Download the effects of line tripping modes on fatigue life losses of turbine

IEEE ICSS2005 International Conference On Systems & Signals
THE EFFECTS OF LINE TRIPPING MODES ON
FATIGUE LIFE LOSSES OF TURBINE
GENERATORS
C. H. Lin

Abstract-- In this paper, the effects of two types of line tripping
mode, i.e. sequential mode and resistor-plug-in mode, on torsional
vibrations of turbine generators are studied. And the fatigue life
losses are estimated, based on the results of an EPRI and a GE
testing reports, by using a verified program developed by the
Aberdeen University. It is shown in the results that the losses
induced by a three-phase-to-ground fault will be significantly
reduced under the sequential tripping mode, yet those by a singlephase-to-ground fault will be increased. As to the resistor-plug-in
mode, worse fatigue conditions will be made under all types of
fault.
generators because electric power will not vary strictly but step
by step. In circumstance of clearance of a three-phase-toground fault, the fault type will change from the three-phaseto-ground fault (3P-G) to the double-phase-to-ground fault
(2P-G), then to the single-phase-to-ground fault (1P-G), and to
the open circuit eventually.
2. Resistor-plug-in mode: This mode is primarily applied to
limit the surge voltage induced by circuit breaker switching
operations on an EHV line. The resistor is inserted prior to the
operation of a circuit breaker, with the resistane of about
200~800 ohms and the period of about 2 cycles.
Index Terms-- Power System, Steam Turbine, Trip, Torsional
Vibration, Fatigue
II. SYSTEM STUDIED
I. INTRODUCTION
Power system faults may give rise to torsional vibrations
on turbine generators [1], leading to excessively stressing on
shafts and blades. Since the progress in materials is limited,
this problem becomes more and more serious following the
development of the large-scale turbine generators. According
to the statistics in [2], there were 41 events that might attribute
to power system faults among the 144 events recorded by a
torsional vibration monitoring. So it receives a lot of attentions
for fatigue damages causing by power system faults [3, 4].
Since the line tripping and reclosing would follow faults, it
can be inferred that what a significant role they will play on
torsional vibrations of turbine generators. In practice, it has
been proved that the different line reclosing modes, e.g. high
speed reclosing, delayed reclosing and selective reclosing,
would induce the different degrees of torsional vibrations on
turbine shafts [5-7]. However, hardly any similar studies have
been proposed with respect to line tripping modes. In actual,
the line tripping modes are more and more flexible following
the progress in electric technologies. So their effect on
torsional vibrations of turbine generators will become more
and more significant. Thus, it is studied in this paper the
effects of following two types of line tripping modes, so as to
make up the deficiency of previous works.
1. Sequential tripping mode: Under such a type of tripping, the
faulty lines are tripped phase by phase with one cycle of
interval. It is good from the viewpoint of impacts to turbine
C. H. Lin is with the Department of Electrical Engineering, Kao Yuan
Institute of Technology, Kaohsiung, Taiwan, R.O.C.
(e-mail: [email protected])
2.1 Electric System
The system studied has been simplified to a singlemachine-to-infinite-bus system. A 4-poles/60Hz/951MW
generator, driven by a steam turbine unit, supplies power to the
infinite bus via a step-up transformer (with rating of
1057MVA/345kV) and two parallelled transmission lines. An
IEEE TYPE-1 AVR regulates the generator terminal voltage.
The entire system is modeled using the Matlab/Simulink and
Power System Block-set, with parameters listing in Table 1.
Rs
Ll
Lmd
Lmq
Rf
RT
Table 1 System Parameters
Generator (pu)
AVR
0.00359 Llfd
0.168
Tr
0.001
Kf
0.046
0.19
Rkd 0.0257 Ka
50
Tf
0.578
1.574
Lkd
0.11
Ta
0.02
Efmax
1.0
1.49
Rkq 0.0257 Ke
-0.029
Efmin
-0.95
0.0007 Lkq
0.49
Te
0.1169
Kp
0
Transformer (pu)
Transmission line (pu)
0.00192 XT 0.14304 RL 0.0073
XL
0.1088
2.2 Mechanical system
The steam turbine unit, including a high-pressure stage (HP)
and two low-pressure stages (LP1, LP2) steam turbines, is a
close-coupled and cross-compound reheat unit that operates at
a rotational speed of 1800 rpm. Each of the LP-turbines had F
and R spindles, using a shrunk-on rotor with eleven stages in
each spindle, including rotary and stationary blade stages.
There are eleven rows of blades, twisted in structure and with
a serrated type of root, in the LP-turbine. The first nine rows of
blades sheathed the disc with shrouds. The last two rows of
blades were freestanding structure in which the rotational
diameter of the longest blades was 4531 mm.
It is very difficult to characterize such a complex turbine
generator structure, yet it was generally acceptable for using
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IEEE ICSS2005 International Conference On Systems & Signals
the lumped mass-damping-spring model on the studies of
torsional vibrations. By modeling with such a type of model,
the parameters are listed in Table 2.
Torque
distribution
HP
31
LP1F 14.45
LP1R 14.45
LP2F 14.45
LP2R 14.45
GEN －
REC －
EXC －
B1F 2.8
B1R 2.8
B2F 2.8
B2R 2.8
Table 2 Parameters of the Mechanical Model
Inertia constant
Damping coefficient Stiffness coefficient
(MW-s/MVA)
(MW-s/MVA-rad)
(MW/MVA-rad)
HHP
0.1787
DH
0.00180
KH1
144.15
HLP1F
0.6462
D1F
0.00023
K1FR
1595.0
HLP1R
0.6410
D1R
0.00021
K12
206.0
HLP2F
0.6499
D2F
0.00021
K2FR
1584.9
HLP2R
0.6602
D2R
0.00021
K2G
325.28
HGEN
1.1616
DG
0.00012
KGR
117.16
HREC
0.00344
DR
0.00000
KRE
1.61
HEXC
0.00236
DE
0.00000
－
－
HB1F
0.0344
DB1F
0.00004
KB1F
36.2
HB1R
0.0344
DB1R
0.00004
KB1R
36.2
HB2F
0.0344
DB2F
0.00004
KB2F
36.2
HB2R
0.0344
DB2R
0.00004
KB2R
36.2
III. FUNDAMENTAL STUDIES
5.00
0.50
3.00
0.30
B2F Torque (pu)
LP2R/GEN Torque (pu)
3.1 Frequency domain analysis
The frequency characteristics of turbine shafts and blades
were evaluated by using the frequency scanning. The
excitation signal is applied to the generator rotor terminal, of
which the frequency is increased from 0.01Hz to 140Hz with
an interval of 0.01Hz. The results show that there are eight
peaking responses, of which the frequencies are 19.5Hz,
37.2Hz, 46.2Hz, 49.8Hz, 52.0Hz, 53.2Hz, 112.3Hz and
115.7Hz, respectively. These are the natural modes of the
mechanical system.
3.2 Time domain analysis
Transient simulations are made to obtain the time
behaviors of shafts and blades subjecting to power system
faults. Suppose a fault is applied at 0.1 second to one of the
transmission lines. The faulty line is tripped by circuit breakers
2.5 cycles later, and is re-closed onto the same fault after 20
cycles. The fault is cleared again without subsequent reclosing.
From the simulation results for a three-phase-to-ground
fault, it can be seen from the shaft torques that the LP2R/GEN
shaft vibrates strictest, and from the blade torques that the B2F
blade vibrates strictest. Fig. 1 demonstrates torques of these
two sections.
1.00
-1.00
-3.00
-5.00
with the results tabulating in Table 3.
IV. COMPARISON OF TORSIONAL VIBRATIONS
4.1 The effects of sequential tripping mode
For comparison, transient simulations are made again
under the same condition except the faults are cleared with the
sequential tripping mode rather than the simultaneous tripping
mode. The results about peak-to-peak torques of shafts and
blades are listed in Table 4. By comparing Table 4 with Table
3, it can be seen that the peak-to-peak torque of B2F blade is
reduced from 0.6143pu to 0.547pu (about 11% of reductions)
under the three-phase-to-ground fault, and from 0.4797pu to
0.4564pu (about 4.9% of reductions) under the double-phaseto-ground fault. However, it is increased from 0.3711pu to
0.3818pu (about 2.9% of increase) under the single-phase-toground fault. This phenominen still holds for other blades as
well as for shafts. Thus, the effect of the sequential tripping
mode is dependent on the fault types. Under the three-phaseto-ground fault, the sequential tripping mode gives rise to soft
power variation, leading to less impact to turbine generators.
However, there is no longer the effect of soft power variation
under the single-phase-to-ground fault, thus leading to adverse
results.
Table 3 The Peak-to-peak Torques (pu) of Shafts and Blades under Various
Faults
B1R
B2F B2R
Fault HP/LP1F LP1R/LP2F LP2R/GEN B1F
3P-G
0.9877
2P-G 0.7447
1P-G 0.5210
0.5
1
Time (sec)
1.5
2
5.7620
4.2175
0.2441 0.2539 0.4797 0.4192
1.6231
2.7575
0.1934 0.2047 0.3711 0.3215
Table 4 The Peak-to-peak Torques (pu) of Shafts and Blades under the
Sequential Tripping Mode
B1R
B2F
B2R
Fault HP/LP1F LP1R/LP2F LP2R/GEN B1F
3P-G
0.2808 0.2839 0.5470 0.4391
2P-G
0.9820
0.6893
3.7161
2.4035
5.3290
3.9089
0.2189 0.2264 0.4564 0.3710
1P-G
0.5428
1.6431
2.9295
0.2051 0.2132 0.3818 0.3356
Table 5 The Peak-to-peak Torques (pu) of the LP2R/GEN Shaft under the
Resistor-plug-in Mode
200Ω
400Ω
600Ω
800Ω
Fault
3P-G
9.2
8.8
8.6
2P-G
1P-G
6.9
4.9
6.5
4.2
6.2
4.0
8.5
6.0
3.9
Table 6 The Peak-to-peak Torques (pu) of the B2F Blade under the Resistorplug-in Mode
200Ω 400Ω
600Ω
800Ω
Fault
0.10
-0.10
3P-G
0.80
0.79
0.78
-0.30
2P-G
1P-G
0.63
0.45
0.60
0.44
0.59
0.43
-0.50
0
0.3079 0.3158 0.6143 0.5479
3.9275
2.6304
0
0.5
1
1.5
2
0.77
0.58
0.43
Time (sec)
Fig.1 Torques due to the three-phase-to-ground fault
For comparison purpose, define the peak-to-peak torque as
the difference between the maximal and the minimal torques.
The peak-to-peak torques of shafts and blades under various
faults then can be evaluated according to transient simulations,
4.2 The effects of resistor-plug-in mode
By replacing the sequential tripping mode with the resistorplug-in one, the transient simulations are made again, and the
results are compared to those in fundamental studies. In Tables
5 and 6, it depicts the peak-to-peak torques of LP2R/GEN
shaft and B2F blade respectively. Since there is an additional
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IEEE ICSS2005 International Conference On Systems & Signals
V. ESTIMATION OF FATIGUE LIFE LOSS
A verified program developed by the Aberdeen University
[8] was used to evaluate the fatigue life loss of steam turbine
shafts and blades stressing by torsional vibrations, which is
based on the linear damage acumulation by the PalmgrenMiner rule.
According to the results of a series of ultrasonic frequency
corrosion fatigue tests made by the EPRI for some widely used
turbine blade materials under 18 different environments [9],
the fatigue behavior of the B2F blade, made by the AISI-403
alloy, is characterized by the stress-life cycle curve shown in
Fig. 2(a). Likewise, according to a three-years project
conducted by the General Electric Co. which aimed at
predicting the fatigue damage of some turbine rotor materials
[10], the fatigue behavior of the LP2R/GEN shaft, made by the
ASTM A470 alloy, is characterized by the stress-life cycle
curve shown in Fig. 2(b).
and comparing the fatigue life loss of shafts and blades under
different line tripping modes. The safety factor, suming up all
of the factors influencing the stress distribution on the shafts
and blades, relates the torque to the stress beared by shafts and
blades by following formula.
[Stress beared]={[torque beared]/[steady-state working
torque]}*[stress in relevance to softening point]/[safety factor]
In general, the softening point of turbine rotor alloys is at
the 105 cycles-to-failure of a stress-life cycle curve [11]. In
circumstance of 0.9pu of power generated by the generator, the
steady-state working torques of HP/LP1F, LP1R/LP2F and
LP2R/GEN shafts will be 0.28pu 、 0.59pu and 0.90pu
respectively according to the torque distributions tabulated in
Table 2. Likewise, the steady-state bending torque of B2F
blade will be 0.0253pu, which results to the shear stress on
blade. In addition to that, the inertia would give rise to
centrifugal stress on blade, which is 0.0344pu according to
model parameters. Thus the steady-state working torque of
B2F blade will be 0.0427pu by using the vector operation.
Accordingly, the stress-life cycle curves can be
transformed to the torque-life cycle curves. Figs. 3(a) and 3(b)
demonstrate such curves for the LP2R/GEN shaft and B2F
blade respectively under different safety factors.
LP2R/GEN Torque (pu)
disturbance at the moment of resistor inserting, the vibrations
induced on both the two sections are seen to become strict no
matter under what types of fault. Furthermore, the vibrations
tend to be stricter following the decrease in resistance inserted
in. In circumstance of inserting a 200-ohms of resistor, the
peak-to-peak torque of LP2R/GEN shaft increases from 3.8pu
to 4.9pu (about 30% of increase) under the single-phase-toground fault. As to the one of B2F blade, it increases from
0.54pu to 0.63pu (about 12.5% of increase) under the doublephase-to-ground fault. With such a large amount of increases
in peak-to-peak torques, it shows clearly the significance of
line tripping with the resistor-plug-in mode.
500
4
sf=1
sf=2
3
2
1
0
0
2
4
6
8
logarithm of cycles-to-failure
10
A470
(a)
300
200
B2F Torque (pu)
stress-MPa
400
100
0
0
2
4
6
8
logarithm of cycles-to-failure
10
(a)
800
stress-MPa
sf=1.5
sf=2.5
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
sf=3
sf=4
sf=5
0
600
AISI-403
2
4
6
8
logarithm of cycles-to-failure
10
(b)
400
Fig. 3 The torque-life cycle curves for LP2R/GEN shaft and B2F blade
200
5.1 Fatigue life loss under the sequential tripping mode
Since there is a great effect on blade vibrations under the
three-phase-to-ground fault, a comparison in fatigue life loss is
made under such a condition. The results are listed in Table 7.
It can be seen that the reductions in fatigue life loss are
tremendous. For example of the B2F blade, the fatigue life loss
under simultaneous tripping is about 8 times the one under
sequential tripping for safety factor varing from 4.5 to 5.5. As
the safety factor decreased to 4.0, fatigue damage will take
place under the simultaneous tripping, while only 28% of
0
0
2
4
6
8
10
logarithm of cycles-to-failure
(b)
Fig.2 The stress-life cycle curves for ASTM A470 and AISI-403 alloys
Since the fatigue life characteristics are extremely nonlinear, a concept of safety factor (sf) is used when evaluating
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IEEE ICSS2005 International Conference On Systems & Signals
fatigue life losses will be accumulated under the sequential
tripping. Thus, the sequential tripping mode is good for
preventing turbine damages subjecting to a three-phase-toground fault.
Table 7 The Fatigue Life Losses (%) of Blades under the 3P-G Fault
B1F
B1R
sf
Normal
Sequential
Sequential
Normal
2
2.5
3.0
3.5
sf
4.0
4.5
5.0
5.5
Failure
5.415932
0.118155
0.005421
55.533535
0.508502
0.011899
0.000802
Failure
11.690680
0.252637
0.011059
Sequential
28.520653
2.378355
0.260075
0.035105
Normal
25.347399
2.118950
0.231502
0.031524
B2F
Normal
Failure
18.298645
1.973222
0.269037
74.952873
0.688496
0.015749
0.000802
B2R
Sequential
0.143413
0.012626
0.001538
0.000256
REFERENCES
[1]
Table 8 The Fatigue Life Losses (%) of Shafts under the 1P-G Fault
HP/LP1F
LP2R/GEN
LP1R/LP2F
sf
Normal
1.15
1.25
1.5
1.75
2.0
2.25
2.5
2.75
3.0
0.062581
0.013483
0.000480
0.000030
0.000002
0.000000
-
Resistorplug-in
Failure
Failure
Failure
25.670
1.989
0.208
-
Normal
0.001508
0.000094
0.000007
0.000000
0.000000
0.000000
0.000000
Resistorplug-in
Failure
Failure
Failure
Failure
Failure
28.291
5.419
Normal
0.026932
0.002304
0.000273
0.000041
0.000006
0.000001
torsional vibrations and fatigue life losses of turbine shafts and
blades are studied. It is anticipated that the results could be
useful to safety operations of a steam turbine generator system.
Followings are some conclusions summarized.
1. The sequential tripping mode will significantly reduce the
fatigue life losses of turbine shafts and blades due to the threephase-to-ground and double-phase-to-ground faults. On the
contrary, it will lead to adverse results under the single-phaseto-ground fault. So the fault type is a critical factor.
2. The resistor-plug-in mode will worsen the fatigue condition
of turbine shafts and blades. The smaller the resistance is, the
more life losses will be. So it seems significant to consider this
phenomenon when utilizing such a type of mode for alleviating
the surge voltage induced by breaker switchings.
Resistorplug-in
Failure
Failure
Failure
Failure
Failure
19.189
5.2 Fatigue life loss under the resistor-plug-in mode
For the line tripping with resistor-plug-in mode, there is a
greater effect on the shaft sections under the single-phase-toground fault, thus a comparison in fatigue life loss is made
under such a condition. Table 8 listed the results for inserting a
200-ohms of resistor. It can be seen that the effect is so great
that the LP2R/GEN shaft with sf=2.75 would be damaged
under the tripping with resistor-plug-in mode, yet it just
consumed 0.000006% of life time under the normal tripping
mode. Therefore, it would be necessary to assess the adverse
effect on turbine fatigue when utilizing the resistor-plug-in
tripping mode to alleviate the surge voltage induced by circuit
breaker switchings. However, it ought to be pointed out that
the results in Table 8 are just for comparison purpose. In
practice, a turbine generator would be designed to withstand
the strictest three-phase-to-ground fault. It goes without saying
that it can withstand the single-phase-to-ground fault.
VI. CONCLUSIONS
In this paper, the effects of liner tripping modes on
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