Download Power System Stabilization by Fault Current Limiter and Thyristor

Power System Stabilization by
Fault Current Limiter and Thyristor Controlled Braking Resistor
Masaki Yagami
Junji Tamura
Member, IEEE
Hokkaido Institute of Technology
7-15 Maeda, Teine-ku,
Sapporo-shi, 006-8585, Japan
[email protected]
Senior Member, IEEE
Kitami Institute of Technology
165 koen-cho,
Kitami-shi, 090-8507, Japan
[email protected]
Abstract -- This paper presents a power system stability
enhancement scheme using combination of fault current limiter
and thyristor controlled braking resistor. The fault current
limiter operates for limiting of fault currents, enhancement of
the power system stability and suppression of turbine shaft
torsional oscillations. After that, the thyristor controlled
braking resistor operates with the objective of fast control of
generator disturbances. The effectiveness of both devices has
been demonstrated by considering 3LG (three-lines-to-ground)
fault in a two-machine infinite bus system. Also, temperature
rise effect of both devices has been demonstrated. Simulation
results indicate a significant power system stability
enhancement and damping turbine shaft torsional oscillations as
well as with allowable temperature rise.
system enhancement scheme using combination of FCL and
TCBR for the purpose of a significant power system stability
enhancement and damping turbine shaft torsional oscillations.
If both devices-FCL and TCBR operate at the same bus, the
stabilization control scheme can be carried out continuously
and with flexibility. Namely, FCL operates from the fault
occurrence instance to the fault clearing, and then TCBR
operates dynamically until the generator disturbance becomes
small. Through the simulation analysis, the effectiveness of
combination of FCL and TCBR on power system stability
enhancement is demonstrated.
Moreover, this paper presents the results of analyses about
temperature rise effect of resistance materials of both devices.
FCL and TCBR dissipate accelerating energy of the generator
in the form of heat. Therefore, temperature of the resistor
material rises above ambient temperature. In particular,
TCBR may become high-temperature state because it
operates for a long duration. Higher temperature may cause
the resistor material to melt away and due to higher resistance
value, the system response may be somewhat affected. In
order to confirm the temperature rise effect, both devices
with various resistance values are tested in the simulation.
These analyses are performed using EMTP.
Index Terms—Power system stability, Fault current limiter,
Thyristor controlled braking resistor, Temperature rise effect
I.
INTRODUCTION
The use of fault current limiter (FCL) is being evaluated as
one element necessary to limit the fault currents and enhance
the power system stability [1]-[3]. FCL is a device that limits
the fault currents by generating an impedance when a fault
occurs. In addition, the limiting impedance generated to limit
fault currents proves helpful in increasing generator output
degraded by a fault, thus providing stabilization of power
system. However, as FCL installed in series with
transmission line can be just operated during the period from
fault occurrence to fault clearing, FCL cannot control the
generator disturbances after the clearing of fault.
The braking resistor is also known as a very effective
device for power system stability control. Besides, with the
recent development of power electronics technology,
replacing the circuit breaker with the semiconductor device is
becoming feasible. Several thyristor-based control techniques
have been proposed in the literature for the switching of
braking resistor [4]-[6]. Since the thyristor controlled braking
resistor (TCBR) can control an accelerating power in
generator with flexibility, the power system stability may be
enhanced more than that of the use of braking resistor
controlled by mechanical device. However, as TCBR is
installed in parallel with the transmission line, TCBR cannot
be operated before the clearing of faults.
From these viewpoints, we have proposed the power
978-1-4244-2893-9/09/$25.00 ©2009 IEEE
II.
MODEL SYSTEM
A.
Power system
The two-machine infinite bus system model used for the
simulation is shown in Fig. 1. It consists of two generators,
an infinite bus, transformers, FCL, TCBR and double-circuit
transmission lines. The line constants in the diagram are
given in terms of R + jX (jB/2) per circuit. Turbine shaft
model has six masses namely high-pressure (HP) turbine, an
intermediate-pressure (IP) turbine, two low-pressure turbines
(LPA, LPB), the generator (GEN) and exciter (EXC) as
shown in diagram. Table I and Table II show the generator
parameters [7] and turbine shaft parameters [8] respectively.
The models of AVR and governor are shown in Fig. 2.
FCL is installed on Y-side of the transformer, Tr.1. In
general, FCL should be installed wherever fault current is
extremely strong. However, FCL is installed only at the
generator terminal because this study is focused mainly on
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(P/Q=1.0/0.35)
(P/Q=1.9/0.1)
RFCL
0.017+j0.144
(j0.0373)
j0.0625
0.0238+j0.2016
(j0.0523)
j0.0586
(P/V=1.2/1.02)
G1
G2
FCL
Tr.1
Tr.2
Δω
PI
0.064+j0.322
(j0.0765)
3LG
0.078+j0.340
(j0.0895)
RTCBR
TCBR
0.020+j0.170
(j0.044)
0.034+j0.184
(j0.0395)
(P/Q=
1.25/0.5)
*Unit is pu value on system base (100 MVA)
Fig. 1.
(pu)
(pu)
(pu)
(pu)
(pu)
(pu)
(pu)
0.003
0.102
1.651
1.59
0.232
0.38
0.171
G2
ra
Xl
Xd
Xq
X’d
X’q
X’’d
(pu)
(pu)
(pu)
(pu)
(pu)
(pu)
(pu)
0.004
0.078
1.22
1.16
0.174
0.25
0.134
200
(pu)
(pu)
(sec)
(sec)
(sec)
(sec)
(sec)
0.171
0.13
5.9
0.535
0.033
0.078
9.0
Rating (MVA)
130
(pu)
(pu)
(sec)
(sec)
(sec)
(sec)
(sec)
0.134
0.13
8.97
1.5
0.033
0.141
6.0
X’’q
X0
T’d0
T’q0
T’’d0
T’’q0
H
X’’q
X0
T’d0
T’q0
T’’d0
T’’q0
H
TABLE II
TURBINE SHAFT PARAMETERS
G1
HP Turbine
LP Turbine
LPA Turbine
LPB Turbine
Generator
Exciter
G2
HP Turbine
LP Turbine
LPA Turbine
LPB Turbine
Generator
Exciter
Inertia constant (s)
0.288890
0.483849
2.670287
2.749726
2.700840
0.106406
Inertia constant (s)
0.192593
0.322566
1.780191
1.833151
1.800560
0.070937
Spring constant (pu T/rad)
19.303
34.929
52.038
70.858
2.82
IP
LPA
LPB
GEN
EXC
High-Pressure Turbine
Intermediate-Pressure Turbine
Low-Pressure Turbine
Generator
Exciter
Power system model
Vso
Rating (MVA)
HP
HP:
IP:
LPA, LPB:
GEN:
EXC:
Infinite bus
TABLE I
GENERATOR PARAMETERS
G1
(P/Q=
0.9/0.3)
j0.0576
Tr.3
1.04 ∠ 0 .0 
ra
Xl
Xd
Xq
X’d
X’q
X’’d
Turbine Shaft System
Rout
(α )
-
Vs
+
Efdo
25
1+0.2S
4.0
+ +
Efd
-4.0
(a) AVR
ωm0
ωm
-
+
Po
20
1+2.0S
(b) Governor
Fig. 2.
1.05
+ +
P
0.0
AVR and governor models
the stabilization of the generator. Commutation-type FCL
which consists of a shunt resistor with RFCL value and a
variable resistor is used.
TCBR is installed in parallel at the same bus. Resistor
with RTCBR value is connected to the grid through the thyristor
switching circuit. Thyristor switch is controlled by firingangle α which is calculated based on the generator speed
deviation Δω .
In the simulation study, it has been considered that the
three-lines-to-ground (3LG) fault occurs near the generator
G1 at 0.1 (sec). The circuit breakers on the faulted line are
opened at 0.2 (sec) and reclosed at 1.0 (sec). It is assumed
that the circuit breakers clear the line when the current
through it crosses the zero level.
B.
Spring constant (pu T/rad)
19.303
34.929
52.038
70.858
2.82
FCL
Commutation-type FCL which consists of the shunt
resistor with RFCL value and the variable resistor is used. The
value of the variable resistor is 0 (pu) during a normal
condition. When the fault currents exceed a critical value
which is set to 2.5 (pu), the resistance value of the variable
resistor increases linearly to 25 (pu) within 1 (ms) (such a
characteristic can be achieved by a superconducting coil [9]).
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Therefore, majority of the current flows into the shunt
resistor, and then limited. To avoid an excess load, we have
assumed that the resistance value of the variable resistor
returns to 0 (pu) at the same time when the circuit breakers
are opened at 0.2 (sec).
TCBR
As shown in Fig. 1, the generator speed deviation Δω
and the desired resistance value Rout are selected as the
signals of input and output respectively. Following a fault in
the power system, Δω of the generator is measured, and
then Rout is determined by PI controller device which is
tuned by trial and error method. Firing-angle α for the
thyristor switch is calculated from the output of the PI
controller (i.e., Rout ). The desired power consumption
determined by Rout and the real power consumption
determined by RTCBR are equal and hence α can be
calculated from this relationship. When Δω becomes less
than 0.001 (pu), TCBR is removed from the grid.
temperature coefficient (0.0012°C-1 [13]).
TABLE III
RESISTOR MATERIAL PARAMETERS OF BOTH DEVICES
specific heat
mass
heat exchange coefficient
surface area
C.
D.
Resistor Material
In this work, we have used an austenitic stainless steel
[10] as resistor materials of both devices. For simplicity, the
same values of material parameters (i.e., mass, surface area,
heat exchange coefficient and specific heat) are used for both
devices. The material parameters are shown in Table III.
When a current, I, flows into the resistor (i.e., the device is
in ‘ON’ condition), temperature of the resistor can be
calculated from the following equation [12]:
C
M
K
S
520 (J/(kg·°C)) [11]
300 (kg)
16.5 (W/(m2·°C)) [11]
8 (m2)
III. SIMULATION RESULTS
A.
Power system stability
Fig. 3 shows the load angle responses of each generator
in cases of “no devices”, “only FCL with RFCL=1.1 (pu)”,
“only TCBR with RTCBR=0.6 (pu)” and “both devices-FCL
and TCBR with RFCL=1.1 (pu) and RTCBR=2.5 (pu)”. Because
of the absorption of real power by FCL and TCBR, the load
angle oscillations are restrained in the case of “with devices”.
In particular, the load angle oscillations in the case of “both
devices” are restrained effectively for the overall duration of
simulation. In “both devices”, FCL dissipates majority of the
accelerating energy of the generator, and then TCBR
dissipates the accelerating energy of the remainder. As a
result, the use of both devices makes the system stabile
quickly more than the use of “one-unit”.
100
2
RI tON
CM + KS
(1)
where R is resistance of the resistor, tON is ‘ON’ duration time
of the device and TON0 is initial temperature of the resistor.
On the other hand, when the device is not in the circuit
(i.e., the device is in ‘OFF’ condition), it gets cooled down
by dissipating heat into the air. Therefore, temperature of the
resistor decreases exponentially. The temperature decrease
can be calculated from the following Newton’s law of
cooling:
TOFF = Ta + ( TOFF 0 − Ta ) e − nt
OFF
60
N o d e v ic e s
FC L
TCBR
FCL & TCBR
40
20
0
1
2
3
4
5
6
7
T im e (s )
(a) G1
(2)
where TOFF is temperature of the resistor in ‘OFF’ condition,
Ta is ambient temperature (20 °C), TOFF0 is initial temperature
of the resistor, n is positive constant (0.01 for this work) and
tOFF is ‘OFF’ duration time of the device.
When temperature of the resistor changes, resistance value
of the resistor also changes according to the following
equation [13]:
R = R0 { 1 + γ ( TON / OFF − Ta ) }
Load angle (deg)
80
100
N o d e v ic e s
FCL
TCBR
FCL & TCBR
80
Load angle (deg)
TON = TON 0 +
(3)
60
40
20
0
1
2
3
4
5
6
T im e ( s )
where R is resistance after the temperature change, R0 is
initial resistance in the ambient temperature, γ is
(b) G2
Fig. 3.
Load angles of each generator
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7
Fig. 4 shows the firing-angle responses of the thyristor
switch for phase ‘a’ in the cases of “only TCBR” and “both
devices”. The firing-angle α varies from 0 to 180 (deg)
according to the value of Δω . When Δω becomes less
than 0.001 (pu), α is compulsorily set to 180 (deg) (i.e.,
TCBR is removed from the grid). As can be seen in Fig. 4(a),
α in the case of “only TCBR” varies until about 2.7 (sec).
On the other hand, α in the case of “both devices” has a
constant value of 180 (deg) from the early time. This is
because majority of the accelerating energy are dissipated by
FCL before TCBR operates. This indicates that the
temperature rise of TCBR can be limited as shown in section
III-C.
Fig. 5 shows the stability index Wc for the resistance
values of each device (i.e., RFCL and RTCBR) varied in the
range from 0.6 to 2.6 (pu) with a step of 0.1 (pu). In “both
devices”, RFCL is set to the constant value of 1.1 (pu). From
the results in the cases of “one-unit”, the most effective value
of FCL (RFCL) and TCBR (RTCBR) are 1.1 (pu) and 0.6 (pu)
respectively. Also, it can be seen that the resistance which
can dissipate large energy is effective. In the case of “both
devices”, although all results indicate less than the most
effective value of “one-unit”, in particular, large value is
effective (minimum point is 2.5 pu). This is because TCBR
does not need to dissipate the accelerating energy of the
generator so much.
3 .0
FCL
2 .5
120
Wc (s)
Firing-angle (deg)
180
60
TCBR
2 .0
FC L & TC BR
1 .5
0
0
1
2
3
4
5
6
7
1 .0
T im e (s )
0 .5
1 .0
(a) TCBR
1 .5
2 .0
2 .5
R e s is ta n c e (p u )
Fig. 5.
Stability index Wc for resistance of each device
180
Firing-angle (deg)
B.
120
60
0
0
1
2
3
4
5
6
7
T im e (s )
(b) FCL and TCBR
Fig. 4.
Firing-angle of TCBR (phase ‘a’)
To evaluate numerically the power system stability, we
have used a stability index Wc given by
Wc (sec) =

T
0
d
Wtotal dt /
dt
system base power
(4)
where Wtotal is a summation of kinetic energy of each
generator and T is a simulation time selected to 7 (sec). By
using Wtotal, we can evaluate the stability of overall power
system, taking each generator power rating into account. Wc
is the integrated variation of the energy exchanged between
the generator rotor and the system; thus, the lower the value
of the parameter, the smaller the transient swing, and the
better the overall system stability.
Turbine shaft torsional oscillations
The rotor of generator has a very complex mechanical
structure consisting of several predominant masses (such as
rotors of turbine sections, generator rotor, couplings, and
exciter rotor) connected by shafts of finite stiffness.
Therefore, when the generator is perturbed, torsional
oscillations occur between different sections of the turbinegenerator rotor. The certain electrical system disturbance can
significantly reduce the life expectancy of turbine shafts [14].
Therefore, sufficient damping is needed to reduce the turbine
shaft torsional oscillations.
To analysis the torsional oscillations of the turbine shaft,
we have used the structure of a typical lumped-mass of the
generator driven by a tandem turbine as shown in Fig. 1. It
consists of six torsional masses. Fig. 6 shows the turbine
shaft torque responses of generator G1. In the case of “both
devices”, the torques of turbine shafts between each mass are
effectively restrained.
Fig. 7 shows the integrated variation of the turbine shaft
torque in the range of 0 to 7 (sec). The lower value improves
the life expectancy of turbine shaft. As seen, the use of FCL
is effective in comparison with the use of TCBR on the
damping of shaft torque oscillations. In the case of “both
devices”, all results indicate less than the most effective value
of “one-unit” for all shafts.
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H P -IP
2 .5
IP -L P A
L P A -L P B
L P B -G E N
1 .8
Integrated value
Turbine shaft torqeue (pu)
2 .0
1 .5
1 .0
0 .5
1 .2
TCBR
FCL
0 .6
0 .0
FCL & TCBR
0 .0
-0 .5
0
1
2
0 .5
3
1 .0
IP -L P A
2 .0
2 .5
(a) HP-IP
(a) No devices
H P -IP
2 .5
1 .5
R e s is ta n c e (p u )
T im e (s )
L P A -L P B
L P B -G E N
1 .8
Integrated value
Turbine shaft torque (pu)
2 .0
1 .5
1 .0
0 .5
1 .2
TCBR
FC L
0 .6
0 .0
FCL & TCBR
-0 .5
0 .0
0
1
2
3
0 .5
1 .0
T im e (s )
Fig. 6.
1 .5
2 .0
2 .5
R e s is ta n c e (p u )
(b) FCL and TCBR
Turbine shaft torque of G1
(b) IP-LPA
1 .8
Integrated value
1 .2
FC L
0 .6
FC L & TCBR
0 .0
0 .5
1 .0
1 .5
2 .0
2 .5
R e s is ta n c e ( p u )
(c) LPA- LPB
1 .8
TCBR
Integrated value
Temperature
Fig. 8 shows the responses of temperature and resistance
of the resistor in the case of “both devices”. RFCL and RTCBR
are set to 1.1 and 2.5 (pu) at 20 (°C) respectively. As
mentioned earlier, FCL operates from the fault occurrence
instance (0.1 sec) to the fault clearing (0.2 sec), and then
TCBR operates dynamically until the generator disturbance
becomes small. In the case of “both devices”, as shown in Fig.
4, TCBR only operates from about 0.3 to 0.7 (sec). As seen,
temperature and resistance of FCL rise up to about 65 (°C)
and 1.16 (pu) respectively. Those of TCBR rise up to about
70 (°C) and 2.65 (pu) respectively. As TCBR operates for a
long time in comparison with FCL, temperature of TCBR
rises more than that of FCL. However, the temperature rise of
TCBR is not so large, and the resistance rise of TCBR is also
small.
Fig. 9 shows the maximum temperature for each
resistance value. In “both devices”, RFCL is set to the constant
value of 1.1 (pu). As can be seen, the maximum temperature
of RFCL is in inverse proportion to the resistance value. On the
other hand, RTCBR is not always in inverse proportion to the
resistance value due to the dynamic operation of TCBR.
Japanese Industrial Standards (JIS) [15] indicates that an
upper temperature limit of the austenitic stainless steel is 300
(°C). As seen, the maximum temperatures of all cases are
below the upper temperature limit. However, majority of the
TCBR
C.
1 .2
FC L
0 .6
FCL & TCBR
0 .0
0 .5
1 .0
1 .5
2 .0
2 .5
R e s is ta n c e (p u )
(d) LPB- GEN
Fig. 7.
Integrated values of the turbine shaft torque responses
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80
1.30
Temperature (deg C)
A phase
B phase
C phase
tem perature
40
1.20
1.15
Resistance (pu)
1.25
60
maximum temperatures in the case of “only TCBR” exceed
200 (°C). Therefore, if a large disturbance such as an
unsuccessful reclosing occurs, the temperature of RTCBR may
exceed the limit value of 300 (°C). On the other hand, the
maximum temperature in the case of “both devices” can be
decreased to about 70 (°C).
IV. CONCLUSION
20
re sistance
1.10
0
0.0
0.2
0.4
0.6
0.8
1.0
T im e (s)
(a) FCL
2.9
80
Temperature (deg C)
te m p e ra tu re
A p h a se
B p h a se
C p ha se
2.7
40
Resistance (pu)
2.8
60
In order to enhance the power system stability and damp
the turbine shaft torsional oscillations, the use of combination
of the fault current limiter and the thyristor controlled
braking resistor is proposed in this paper. Furthermore, the
temperature rise effect of both devices is included in the
simulation. The simulation results indicate a significant
power system stability enhancement and damping turbine
shaft torsional oscillations as well as with allowable
temperature rise.
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2.6
20
re sista n ce
2.5
0
0.0
0 .2
0 .4
0 .6
0.8
1 .0
T im e (s)
Fig. 8.
[2]
[3]
(b) TCBR
Temperature and resistance in the case of “both devices”
[4]
160
Temperature (deg C)
140
A phase
B phase
C phase
120
100
[5]
[6]
80
60
40
[7]
20
[8]
0 .5
1 .0
1 .5
2 .0
2 .5
R e s is ta n c e ( p u )
(a) FCL
300
u p p e r te m p e ra tu re lim it
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[10]
[11]
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C phase
50
20
0
0 .0
0 .5
[14]
[15]
a m b ie n t te m p e ra tu re
1 .0
1 .5
2 .0
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2 .5
R e s is ta n c e (p u )
(b) TCBR, and FCL and TCBR
Fig. 9.
Maximum temperature for each resistance
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