SIDDANNA M BALAPGOL

1. 1
New Direct Torque Control of DFIG under
Balanced and Unbalanced Grid Voltage
B. B. Pimple, V. Y. Vekhande and B. G. Fernandes
Department of Electrical Engineering,
Indian Institute of Technology Bombay,
Powai, Mumbai 400076, India.
Tel. - +91 2225764422 Fax. - +91 22 2572 3707
email: bbpimple@ee.iitb.ac.in,vekhande@ee.iitb.ac.in,bgf@ee.iitb.ac.in
Abstract—This paper presents a direct torque control method
for doubly-fed induction generator (DFIG) based wind power
generation systems. The angle and magnitude of rotor voltage
are controlled to achieve independent control of electromagnetic
torque and reactive power respectively. Space vector modulation is
used to address the limitations like, variable switching frequency
and torque ripple, of hysteresis based schemes. Further, this paper
presents a technique to reduce the torque pulsations of DFIG under
unbalanced grid voltage condition. Under unbalanced grid voltage
condition, the torque angle (𝛿) is controlled so that electromagnetic
torque pulsations are reduced. To achieve this, a compensation
method based on proportional-integral and resonant (PI+R) con-
troller is explored. The proposed control method does not require
rotating frame transformations and it maintains the simplicity
of DTC. It has fast dynamic response, which is comparable to
vector control. Simulation results for a 2 MW DFIG system
demonstrates the effectiveness of the proposed control strategy with
various loading conditions under both balanced and unbalanced
grid voltage.
Index Terms—Doubly-Fed Induction Generator, Direct
Torque Control, Unbalanced Grid Voltage, Torque pulsations,
Proportional-Integral and Resonant Controller.
I. INTRODUCTION
DOUBLY-FED Induction Generators (DFIGs) are used
mainly for wind energy conversion in MW range. The
stator is directly connected to grid while the rotor is fed through
power electronic converter. The power electronic converter is
rated at 25% to 30% of the generator rating for a variation
in synchronous speed around ±25%. The major advantages of
the DFIG based wind turbines are variable speed operation and
stator power factor control from rotor side converter.
The direct torque control (DTC) method is an alternative
to vector control for DFIG based wind power generation.
Variable switching frequency and high torque ripple are the
main limitations of hysteresis based DTC. To address these
limitations, DTC with space vector modulation based on syn-
chronous reference frame transformation, predictive control and
deadbeat control are reported in the literature [1], [2]. This
paper proposes a new DTC method wherein rotor voltage
vector is generated in polar form. Hence, the implementation of
DTC using space vector modulation becomes simple compared
to above mentioned methods. The method is also capable of
independent control of torque and reactive power.
When the stator of DFIG is connected to unbalanced grid,
the torque produced by doubly-fed induction generator would
pulsate. The torque has periodic pulsations at twice the grid
frequency, which can result in acoustic noise at low levels and
at high levels can damage the rotor shaft, gearbox or blade
assembly. Also, DFIG connected to an unbalanced grid will
draw unbalanced current. These unbalanced current tend to
increase the grid voltage unbalance. Generally the wind power
generator in the range of 1 to 5 MVA are connected to 11 to
66 kV grid. For this voltage level, the permissible unbalance is
up to 3% [3]. Methods to compensate the effects of unbalanced
grid voltage based on positive sequence and negative sequence
rotating reference frame theory are well reported in literature.
In [5], control of DFIG with grid side converter (GSC) was
explored. The stator unbalanced currents and voltages were
compensated by injecting currents into grid by GSC. In this
paper, two synchronously rotating reference frames were used to
determine positive and negative sequence stator currents. In [6],
the positive and negative sequence rotor currents were controlled
to reduce pulsations in any one of the following; torque, active
power, stator current or rotor current. In [7], grid side converter
and rotor side converter control were used to compensate the
effects of unbalanced grid. In [8], rotor side control based
on positive sequence rotating frame was used. The positive
sequence rotor current was regulated by PI regulator while
negative sequence rotor current appears at double frequency was
regulated by resonant regulator.
Reduction of torque pulsation under unbalanced grid voltage
with direct torque control is not explored in literature. This paper
proposes the reduction of torque pulsation of DFIG connected
to unbalanced grid. The magnitude and angle of rotor voltage
vector are controlled independently. The torque angle 𝛿, is
controlled in such a way that torque pulsations are reduced.
To achieve this a proportional-integral and resonant (PI+R)
controller are used. The proposed control method is a scalar
control method, it does not require multiple reference frame
transformation, sequential decomposition and notch filters to
remove second harmonic components. The scheme of (PI+R)
control in stationary frame is simple and complexity in calcu-
lations is significantly reduced.
978-1-4244-6890-4/10/$26.00 ©2010 IEEE TENCON 20102154

2. II. DYNAMIC MODEL OF DOUBLY-FED INDUCTION
GENERATOR
The voltage equations of DFIG in stationary reference frame
are as follows:
𝑉 𝑠 = 𝑅 𝑠 𝐼 𝑠 +
𝑑𝜓 𝑠
𝑑𝑡
(1)
𝑉 𝑟 = 𝑅 𝑟 𝐼 𝑟 +
𝑑𝜓 𝑟
𝑑𝑡
− 𝑗𝜔 𝑟 𝜓 𝑟 (2)
𝑉 𝑑𝑠 = 𝑅 𝑠 𝐼 𝑑𝑠 +
𝑑𝜓 𝑑𝑠
𝑑𝑡
(3)
𝑉 𝑞𝑠 = 𝑅 𝑠 𝐼 𝑞𝑠 +
𝑑𝜓 𝑞𝑠
𝑑𝑡
(4)
𝑉 𝑑𝑟 = 𝑅 𝑟 𝐼 𝑑𝑟 +
𝑑𝜓 𝑑𝑟
𝑑𝑡
+ 𝜔 𝑟 𝜓 𝑞𝑟 (5)
𝑉 𝑞𝑟 = 𝑅 𝑟 𝐼 𝑞𝑟 +
𝑑𝜓 𝑞𝑟
𝑑𝑡
− 𝜔 𝑟 𝜓 𝑑𝑟 (6)
where 𝜔 𝑟, is the rotor angular speed in radian per second.
The stator and rotor flux linkages are
𝜓 𝑑𝑠 = 𝐿 𝑚 𝐼 𝑑𝑟 + 𝐿 𝑑𝑠 𝐼 𝑑𝑠 (7)
𝜓 𝑞𝑠 = 𝐿 𝑚 𝐼 𝑞𝑟 + 𝐿 𝑞𝑠 𝐼 𝑞𝑠 (8)
𝜓 𝑑𝑟 = 𝐿 𝑚 𝐼 𝑑𝑠 + 𝐿 𝑑𝑟 𝐼 𝑑𝑟 (9)
𝜓 𝑞𝑟 = 𝐿 𝑚 𝐼 𝑞𝑠 + 𝐿 𝑞𝑟 𝐼 𝑞𝑟 (10)
III. DIRECT TORQUE CONTROL OF DFIG UNDER
BALANCED GRID VOLTAGE CONDITION
In DFIG, the rotor flux vector 𝜓 𝑟 leads the stator flux vector
𝜓 𝑠 by an angle 𝛿. The rotor voltage vector 𝑉 𝑟 leads (sub-
synchronous speed) or lags (super-synchronous speed) the rotor
flux vector by an angle 𝛼, rotor impedance angle. The angle
(𝛿 + 𝛼) gives the position of rotor voltage vector with respect to
the stator flux vector 𝜓 𝑠. The stator flux angle 𝜃 𝑠 is calculated
as
𝜓 𝑑𝑠 =
∫
(𝑉 𝑑𝑠 − 𝑅 𝑠 𝐼 𝑑𝑠)𝑑𝑡 (11)
𝜓 𝑞𝑠 =
∫
(𝑉 𝑞𝑠 − 𝑅 𝑠 𝐼 𝑞𝑠)𝑑𝑡 (12)
The stator flux angle is
𝜃 𝑠 = tan−1 𝜓 𝑞𝑠
𝜓 𝑑𝑠
(13)
The total angle (𝛿 + 𝛼 + 𝜃 𝑠) gives the position of rotor voltage
vector with respect to the stationery axis. The phasor diagram
for sub-synchronous operation of DFIG is shown in Fig. 1.
The block diagram for the implementation of proposed control
scheme is shown in Fig. 2. The DFIG is modelled in stationary
reference frame and space vector notation is used to represent
the variables. The error between the reference torque and actual
torque is processed by the PI controller. The output of the PI
controller is proportional to (𝛿 + 𝛼) [4]. Similarly, the error
between reference rotor flux vector and actual rotor flux vector is
processed by the PI controller. The output of the PI controller is
proportional to the magnitude of rotor voltage vector 𝑉 𝑟. Using
this magnitude and angle (𝛿 + 𝛼 + 𝜃 𝑠), the d-axis and q-axis
components of reference rotor voltage are determined. These
stationary reference frame (SRF) components are transformed to
rotor reference frame components (RRF) using the rotor position
Fig. 1. Phasor Diagram of DFIG for Sub-synchronous Generation
angle 𝜃 𝑟. Under balanced grid voltage condition, the function
of grid side converter (GSC) is to maintain a constant dc link
voltage and to draw unity power factor current from the grid.
A. Rotor Flux and Torque Estimation
The magnitudes of the rotor fluxes are determined in sta-
tionery reference frame as follows:
𝜓 𝑑𝑟 = 𝐿 𝑚 𝐼 𝑑𝑠 + 𝐿 𝑑𝑟 𝐼 𝑑𝑟 (14)
𝜓 𝑞𝑟 = 𝐿 𝑚 𝐼 𝑞𝑠 + 𝐿 𝑞𝑟 𝐼 𝑞𝑟 (15)
The magnitude of net rotor flux is given by
𝜓 𝑟 =
√
𝜓2
𝑑𝑟 + 𝜓2
𝑞𝑟 (16)
The reference rotor flux is calculated using the reference reactive
power or power factor. Here, the magnitude of reference rotor
flux is selected such that, the stator operates at nearly unity
power factor for rated torque. For torque less than the rated
value, stator of DFIG supplies reactive power to the grid. The
maximum limit of reference rotor flux is decided by the reactive
component of rotor current. In order to maintain the stability,
the reactive component of current drawn by the rotor should not
be greater than twice the net magnetizing current of the DFIG
[10].
The electromagnetic torque developed by DFIG is estimated
as
𝑇 𝑒 =
3
2
𝑝
2
(𝜓 𝑑𝑟 𝐼 𝑞𝑟 − 𝜓 𝑞𝑟 𝐼 𝑑𝑟) (17)
The magnitude of reference torque is determined by wind speed.
B. Salient Features of New Direct Torque Control Scheme
1. It is a scalar control. No synchronously rotating reference
frame transformation is required.
2. As the controlled rotor voltage is in polar form, it is easy to
apply space vector modulation. Therefore, switching frequency
of inverter remains constant.
3. It reduces the torque ripple and makes the stator current
almost sinusoidal.
4. As there are no cascaded regulating loops, its structure is
simple and easy to implement.
5. Fast dynamic response of rotor flux and torque.
6. As the angle and magnitude of rotor voltage vector is
controlled independently, decoupled control of torque and
reactive power is possible.
7. By controlling 𝛿, the direct torque control method can be
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3. Fig. 2. Block Diagram of New Direct Torque Control of DFIG Under Balanced Grid Voltage Condition
explored to reduce torque pulsations under unbalanced grid
voltage condition.
IV. DIRECT TORQUE CONTROL OF DFIG UNDER
UNBALANCED GRID VOLTAGE CONDITION
The torque developed by DFIG is also given by
𝑇 𝑒 =
3
2
𝑝
2
𝐿 𝑚
𝐿 𝑟 𝐿′
𝑠
𝜓 𝑠 𝜓 𝑟 𝑠𝑖𝑛𝛿 (18)
where
𝐿′
𝑠 = 𝐿 𝑠 −
𝐿2
𝑚
𝐿 𝑟
(19)
and 𝛿 is the angle between stator flux vector and rotor flux
vector. Under balanced condition, the reference torque and
actual torque are steady (dc) quantities. Single PI regulator
is required to process the error between reference torque and
actual torque. The output of PI regulator generates the signal
proportional to (𝛿+𝛼). Under unbalanced grid voltage condition,
the stator flux vector consists of double frequency component
which results in the oscillation of torque at this frequency.
To eliminate the torque oscillation, it is required to modulate
the rotor flux vector by controlling 𝛿. Under unbalanced grid
condition, the actual torque has an average dc value along with
double frequency component. To process this double frequency
fluctuating component of torque, the resonant regulator tuned
at same frequency is used. PI regulator offers infinite gain for
steady quantity, while resonant regulator offers an infinite gain
at the selected resonant frequency. In addition, there is no phase
shift and gain at other frequencies [9]. The block diagram of
proportional-integral and resonant (PI+R) controller is shown
in Fig. 3. The output of PI regulator is a steady value of angle
(𝛿 + 𝛼) which corresponds to steady error between reference
torque and average value of actual torque. The output of reso-
nant regulator is a double frequency component of torque angle.
As a result, the proposed PI+R controller forces the steady-
state errors to be null for both steady and double frequency
components of torque. The open loop transfer function (OLTF)
Fig. 3. Block Diagram of Proportional-Integral and Resonant Regulator
of PI+R regulator is as follows:
𝑂𝐿𝑇 𝐹 = 𝐾 𝑝 +
𝐾 𝐼
𝑠
+
𝑠𝐾 𝑅
𝑠2 + 𝜔2
0
(20)
where, 𝐾 𝑅 is the gain of resonant regulator, 𝜔0 is the tuned
resonant frequency, which is selected as, double the supply
frequency. It may be noted that a low value of 𝐾 𝑅 gives
a very narrow frequency band. The block diagram for the
implementation of proposed control scheme is shown in Fig. 4.
Under unbalanced grid voltage condition, the grid side converter
(GSC) maintains the dc link voltage constant.
V. SIMULATION RESULTS
Simulation of the proposed direct torque control strategy for
a DFIG based wind generation system is carried out using
MATLAB/ Simulink. The parameters of DFIG are taken from
[7] and given in Table 1. Fig. 5 shows the torque developed
by DFIG for step change in reference torque under balanced
grid voltage condition. At t=5 s, rated torque is applied and
the corresponding stator current waveform is shown in Fig. 6.
The stator current is almost sinusoidal. Fig. 7 shows the stator
voltage and current waveforms. It can be seen that, the stator
operates nearly at unity power factor for rated torque. For below
rated torque condition, it supplies reactive power to the grid. Fig.
8 shows the dynamic response of rotor flux for step change in
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4. Fig. 4. Block Diagram of New Direct Torque Control of DFIG Under Unbalanced Grid Voltage Condition
reference flux. Similarly, dynamic response of torque can be
seen in Fig. 9.
For the same DFIG system, simulation study is carried out
for 3% unbalance in grid voltage. Fig. 10 shows the torque
developed by DFIG for step changes in reference torque, after
compensation under unbalanced grid voltage condition. Fig. 11
shows the reduction in second harmonic pulsation in torque. At
t=6 s, resonant regulator is enabled. For the generated torque
of 4000 Nm, the torque pulsation before compensation is 2290
Nm and torque pulsation after compensation is 172 Nm. Fig. 12
shows output of resonant regulator which is a double frequency
component of torque angle.
4 5 6 7 8 9
−8000
−6000
−4000
−2000
0
2000
time in sec
torqueinNm
Fig. 5. Direct torque control of DFIG under balanced grid voltage condition
4.95 5 5.05 5.1
−1500
−1000
−500
0
500
1000
1500
time in sec
statorcurrentinamp.
Fig. 6. Stator current of DFIG under balanced grid voltage condition
4.9 4.95 5 5.05 5.1 5.15 5.2
−1000
−500
0
500
1000
time in sec.
stator voltage (V)
stator current (A)
Fig. 7. Stator voltage and current of DFIG
7.8 8 8.2 8.4 8.6 8.8
1.85
1.9
1.95
2
2.05
2.1
time in sec
fluxinWb
act. rotor flux
ref. rotor flux
Fig. 8. Response of rotor flux for step change in reference flux
4.95 5 5.05 5.1 5.15
−8000
−6000
−4000
−2000
0
2000
time in sec
torqueinNm
ref. torque
act. torque
Fig. 9. Response of torque for step change in reference torque
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5. 6 7 8 9 10
−7000
−6000
−5000
−4000
−3000
−2000
time in sec.
torqueinNm
Fig. 10. Torque of DFIG for step change in reference torque after compensation
under unbalanced grid condition
5.9 6 6.1 6.2 6.3
−5500
−5000
−4500
−4000
−3500
−3000
−2500
time in sec.
torqueinNm
Fig. 11. Reduction of second harmonic pulsation in torque after compensation
VI. CONCLUSION
This paper presents a new direct torque control method for
DFIG based on polar control of rotor voltage. The control
scheme is simple and space vector modulation is used. The
stator current is nearly sinusoidal and there is a significant
reduction in torque ripple. The same direct torque control
method is explored to control DFIG under unbalanced grid
voltage condition. A torque angle control strategy based on
PI+R controller is proposed. Without using the rotating refer-
ence frame and sequential decomposition, the control scheme
reduces the pulsations in the torque. Simulation results show
the effectiveness of proposed control strategies.
TABLE I
DATA OF DFIG
Rated Power 2 MW
Stator Voltage 690 V
Stator Frequency 50 Hz
Stator to Rotor turns ratio 0.333
Stator Resistance, Rs 0.0025709 Ω
Rotor Resistance, Rr 0.0028802 Ω
Mutual Inductance 2.547 mH
Stator Leakage Inductance 0.07728 mH
Rotor Leakage Inductance 0.08335 mH
Number of Poles 4
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