1
Effect of Neglecting Stator Transients in Doubly
Fed Induction Generators Models
Pablo Ledesma, Member, IEEE, Julio Usaola, Member, IEEE,
Universidad Carlos III de Madrid
Butarque 15, 28911 Leganés, Madrid, Spain
encoder
Abstract— This paper studies the effect of neglecting stator
transients in doubly fed induction generators. The simulated
cases involve two extreme operation points: one at subsynchronous speed, and one at supersynchronous speed. A shortcircuit fault is applied at the generator terminals. The evolution
of different variables is examined using two different models:
one of them accounts for the stator transients and the other one
neglects them.
inverter
rotor
current
rotor
position
I. I NTRODUCTION
II. S IMULATED CASES
The simulated cases involve two extreme operation points:
one at subsynchronous speed, where rotor speed is 90% of
the nominal speed, and one at supersynchronous speed, where
rotor speed is 110% of the nominal speed.
Fig. 1 shows the simulated system. The inverter imposes a
sinusoidal current on the rotor winding. Following a vectororiented scheme, the rotor current is divided in two components:
is in phase with the stator flux linkage and provides
1)
machine excitation.
2)
is in quadrature with the stator flux linkage and
controls electromagnetic torque.
A short-circuit fault is applied at the generator terminals
at time t=0, and cleared after time t=100ms. Two different
models are compared:
A fifth-order model, which includes stator transients and
whose state variables are the two components of the stator
Fig. 1.
Simulated system
flux linkage, the two components of the rotor flux linkage
and the rotor speed.
A third-order model, which neglects the stator transients,
and whose state variables are the two components of the
rotor flux linkage and the rotor speed.
III. S IMULATION RESULTS
A. Generator Working at Subsynchronous Speed
Fig. 2 shows the evolution of the stator current in d-q axis. A
similar discussion to that applied in synchronous generators [1,
sec. 5.1.1] is applicable. When stator transients are neglected,
only the fundamental frequency, smooth components appear.
including stator transients
10
(p.u.)
Neglection of the flux linkage derivatives in the stator equations, is a common issue in transient stability studies involving
synchronous machines [1] and induction machines [2] [3].
Among the advantages of this simplification are a reduced
order model, an easy interface with the grid model, and longer
integration steps.
Nowadays, the increase in the number of windmills with
doubly fed induction generators (DFIGs) in several power
systems, has lead to the development of models of these
generators which also neglect the stator electromagnetic transients [4].
The simplification seems accurate when the DFIG works
close to synchronous speed, because the rotor current frequency is close to zero and the DFIG operation point is similar
to that of a synchronous generator. This paper studies the effect
of neglecting stator transients when the DFIG works at speeds
which are different from the synchronous speed.
stator voltage
and current
current
control
neglecting stator transients
5
0
-5
-10
-0.02
Fig. 2.
0
0.02
0.04
0.06
time (s)
0.08
0.1
0.12
0.14
Subsynchronous operation: effect on stator current
The effect on electromagnetic torque is shown in fig. 3.
When the stator transients are neglected, only a fundamental
frequency close to zero appears. When the stator transients are
accounted, a sinusoidal component appears in the torque. The
medium torque is slightly greater when the stator transients
are included. This is due to two reasons:
2
1.14
1) The losses in the rotor resistance are greater due to the
fundamental frequency currents induced in the rotor.
2) The first torque oscillation is positive.
including stator transients
neglecting stator transients
1.125
1.12
1.115
1.11
4
1.105
including stator transients
2
1.1
neglecting stator transients
1.095
0
0
Fig. 6.
-4
-0.02
Fig. 3.
0
0.02
0.04
0.06
time (s)
0.08
0.1
0.12
0.3
0.4
time (s)
0.5
0.6
0.7
Supersynchronous operation: effect on rotor speed
1
Subsynchronous operation: effect on electromagnetic torque
0.8
0.6
0.4
including stator transients
neglecting stator transients
0.2
0.92
including stator transients
0.915
0
neglecting stator transients
0
0.91
rotor speed (p.u.)
0.2
0.14
Both effects act in the sense of reducing rotor speed. As a
result, speed increase after the fault is slightly greater when
the stator transients are neglected, as shown in fig. 4.
0.05
0.1
0.15
0.2
time (s)
0.25
0.3
0.35
0.4
0.905
Fig. 7.
0.9
Supersynchronous operation: effect on stator voltage
0.895
0.89
IV. C ONCLUSION
0.885
The studied simulations show that the arguments applied to
the effect of the stator transients on the synchronous generator
model are also applicable to the DFIG model.
Stator transients in the DFIG model are negligible because
The results are very similar from the transient stability
point of view.
Attending to the DFIG rotor speed, the results are more
conservative.
0.88
0
Fig. 4.
0.1
0.2
time (s)
0.3
0.4
0.5
Subsynchronous operation: effect on rotor speed
Attending to stator voltage oscillations, and excluding the
initial oscillations due to the stator transients, the results are
similar with both models, as shown in fig. 5
ACKNOWLEDGMENT
1.2
The authors would like to thank José Román Wilhelmi
for his help in searching bibliography about the induction
machine.
1
stator voltage (p.u.)
0.1
-2
stator voltage (p.u.)
electromagnetic torque (p.u.)
1.13
rotor speed (p.u.)
8
6
1.135
0.8
0.6
R EFERENCES
0.4
including stator transients
0.2
neglecting stator transients
0
0
Fig. 5.
0.05
0.1
0.15
0.2
time (s)
0.25
0.3
0.35
0.4
Subsynchronous operation: effect on stator voltage
B. Generator Working at Supersynchronous Speed
Figs. 6 and 7 show the evolution of rotor speed and
stator voltage when the DFIG is operated at 110% of the
synchronous speed. The same discussion applied to the subsynchronous operation is applicable to this case.
[1] P. Kundur, Power System Stability and Control. California: McGrawHill, 1994.
[2] T. Skvarenina and P. Krause, “Accuracy of a reduced order model of
induction machines in dynamic stability studies,” IEEE Transactions
on Power Apparatus and Systems, vol. PAS-98, no. 4, pp. 1192–1197,
July/Aug 1979.
[3] N. A. Khalil, O. T. Tan, and I. U. Baran, “Reduced order models for
double-cage induction motors,” IEEE Transactions on Power Apparatus
and Systems, vol. PAS-101, no. 9, pp. 3135–3140, September 1982.
[4] A. Feijóo, J. Cidrás, and C. Carrillo, “A third order model for the doublyfed induction machine,” Electric Power Systems Research, vol. 56, pp.
121–127, 2000.