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Transient Stability Improvement Using
Non-superconducting Fault Current Limiter
M. Tarafdar Hagh, M. Jafari, S. B. Naderi
Faculty of Electrical and Computer Engineering, University of Tabriz,
Tabriz, Iran
Emails: [email protected], [email protected], [email protected]
Abstract-In this paper, transient stability of Single Machine
Infinite Bus (SMIB) system with a Non-superconducting Fault
Current Limiter (NSFCL) is proposed. Analytic analysis of
system stability is discussed in detail and as result, optimal value
of NSFCL resistance during fault that leads to effective
improvement of stability is calculated. Equal area criterion is
used for this calculation.
Study system is simulated by
EMTDC/PSCAD to verify the effectiveness of the optimal
resistor value of the proposed NSFCL.
I.
INTRODUCTION
As electric power systems grow and become more
interconnected, at some points, the available fault currents
level may exceed the maximum short-circuit ratings of the
switchgear. Traditionally, to alleviate the cost of switchgear
and bus replacements, the most common ways to limit highlevel fault currents are: up rating of switchgear and other
equipment, splitting the power grid and introducing higher
voltage connections (AC or DC), using current-limiting fuses
or series reactors or high-impedance transformers, and using
complex strategies like sequential network tripping [1].
A novel idea to limit the fault currents and prevent up
grading of the switchgears is usage of FCLs.
The
implementation of FCLs in electric power systems is not
restricted to suppress the amplitudes of the short circuits; they
are also utilized to variety of performances such as the power
system transient stability enhancement, power quality
improvement, reliability improvement, increasing transfer
capacity of system equipment, and inrush current limitation in
transformers [2]-[5].
Recent studies on system applications of FCLs are done on
superconducting types FCLs, mostly. At stability issues, they
are discussing on Resistive type SFCL (RSFCL) and its effect
on transient stability of system, in general [6]-[11]. RSFCL is
capable of consuming the excessive accelerating generator
power, increasing the stability-limit of the system and then
enlarging the stability-region after the short circuit.
In some papers, optimum value for resistor of
superconductor at fault interval which leads to best
improvement of stability is discussed [8], [11]. They try to
make a RSFCL that has optimal resistor value at fault
condition. But there are two problems. Firstly, because of
high technology and cost of superconductors, these devices
are not commercially available, unfortunately. Especially in
third world countries, design, manufacture and operation costs
providing is impossible approximately. Secondly, resistance
that RSFCL shows at fault condition is not constant during the
fault due to its quenching characteristics [8]. So, it is not
possible to equate RSFCL’s resistance to calculated optimal
value.
In this paper, a topology of non-superconducting FCL is
introduced and its effect on transient stability of power system
is studied. Analytic analysis of stability for pre-fault and
during fault conditions is presented in detail. Equal area
criterion is used to calculate the optimum value of resistance
which leads to maximum critical load angle. Simulation
results are performed by EMTDC/PSCAD and analytic
analysis is presented..
II. POWER CIRCUIT TOPOLOGY OF NSFCL AND ITS
OPERATION
Fig. 1 shows the three phase topology of proposed NSFCL.
This circuit is composed of four main parts that are described
as follows.
1) Three sets of single phase transformers, utilized as
power isolation transformer, are connected to a threephase diode bridge rectifier. The three phase diode
bridge is called “isolation transformer rectifier”.
2) A non-superconductor (copper coil) magnet that is
modeled by a resistor ( rd ) and an inductor ( Ldc ).
Figure. 1. Three phase topology of proposed NSFCL
3)
4)
A parallel connection of a resistor ( R ) and a
semiconductor switch (IGBT) that are connected in
series with the dc reactor.
A dc voltage source ( Vdc ) used to compensate the
voltage drop that take place in both dc reactor
resistance and semiconductor devices. So, it equals
to [12]:
Vdc  2VDF  VSW  rd I dc
III. TRANSIENT STABILITY STUDY ON POWER SYSTEM WITH
NSFCL
Fig. 2 shows single line view of power system with
proposed NSFCL. In the pre-fault condition, transfer power
can be expressed by:
EV
sin  0
X
Ig 
(1)
Where VSW stands for the voltage drop across IGBT and the
forward voltage drop across rectifier diodes is defined as VDF .
In normal operation of utility, the semiconductor switch is
closed and the resistor is bypassed. By choosing appropriate
value for Ldc , it is possible to achieve an almost dc current
through the dc reactor. By compensating voltage drop on
semiconductor devices and natural resistance of dc reactor,
voltage drop on NSFCL becomes almost zero and
consequently it does not affect normal operation of system.
As fault occurs, the current of dc reactor starts to charge.
When its current reach to a pre-defined value, control system
operates and turns off the IGBT. So, R enters to the current
path and limits the fault current. After removal of the fault,
IGBT turns on and FCL returns to pre-fault condition.
By selecting proper value for RFCL , ac (Resistance that
NSFCL shows in fault condition at ac side of rectifier bridge),
power system will have maximum transient stability at fault
situations.
Value of RFCL , ac is proportional to value of R . It is
important to note that, value of Ldc doesn’t effect the
impedance of NSFCL.
P
resistor must be entered to line during fault. In addition, at
fault condition, mechanical power ( Pm ) is assumed constant.
Fig. 3 shows the equivalent circuit at fault state by using
NSFCL, after applying star to delta transformation in Fig. 2.
Output current of generator, I g , is calculated by:
E 
E   V 0

Zb  2
Z a 1
Z a  RFCL,ac  j ( X   X L ) 
Zb  RFCL,ac  jX   Z f 
( RFCL,ac  jX ) jX L
Zf
Z f ( RFCL,ac  jX )
X   X d  X t
jX L
(4)
(5)
(6)
Where Z f and X d are fault impedance and unsaturated
transient respectively. Electrical power of system ( Pf ) can be
expressed by:
Pf  real ( I g  E  )
Pf 
2
(7)
2
E
E
EV
cos  2 
cos 1 
cos(  1 )
Zb
Za
Za
(8)
Equation (8) is sum of transfer power and consumed power
of NSFCL resistance. In worst condition (three phase fault),
Z f , is equal to zero, approximately. In this state and
considering (4) and (5), Z a is infinite and Z b is equal to
RFCL ,ac  jX  . So, electrical power can be defined as follow:
Pf 
E2
cos  2
Zb
(9)
Equation (9) depends on RFCL , ac , in fact, value of RFCL , ac
must be chosen in a way that critical load angle be maximum.
In next section, optimum RFCL , ac is achieved and analytical
analyses are explained in detail.
(2)
Where:
E : RMS line to line synchronous generator voltage
V : RMS line to line infinite bus voltage
X : Total reactance ( X t  X d  X t  X L )
X d : Unsaturated reactance of generator
X t : Transformer reactance
X L : Line reactance
 0 : Load angle
As a fault occurs at point F, without NSFCL, transfer power
is reduced (depends on fault type).
In this state, if a consumer of active power doesn’t exist
between generator and point F, Synchronous generator will be
unstable probability.
That means, even, using SFCL
(Inductive type) can not ensure stability of generator. So, a
(3)
Figure 2. Single line view of power system
Figure 3. The equivalent circuit after transformation
IV. OPTIMAL RESISTOR CALCULATION USING EQUAL AREA
CRITERION
By using (2) and (9), power-angle curve is plotted in Fig. 4.
Region A1 and A2 are accelerating and de-accelerating
regions, respectively. Applying the equal area criterion to the
power-angle curve gives the critical load angle (  c ), which is
the boundary point to make the system remain stable.
To calculate  c , (10) can be used:
c
u
0
c
 ( Pm  Pf )d 
 ( P  Pm )d
(10)
To obtain the relation between RFCL , ac and RFCL , dc , ac and
dc sides active power ( PFCL,ac and PFCL,dc , respectively)
must be considered equal. So:
PFCL, ac  PFCL,dc
2

6

 Vm



  sin( 3 )Vm 
2

3

RFCL,ac
RFCL,dc
(13)
2
(14)
Where, Vm is the peak of isolation transformer secondary
voltage.
As result:
Consequently:
R
E2
EV
Pm (  2 0 ) 
( c   0 ) cos  2 
(cos  c  cos  0 )  0 (11)
X  XL
X 2  R 2
To achieved maximum  c , from (11), derivative is taken
respect to RFCL , ac . In this case, optimum RFCL , ac which leads
to maximum  c , can be expressed by:
RFCL ,ac  X   X d  X t
(12)
Fig. 5 shows variation of  c corresponding to RFCL , ac . It is
obvious that for RFCL, ac  0.602 pu , maximum value for  c is
obtained. In other word, this RFCL , ac is the best value for
enhancement of stability region of power system.
The resistance that NSFCL shows at fault condition
( RFCL , ac ) is not equal to numerical value of dc side resistor of
diode rectifier bridge ( RFCL , dc ). Therefore, value of RFCL , dc
should be calculated according to optimum RFCL , ac value.
Power

 RFCL ,ac

(15)

  0.602  1.098 pu

(16)
FCL , dc 
 18
 2

Then:
R
FCL , dc 
 18
 2

It should be noticed that RFCL , dc is equal to R  rd . Since
rd is negligible respect to R , RFCL , dc is equal to R ,
approximately.
V. SIMULATION RESULTS
The power circuit topology of Fig. 2 is used for simulation
in fault condition. The simulation parameters are as follows:
Generator data:
Sbase  18.26kVA , E  200V (rms , L  L) , f  50Hz
X d  1.227 pu , X d  0.394 pu
And number of generator poles is 4.
System parameters:
A2
Pm
X t  0.208 pu , X L  0.23 pu
V  210V (rms, L  L)
A1
Pf
0
δ0
0
δc
Load angle
δu
Figure 4. Power-angle curve during steady state and fault condition
FCL parameters:
R  1.098pu  2.4 , rd  0.1 , Ldc  150 mH ,
VDF  VSW  3V
2.5
Critical delta (rad)
2.17651
2
1.5
1
0.5
0
0.01
0.41
0.602
0.81
1.21
1.61
2.01
2.41
2.81
R (pu)
Figure 5. Variation of  c corresponding to RFCL ,ac
Fault occurs at 6 (sec) and continues until 0.16 (sec) (8
cycles of power frequency).
As fault occurs, without using FCL, the fault current
increases extremely and generator becomes unstable. But, by
using proposed NSFCL, fault current is limited properly and
generator became stable.
Fig. 6 shows the generator current with and without using
proposed FCL.
VI. CONCLUSIONS
Generator current, phase a (kA)
0.4
This paper presented a new power circuit topology for
improvement of transient stability by using nonsuperconducting FCL. Analytic analyses are performed for
pre-fault and during fault conditions and optimal resistance of
NSFCL that leads to the best stability improvement is
calculated. Setting the optimal value for resistance of FCL in
this topology is simpler respect to superconductor types.
Simulations are performed in EMTDC/PSCAD for several
values of resistor to show the accuracy of analysis. So, this
NSFCL with optimum resistor can improve transient stability
of system, as well as good fault current limitation. In addition,
there is no need to high technology and costs of
superconductor in proposed FCL.
0.2
0
5.8
6.3
6.8
7.3
6.8
7.3
Fault interval
-0.2
-0.4
Time (s)
(a)
0.15
Current (kA)
0.1
0.05
0
5.8
6.3
REFERENCES
-0.05
-0.1
[1]
-0.15
Time (s)
[2]
(b)
Figure 6. (a) Generator current without NSFCL (b) Generator current with
NSFCL (──) and dc reactor current (▬▬)
Fig. 7 shows the rotor speed response of generator after
fault. Note that the NSFCL with an optimal R value of
1.098p.u. has the best damping performance for oscillations
when compared to that by the NSFCL with other R values
such as 0.5, 2 (p.u.) and the case without NSFCL.
Consumed power of NSFCL resistor ( PFCL,dc ) for three
values of R (0.5, 1.098 and 2(p.u.)) are shown in Fig. 8. As it
can be seen, for optimum value of R , consumed power of
NSFCL resistor is near to pre-fault electrical power. In other
words, accelerating area and consequently, rotor speed
oscillation are minimized.
[3]
[4]
[5]
[6]
[7]
1530
Rotor speed (rpm)
1520
[8]
1510
1500
[9]
1490
1480
1470
5.8
6.3
6.8
7.3
7.8
8.3
8.8
9.3
9.8
[10]
Time (s)
Without NSFCL
with R=0.5pu
with R=1.098pu
with R=2pu
[11]
Figure 7. Rotor speed
[12]
0.03
PFCL,dc (MW)
Fault interval
Pre fault electrical power=18.12kW
0.02
0.01
0
5.99
6.03
6.07
6.11
6.15
Time (s)
R=0.5pu
R=1.098pu
R=2pu
Figure 8. Consumed power of NSFCL resistor
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