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Analysis of the By-Pass Resistance of an Active
Crowbar for Doubly-Fed Induction Generator Based
Wind Turbines under Grid Faults
Wei Zhang, Peng Zhou, Yikang He,Senior Member, IEEECollege of Electrical Engineering, Zhejiang University, China
Email: [email protected], [email protected], [email protected]
Abstract-The doubly-fed induction generator (DFIG) based
wind turbines of today are often equipped with a crowbar, which
can be used to limit the inrush rotor current and protect the ac
excitation converter from damage via a set of resistors that are
connected to the rotor windings of the DFIG. When the rotor
current becomes too high due to the severe grid voltage dips on the
transmission line, the crowbar is activated and the rotor sideconverter is disconnected from the rotor windings at the same
time, which makes the DFIG behave as a squirrel cage induction
generator with increased rotor resistance. This paper analyzes the
influence of the crowbar resistors on the electrical behavior of the
DFIG during the grid voltage dips. Approximate expression of the
fault stator and rotor currents are deduced from mathematical
analysis and verified by simulation. Different crowbar by-pass
resistances and their impacts on the maximal fault currents and
electromagnetic torque are examined by simulations with different
parameter sets of the DFIG. Based on the simulation results, the
appropriate crowbar by-pass resistance can be effectively
predicted.
Index Terms-Crowbar, by-pass resistance, doubly fed induction
generator, wind turbine, grid voltage dip
I. INTRODUCTION
With the steadily increasing of wind turbines connected to the
grid, the interaction between large scale wind farms and the
regional power systems are becoming more and more
remarkable. As the penetration of wind power increases, wind
turbines are required to romaine connected during grid fault and
contribute to system stability, according to the recent grid codes
[1]. Since the doubly-fed induction generator (DFIG) has been
widely used in wind energy conversion, the low voltage ride
through (LVRT) technology of the DFIG has been investigated
extensively in recent times [2-12].
When the grid voltage dips occur, the power generated by the
DFIG can not be transmitted to the grid in time, which will
induce large fault currents in the stator and rotor windings.
Various improved control strategies have been proposed to deal
This work was supported by the National High Technology Research and
Development of China (the 863 Program Number: 2007AA05Z419) and the
National Natural Science Foundation of China (Project Number: 50577056).
with the inrush over-currents [2-3]. However, these methods
basically restrain the faulty rotor current at the expense of higher
rotor control voltage and, thus, the control capability is
restricted seriously by the limited capacity of the rotor side
converter (RSC). In case of severe grid voltage dips, the most
popular and reliable way to protect the RSC is to apply a
crowbar to short circuit the rotor windings and bypass the faultrotor current [4-9], as shown in Fig. 1.
Once the crowbar is activated, all of the IGBTs in the RSC are
turned off simultaneously, then the DFIG operates as an
asynchronous generator and the controllability over the DFIG
will get lost. At this condition, the resistance of the by-pass
resistors is of great importance on the dynamic behavior of the
DFIG. Several papers have discussed the crowbar resistance and
two main requirements are summarized [10-12]. Firstly, the
resistance should be high enough to limit the inrush rotor
current. Secondly, it should be sufficiently low to avoid high
voltage on the rotor terminals, which can result in the
breaking-down of isolation materials and the charging of dc bus
capacitor through the antiparallel diodes in the RSC. However,
some other factors should also be taken into consideration in
order to determine the appropriate crowbar resistance, such as
the maximum transient torque and the decaying speed of the
fault currents, which have not been investigated and published
in detail yet.
In order to determine the crowbar resistance, the transient
behavior of the DFIG during grid faults should be analyzed
firstly. Several papers have discussed the dynamic response of
the DFIG to grid voltage dips. A theoretical analysis of the
DFIG under voltage dips was proposed in [13]. But the focus of
the analysis was only on the transient rotor voltage, and the fault
currents were not detailedly investigated. The short circuitcurrent of the DFIG was discussed in [14], and the Laplace
transformation was applied to calculate the fault current.
However, the calculation was too complicate to be adopted.
Based on the transient equivalent circuit of the DFIG, reference
[15] proposed a simpler method to calculate the short circuit
current. But it is still hard to calculate the amplitude of the fault
current because of the many unknown parameters in the
expression of the current. In [11], the approximate equations for
the maximum short circuit currents were determined and
compared with the simulated results. Moreover, the crowbar
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B. Faulty Stator and Rotor Currents
In this section, the approximate equations of the faulty stator
and rotor currents are deduced. Some assumptions are made
primarily in order to simplify the analysis.
The assumptions are: firstly, the DFIG rotor is short circuited
by the crowbar as soon as the dip occurs. Secondly, the DFIG is
rotating at the synchronous speed s when the dip occurs.
Thirdly, the DFIG is producing the rated active power before thedip occurs. Finally, the three phase grid voltage drops to zero, i.e.
p=0.
Substituting (4) and (5) into (3), the faulty stator current can
be obtained as [11]
' '/ ( ) /0( ) [ ]s s rt T j t t T ss
t e e eL
=
I (6)
where L is the sum of stator and rotor leakage inductances, i.e.
s rL L L = + , and'
s sT L R= ,
'
r rT L R= . And s0 is the
initial value of the stator flux after the dip occurs, which can be
expressed as0 0
( )s s s
t j= U .
According to (3), since the magnetizing inductance of the
DFIG is much bigger than the leakage inductances, the stator
and rotor current vectors possess approximately the same
amplitude and opposite direction. Based on (6), the maximal
faulty stator and rotor currents can be calculated as
max max
2 ss r
s
UI I
L = (7)
The amplitude of the simulated fault rotor current is shown in
Fig. 4. DFIG 1 is used in this simulation and its parameters are
tabulated in the appendix. As the total leakage inductance
L=0.327, the maximal rotor current calculated from (7) is about6pu, which is highly close to the simulated result.
When the crowbar is applied, the equivalent circuit of the
DFIG can be drawn as in Fig. 5.
Assuming that the by-pass resistance Rcrow is much bigger
than the stator and rotor resistance, the stator and rotor side
equivalent impedance can be calculated as
2
( )
( )
m s crows
s crow
r crow
s L L sL RZ s
sL R
Z s sL R
+=
+
= +
(8)
According to (8), the stator and rotor transient time constants
are derived as
2 2' 1
2
1
'
( )
crow ss
s crow
r crow
R L LT
L L R
T L R
+=
=
(9)
Substituting (8) and (9) into (6) and (6) becomes
'
'/
/0 0( ) ( )s
s r
t Tj t t Ts s rdc
s r
s crow
j et t e e
j L R L
=
I I (10)
(
)
rI
pu
( )t s0 0.05 0.1 0.15 0.2
0
1
2
3
4
5
6
Rcrow=0
Rcrow=0.2 pu
Rcrow=0.5 pu
Rcrow=1 pu
Rcrow=2 pu
Fig. 4. The amplitude of the faulty rotor current with different crowbar
resistances applied
sR sL rLsI rR
mL
rI
s rsd
dt
crowR
sZ rZ
Fig. 5. Equivalent circuit of the DFIG after the crowbar applied
AsRcrowgrows bigger, Trwill become smaller than T
s, which
means that the second term on the right hand side of (10)
attenuates faster than the first one, as shown in Fig. 4 when
Rcrow=0.2pu. Therefore, the faulty stator and rotor currents are
primarily determined by the first term in (10), so that the
maximal faulty current can be deduced as
2 2
max max ( )s r s s crowI I U L R = + (11)
The maximal faulty rotor current obtained from simulationand (11) are shown in Fig. 6. As can be seen, the simulated
results are highly close to the calculated ones for crowbar
resistance above a certain value (about 0.5pu). When Rcrow is
relatively small, the errors between the simulated and calculated
results come from rdc0, which has been ignored in (11).
max
(
)
rI
p
u
( )crowR pu0 0.5 1 1.5 2 2.5 3
0
1
2
3
4
5
6
Calculated Results by (11)
Rotor speed 0.7 pu
Rotor speed 1 pu
Rotor speed 1.3 pu+
Simulated Results
Calculated Results by (12)
Fig. 6. The maximal fault rotor current versus the crowbar resistance
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C. Factors that Affect the Faulty Currents
In section B, some important assumptions are made so as to
simplify the transient state analysis of the DFIG. However, these
assumptions are not always valid for a wind turbine driven
DFIG. So that some factors should be taken into account in order
to make the analytical results more veracious.
Firstly, the rotor speed r at the instant of voltage dip is
examined. Generally, the rotor speed of a DFIG is within therange of 0.3pu around the synchronous speed. Based on the
simulation results, it is found that the higher the rotor speed is,
the bigger the maximal faulty currents are. The relationship
between rand the maximal faulty currents can be expressed as
max max 2 2( )
srs r
s r crow
UI I
L R
=
+
(12)
Fig. 6 shows the maximum fault rotor current obtained from
simulation and calculating by using (12). As can be seen, these
two results agree with each other very well when Rcrow is big
enough.
Secondly, the pre-fault operation condition of the DFIG isconsidered. During the above analysis, it is assumed that the
DFIG produces the rated active power and zero reactive power
before the dip occurs. When this operation condition changes,
the dc rotor flux rdc0, rather than the forced rotor flux rf0, will
change accordingly. However, the impact of rdc0 can be
neglected ifRcrowis big enough, so that the pre-fault operation
condition does not play an important role in the DFIG transient
behavior during the dip when the crowbar is applied.
Finally, if the voltage does not drop to zero, the case will
become more complicated. Besides the attenuated dc flux, there
will be non-attenuated ac component in the stator flux [16], as
expressed in (4). As a result, the faulty currents can likewise beseparated into attenuated and non-attenuated components, and
the amplitude of the faulty currents can be expressed as
'/
2 2[(1 ) cos( )]
( )
st Tsrs r s
s r crow
UI I p e p t
L R
= + +
+
(13)
where is the angle related to the pre-fault operation condition
of the DFIG.
Fig. 7 shows the amplitude of the simulated faulty rotor
current when the rotor speed is fixed at 1.3pu. It is clearly shown
that when the grid voltage does not drop to zero, there will be a
non-attenuated component with the frequency of 50Hz existingin the faulty current, which is induced by the remaining grid
voltage after the dip. As p grows bigger, the maximal faulty
current will become smaller, which means that the largest faulty
current will appear when a short circuit occurs right at the
terminals of the DFIG.
III. SELECTION OF THE CROWBAR BY-PASS RESISTANCE
A. Appropriate Value of the Crowbar Resistance
As mentioned in the introduction, the by-pass resistance of the
crowbar should be high enough to limit the fault currents and
low enough to avoid over-voltages on the rotor terminals. Based
on these two considerations, an appropriate range of the crowbar
resistance can be acquired.
Firstly, the fault currents should be limited in a safe range.
Based on the analysis of last section, the largest faulty current
will appear when the grid voltage drops to zero and the pre-fault
rotor speed is the highest, i.e. 1.3pu. According to (12), thefollowing expression can be described
2 2( )
srsafe
s r crow
UI
L R