controller. A current controller
with the bandwidth of 1 kHz was designed.
Minimum Wind Speed
Nominal Wind Speed
Minimum rotor speed
Nominal Rotor Speed
Gear box ratio
4 m/s
14 m/s
9 rpm
18 rpm
1:100
type. The system parameters chosen for 2 MW machine and
laboratory prototype are detailed in Table. I. The wind turbine
parameters chosen for 2MW system are given in Table. II.
The converter ratings for grid side converter and rotor side
converter depend on the operating speed range and selected
as 25% of the rating of DFIG.
Frequency Response of H∞ Controller for Grid Side Converter
From: In(1)
From: In(2)
To: Out(1)
20
0
−20
To: Out(1)
−40
540
360
180
0
−180
40
To: Out(2)
Magnitude(dB);Phase(deg) (dB) ; Phase (deg)
40
20
0
−20
−40
900
To: Out(2)
Once the nominal DFIG system, grid side converter
current controllers and rotor circuit current controllers has
been modeled as described above, various parameter variations
and disturbances have to be added so that a controller can
be synthesized which will desensitize the system from them
and maintain good performance. For the grid-side converter
controller, grid voltage drop of 90% and 100% variations in the
wind power were considered to represent fault condition and
variable nature of wind power. For modeling uncertainty, 10%
variations in the component values of Lg and C, 10% variation
in the grid voltages and 5Hz variation in the supply frequency
are considered. A disturbance signal is added to the model
through a suitable weighting function to representing the
fault condition of 250 ms, so that the synthesized controller
minimizes the disturbance effects. Normalized DC link voltage
error (Vdcerr ) and stator terminal voltage magnitude errors
(Vsmag ) were considered as performance outputs. Suitable
weighting functions were chosen for the desirable output
performance. For the rotor side converter, 90% variation in the
stator terminal voltage and 100% variation in the wind power
are considered. For modeling uncertainty, 10% variations in
system parameters are considered. A disturbance signal with
weighting function is added to take into account fault condition
and change in stator active power. Errors in stator active
power, reactive power and error in electromagnetic torque
are considered as performance outputs and suitable weighting
functions are added to get desired output performance for the
rotor side converter.
W IND T URBINE PARAMETERS FOR 2MW S YSTEM [7]
720
540
360
180
0
−2
10
−1
10
0
1
10
10
2
3
10
−2
10 10
−1
10
0
1
10
10
2
3
10
10
Frequency (Hz)
Fig. 9. Frequency response of GSC H∞ controller for 2MW DFIG System
Frequency Response of H Controller for Rotor Circuit
∞
From: In(1)
From: In(2)
Lm
Lls
Llr
Rs
Rr
Lg
Lc
Vdc
Vg
2 MW System
1.6742 mH
55.8 µH
44.65 µH
2.1 m Ω
2.1 m Ω
0.385mH
0.25 mH
1200 V
680 Vrms
Laboratory
Prototype
221mH
10mH
10mH
3.5 Ω
7.5 Ω
4mH
4mH
100 V
85 Vrms
To: Out(1)
Parameters
20
0
−20
360
315
270
225
180
135
90
40
20
To: Out(2)
Magnitude(dB);Phase(deg) (dB) ; Phase (deg)
DFIG S YSTEM PARAMETERS FOR 2MW S YSTEM [7]
0
−20
−40
−60
180
135
To: Out(2)
TABLE I
To: Out(1)
40
90
45
0
−45
−90
−2
10
0
10
2
10
−2
10
0
10
2
10
Frequency (Hz)
Fig. 10. Frequency response of Rotor H∞ controller for 2MW DFIG System
The systems were implemented in Matlab-Simulink and
the controller were synthesized using Matlab µ-analysis toolbox [8] for 2 MW machine and low power laboratory proto-
The frequency responses of GSC and rotor controllers
obtained for 2MW DFIG system are shown in Fig. 9 and
Fig. 10 respectively.
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DC Link Voltage
4. S IMULATION R ESULTS
2000
DC Link Voltage (V)
1800
Simulation studies were carried out on the 2MW DFIG
system with the parameters detailed in Table. I and Table. II.
The grid voltages were dropped by 90% for 250ms to simulate
the fault condition. The line voltage at the grid and stator
terminal is shown in Fig. 11(a) and Fig. 11(b). The DC link
voltage waveform is shown in Fig. 12. From Fig. 11, it is clear
that the control restores the stator terminal voltage quickly
once the fault is cleared and maintains the DC link voltages
during the fault and post fault condition. Thus the wind turbine
is still connected to grid during and after the fault.
1600
1400
1200
1000
800
600
400
25
26
27
28
Time (s)
29
30
Fig. 12. DC-Link Voltage for 2MW System during 250 msec Fault Condition
Grid Line Voltage Magnitude
Stator Reactive Power Absorbed
800
1
700
0.5
600
Qs(MW)
Voltage (V)
0
500
400
300
−1
−1.5
200
−2
100
0
−0.5
25
26
27
28
Time (s)
29
−2.5
30
(a) Grid Voltages
Fig. 13.
Condition
Stator Line Voltage Magnitude
25
25.5
Time (s)
26
26.5
Reactive Power Waveform for 2MW during 250 msec Fault
800
700
5. H ARDWARE R ESULTS
Voltage (V)
600
The small scale laboratory prototype was used to verify
the control concept is shown in Fig. 14. The H∞ controller
designed was implemented using a DSP-based rapid prototyping environment from dSPACE [9]. Space vector modulation
technique was used to develop the PWM signals for better
utilization of DC-Link voltage. The system is operated at
50 V (rms) grid line voltage. The reference for the sta-
500
400
300
200
100
0
25
26
27
28
Time (s)
29
30
(b) DFIG Stator Terminal Voltages
Fig. 11.
Simulation results for 2MW during 250 msec Fault Condition
The wind power reference and stator reactive power
reference is made zero during the fault condition and normal
operation was restored once the grid was healthy. The reactive
power waveform is shown in Fig. 13. From the Fig. 13,
controller maintains the stator reactive power to its reference
value.
Fig. 14.
Low Power Hardware Prototype
tor terminal voltage and DC link voltages were selected as
55 V (rms) and 100 V (dc). The reactive power required by
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Stator Voltage Magnitude
grid during the fault and post fault control as shown in Fig. 16.
70
60
6. C ONCLUSIONS
A novel control strategy using the robust controller theory
is used to reduce the effects of any faults, disturbances or
low grid voltages. A robust H∞ controller is synthesized to
control the grid-side converter and the rotor circuit, so the
wind turbine is still kept in operating condition during the
fault and post fault condition without any lost of generation.
Modifying the controller from existing method can result in
maintaining the turbine connected for longer duration resulting
in better utilization of wind turbine. The DFIG can supply
reactive power to the grid for voltage support. The control
scheme has been tested on a scaled down laboratory prototype
and found to work satisfactorily.
40
Vs
mag
50
30
20
10
0
0
0.5
1
1.5
Time
(a) DFIG Stator Voltages
DC Link Voltage
120
110
100
R EFERENCES
Vdc
90
80
70
60
50
40
0
0.5
1
1.5
Time
(b) DC Link Voltage
Fig. 15.
Hardware results for 250 msec Fault Conditions
Stator Reactive Power
30
20
10
Qs (W)
0
−10
−20
−30
−40
−50
0
0.5
1
1.5
Time
Fig. 16.
Stator Reactive Power
DFIG is supplied from the rotor side (i.e Qs = 0). A grid
voltage fault of 250 msec was applied to the system. The
stator terminal voltages and DC link voltages are shown in
Fig. 15(a) and Fig. 15(b) respectively. From the Fig. 15, it’s
clear that controller acts effectively and tries to maintain the
DC link voltage constant during the fault condition. The rotor
side controller controls the reactive power absorbed from the
[1] T. Ackermann, Wind Power in Power System. John Willey and Sons,
2005.
[2] American Wind Energy Association, PETITION FOR RULEMAKING
OR, IN THE ALTERNATIVE, REQUEST FOR CLARIFICATION OF
ORDER 2003-A, AND REQUEST FOR TECHNICAL CONFERENCE
OF THE AMERICAN WIND ENERGY ASSOCIATION.
[3] Wind Turbine Generator With A Low Voltage Ride Through Controller
And A Method For Controlling Wind Turbine Components, August
2004.
[4] N. Mohan, T. Undeland, and W. P. Robbins, Power Electronics. John
Wiley and Sons, 2 ed., 1995.
[5] N.
Mohan,
Advanced
Electric
Drives.
MNPERE,
http://www.mnpere.com, 2001.
[6] K. Zhou and J. C. Doyle, Essentials of Robust Control. Prentice Hall,
1998.
[7] J. G. SLOOTWEG, Wind Power : Modelling and Impact on Power System Dynamics. PhD thesis, Technische Universiteit Delft, Netherlands,
2003.
[8] The MathWorks Inc., http://www.mathworks.com, Matlab Reference
Manual.
[9] dSPACE Inc., http://www.dSPACE.de, dSPACE User Manual For
DS1103.
[10] M.Rathi, P. Jose, and N. Mohan, “A Novel H∞ Controller for Wind
Turbine Application Operating in Weak Grids,” in International Electric
Machines and Drives Conference, pp. 320 – 325, 2005.
[11] Eltra Transmission System Planning, Technical Requirement For Connecting Wind Turbine Installation To The Power Network, 2nd edition ed., April 2000. (Unoffical Translation of the official specification
in Danish, Eltra Doc No. 74174).
[12] EESTI ENERGIA AS, Specifications For Connecting Wind Farms To
The Transmission Network, 2001.
[13] S. Heier, Grid Integration of Wind Energy Conversion Systems. John
Wiley and Sons, 1998.
[14] J. Smith and D. Brooks, “Voltage Impacts of Distributed Wind Generation on Rural Distribution Feeders,” in Transmission and Distribution
Conference and Exposition, vol. 1, pp. 492 – 497, 2001.
[15] G. Goodwin, S. Graebe, and M. Salgado, Control System Design.
Prentice Hall, 2001.
[16] T. Brekken and N. Mohan, “A Novel Doubly-fed Induction Wind
Generator Control Scheme for Reactive Power Control and Torque
Pulsation Compensation Under Unbalanced Grid Voltage Conditions,”
in Power Electronics Specialist Conference, vol. 2, pp. 760 – 764, 2003.
[17] http://www.awea.org.
[18] A whitepaper from American Superconductor, How Dynamic VAR
Technology Resolves Key Windfarm Operational and Business Issues.
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