Turbine-Generator Blade and Shaft Torisonal Torques
Due to Line Faults in Six-Phase Transmission
Systems Evolved from Three-Phase Double-Circuit
Line Systems
Jong-Ian Tsai
Rong-Ching Wu+
Tung-Sheng Zhan*
Ting-Chia Ou**
Wen-Yang Li
Yong-Nong Chang#
+*#
**
Department of Electronic Engineering
Department of Electrical Engineering
Atomic Energy Council
+
*
**
Kao Yuan University I-Shou University Kao Yuan University Institute of Nuclear Energy Research #National Formosa
University
Taiwan, R.O.C.
jitsai@cc.kyu.edu.tw
Abstract—Due to a restricted right-of-way and many factors,
some of the local areas in Taiwan have become increasingly
difficult to build new transmission lines. Since the majority of
Taiwan power loads are located in the Norton, the demand of
promoting transmission power could be of great urgency owing
to the large amounts of power transferring from the South to the
Norton. Aimed at overcoming this problem without changing the
original conductors of the double-circuit transmission lines, the
six-phase transmission scheme which could be one of the best
schemes is presented and has several advantages such as
transient stability enhancement, minimal corona, electric and
magnetic fields, and radio interferences. As a result of the
successful commercial operation of six-phase transmissions, the
utility planner inevitably faces with the issue for the impact of
turbine-generator torsional vibrations in the initial stage of the
expansion into the a six-phase network. From the simulation
comparisons between the three-phase double-circuit and evolved
six-phase system, the latter offers better stability characteristic
without deteriorating torsional vibrations from the viewpoint of
the same line voltages. For the case of the same transmission
capability, it significantly reduces the torsional vibrations. These
conclusions provide a constructive suggestion for the department
of generation and transmission.
Under the assumption of the same line-to-line voltage, the
six-phase transmission needs equal space of right-of-way and
can carry up to 73% more power than a conventional double
circuit three-phase line. In 1992, the high phase order
transmission demonstration project converted NYSEG’s 115
kV double circuit short line between Goudey and Oakdale into
a 93 kV six-phase line [1]. The power flow capability of such a
system could be increased by 40%. Subsequently, numerous
studies have been presented and attention has become focused
on the system protection [2-3] and fault analysis [4-6].
Recently, there has been new interest in torsional interaction
between this system and turbine-generator shafts [6]. However,
it lacks for discussing the turbine blade torsional torques,
stability, and comparison under the identical line voltage.
Index Terms—Turbine, Torque vibration, Single-pole
switching, Six-phase transmission, Transmission capability
A. System Model
The existing three-phase system used for investigation of
this paper is shown in Figure 1(a). It consists of a turbinegenerator connected via step-up and -down transformers to an
infinite bus network system through a three-phase, 345 kV
double-circuit transmission line. The converted six-phase
system, shown in Figure 1(b), consists of the same turbinegenerator connected via two pairs of phase conversion
transformers to an infinite bus network system through a sixphase transmission line. One pair of phase converter
transformers is connected wye/delta and the other pair is
connected inverted wye/delta. Therefore, the 60-degree phase
shift between adjacent phases is obtained. The phase diagrams
for the studied three-phase double-circuit and six-phase
systems are plotted in Figures 2(a) and 2(b) respectively. It is
apparent that the line-to-line voltage magnitude of the sixphase system is the same as its phase voltage magnitude.
I.
INTRODUCTION
There are three nuclear power plants in Taiwan, which
serve as base-load units and began their operation in 1977.
According to statistics for these plants, a total of 46, 68 and 62
incidents have occurred in 1997, 1998, and 1999, respectively.
Among these, up to 10 incidents (induced from either typhoons
or earthquakes) even caused tower collapse and serious
disconnection between the northern and southern subsystem,
incurring considerable financial expense to reconstruct the
transmission system. Six-phase transmission technique allows
the towers to be built smaller and more compactly than the
three-phase one for the same power flow capability, effectively
lessening the right-of-way problem without changing existing
conductors. The cost saving could be recycled to strengthen the
tower against collapse.
978-1-4244-2800-7/09/$25.00 ©2009 IEEE
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To investigate these effects is the motivation behind the
development of our article. From the simulation result, it is
found that the six-phase system effectively lessens the torsional
interaction under various transmission line faults. A transient
computer program is developed by using Matlab-Power System
Blockset [7].
II.
SYSTEM DESCRIPTIONS
ICIEA 2009
The steam turbine unit, including one high-pressure (HP)
stage and two low-pressure (LP1, LP2) stage steam turbines, is
a close-coupled and cross-compound reheat unit that operates
at a rotational speed of 1800 rpm. The rated capacity of the
generator set, installed in 1984, is 951MW and is the largest in
Taiwan. Each of the two low-pressure steam turbines has A and
B spindles and uses the shrunk-on rotor with 11 stages of each
spindle, including rotary and stationary blade stages.
sources to stress turbine mechanism, governing the turbine
shaft and blade vibration behaviors.
In this paper, the vibration modes of the turbine system
have been analyzed by using the frequency-scanning method.
Suppose that the terminal of the generator rotor is a shaker with
E/M torque of one p.u., the frequency-scanning inspects the
natural frequencies of steam turbines from 0.01 Hz to 140 Hz
with an interval of 0.01 Hz. Figure 4 demonstrates the
frequency scanning results for the B2F blade and LP2R-GEN
shaft. Nine vibration modes are then presented as listed in
Table 2. Clearly, these modes have been properly avoided from
the forbidden frequency bands defined as 60Hz±5% and
120Hz±5%.
Aimed at the excitations of the aforementioned three
frequency component of E/M torque, it is clearly comparable
that the most considerable blade torque response is excited by
the double system- frequency component (-29.6db at 120Hz).
This will impose supersynchronous oscillations in turbine
blades. However, such an effect cannot be found in turbine
shafts due to their low response (<-25dB at 120Hz). The shaft
is more sensitive to the excitation of the unidirectional
component while the blade is not. Both the blade and the shaft
have the sensitivity of minor importance to the excitation of the
system frequency component.
Figure 1. System studied (a) three-phase double-circuit system (b) six-phase
system
Figure 2. Phase diagram (a) three-phase double-circuit system (b) six-phase
system
B. Simulation System Model
For time-domain simulation investigations, the generator is
represented by a six-order state-space d-q-0 model. The step-up
transformer is represented by lumped model transformers. Each
transmission line is modeled by its equivalent R-L lumped
parameters. Each network source is treated as an infinite bus
modeled by a fixed amplitude sinusoidal voltage source at
nominal frequency. Each CB is represented as an ideal switch
which is able to open at the current zero crossings. Dynamics
of the excitation system modeled by IEEE type 1 exciter are
included in the generator model. A mass-damping-spring
model is adopted for turbine model representation, as Figure 3
illustrated. The simulation data are given in the Table 1. All of
the parameters of this system are in the per-unit (p.u.) system,
based on generator ratings.
III.
FREQUENCY DOMAIN ANALYSIS
It is well-known that the electromagnetic (E/M) torque
induced by power system fault consists of the following three
components, a unidirectional component (<2 Hz), a systemfrequency component, and a double system-frequency
component which correspond to the generator delivering power
(or amplitude of armature current) swing, the generator DC
armature current, and the negative-sequence armature current
arising from the unbalanced operation respectively [8]. These
three frequency types of E/M torques are the main excitation
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Figure 3. Turbine model.
Figure 4. Results of frequency-scanning for LP2R-GEN shaft and B2R blade.
Table 1. 951MW turbine-generator system parameters
Mechanical data
Generator (1057MVA, 24kV)
60Hz
Xd=1.574 Rs=0.00359 Mass Inertia, Damping,
C
4 poles
Xq=1.490 Rfd=0.00070
H
P0=0.90
Xfdl=0.168 Rkd=0.02571 HP
0.1787 0.00180
Q0=0.07
Xl=0.190 Rkq=0.02571 LP1F 0.6546 0.00023
Vt=1.03
Xkd=0.110 Xkq=0.490 LP1R 0.6486 0.00021
Step-up/down TR. 1057MVA (each) LP2F 0.6575 0.00021
24/345kV, Xt1= 0.1430 Rt1=0.00192 LP2R 0.6676 0.00021
3P:Wye-Delta1,6P:Wye-Delta1/Delta11 GEN 1.1616 0.00012
PI transmission line (each)
REC 0.00344
0
R=0.0366 XL=0.108 XC=340.55
EXC 0.00236
0
Torque distribution (%)
Blade 0.0344 0.00004
HP 31 LP1F 14.45 LP2F 14.45 B1F
2.8
B2F
LP1R 14.45 LP2R 14.45 B1R
2.8
B2R
*units: H(MW-S/MVA), C(MW-s/MVA-rad), K(MW/MVA-rad)
Stiffnes
s, K
144.15
1595.0
206.0
1584.9
325.28
117.16
1.61
36.2
2.8
2.8
Table 2. Vibration modes (Hz)
1
2
3
4
5
6
7
8
9
19.40 37.40 40.25 47.02 101.80 104.11 127.05 133.25 134.25
Table 3. The 23 significant fault types of six-phase power systems and
corresponding fault lines of three-phase systems
Fault type
1-phase-G (1L-G)
2-phase-G (2L-G)
2-phase (2L)
3-phase-G (3L-G)
3-phase (3L)
4-phase-G (4L-G)
4-phase (4L)
5-phase-G (5L-G)
5-phase (5L)
6-phase-G (6L-G)
6-phase (6L)
IV.
Number of
combinations
1
3
3
3
3
3
3
1
1
1
1
Six-phase fault
phase
a
ac', ab, aa'
ac', ab, aa'
abc', aa'c',abc
abc', aa'c',abc
abc'a',abcc',aa'c
abc'a',abcc',aa'c
aa'bcc'
aa'bcc'
aa'bb'cc’
aa'bb'cc’
three-phase
fault line
a
ac', ab, aa'
ac', ab, aa'
abc', aa'c',abc
abc', aa'c',abc
abc'a',abcc',aa'c
abc'a',abcc',aa'c
aa'bcc'
aa'bcc'
aa'bb'cc’
aa'bb'cc’
double circuit system, and in Figure 7(b) for the six-phase
system with identical line-to-line voltage (345kV). Obviously,
the six-phase system offers better transient stability
characteristics than the conventional three-phase double-circuit
system on account of the increment of 73% power flow
capability. The damping on the rotor angle helps validate this
assertion.
TIME-DOMAIN SIMULATION RESULTS
There are 11 and 120 possible fault combinations in a threephase and six-phase system respectively. Out of these large
combinations, there are 5 and 23 combinations respectively,
with distinct fault levels and phase interconnections [9]. To
compare the impact on the turbine-generator set, the significant
fault combinations are tabulated in the third column of Table 3
for a six-phase system, and in the fourth column for a threephase double circuit system, where the phase numbers are
defined in Figure 3. Assume that the steady-state condition
occurs at 0 second. Thus, the transient responses of six-phase
phase voltage and phase current shown in Figure 5 agree with
the phase relationship. In the following subsections, the fault is
applied to the middle location (location P) of the transmission
line at 0.1 second.
Figure 5. Phase voltage and phase current for the six-phase system.
A. Short-time Line Faults
A.1 Transient Stability Comparison
In the past, power accidents occurring as three-phase-toground faults were believed to induce the largest torsional
stresses [10]. The peak-to-peak (deviation between maximum
and minimum) shaft and blade torques are plotted in Figure 6
as functions of the three-phase-to-ground (abc-G) fault selfclearing time. It can be seen that the fault clearing time affects
the peak-to-peak torsional torques due to the phase additive or
subtractive effect at the instant of clearing time. There are
similar sensitivity characteristics for the peak-to-peak torque
curve between the three- and six-phase systems and their
worst-case clearing time is 0.19 second (5.4 cycles). The
transient behaviors subjected to a worst-case three-phase-toground fault are indicated in Figure 7(a) for the three-phase
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Figure 6. Peak-to-peak shaft and blade torsional torques as a function of the
fault clearing time for a three-to-ground fault (a) three-phase double-circuit
system (345kV) (b) six-phase system with the same line-to-line voltage
(345kV)
A.2 Torsional Torque Level Comparison
Since the faulted armature current in the six-phase system
has been restricted, the induced E/M torque can be alleviated.
This contributes to the turbine shaft and blade torsional torque
suppression as Figure 8(b) shows. If all the peak-to-peak
torques from the curve in Figure 6 are averaged, the average
peak-to-peak torque (Tpp) under the case of abc-G is derived
and defined. It should be noted that between these two systems,
symmetrical faults (such as abc, abc-G, 6L, and 6LG) bring the
same torsional impact, and a 1L-G fault in the six-phase system
can induce torsional torques higher than those induced due to a
2L fault. Besides, a 4L (aca’c’) fault in the three-phase system
imposes the highest stresses on blades rather than shafts. This is
because considerable negative-sequence current penetrates
through the generator, which induces supersynchronous
oscillations. Fortunately as can be seen from the double-system
component of E/M torque, six-phase system also mitigates the
negative-sequence armature current and then reduces this
phenomenon.
Further Table 4 averages these torque levels from 23 types
of faults. As compared from the table, the six-phase network
faults impose minor torsional stresses especially on turbine
blades based on the same peak-to-peak voltage (the same rightof-way).
It is worth noting that as mentioned in [11], the most
common type of fault in a three-phase system is the single lineto-ground (1L-G) fault, followed in frequency of occurrence by
line-to-line (2L) fault, double line-to-ground (2L-G) faults, and
three-phase (3L) faults. This means that in a six-phase system,
the higher phase faults lead to having a much lower probability
of occurrence. Consequently, aimed at the excitations of line
faults below three phases (e.g. 1L-G, …, 3L, 3L-G), the torque
reduction ratio for all shafts and blades in the six-phase system
is about 20% on average. It is emphasized that a relatively
modest reduction in the amplitudes of the torsional torques has
a very significant impact on decreasing the induced fatigue loss
in the material property of shafts or blades.
A.3 The Case of the Same Power Flow Capability
Based on the demand on restricted right-of-way, the line-toline voltage for the converted six-phase system can be reduced
by 3 (namely 199kV) for the same power flow capability.
Therefore, the rotor swing behavior keeps identical damping
characteristics as shown in Figure 9. According to the line base
voltage reduction, the per-unit impedance of the transmission
line becomes higher. This adds the impedance value between
the fault location and the generator, and diminishes the fault
current. Therefore, all the turbine-generator torques has been
considerably depressed. Figure 9 gives the average peak-topeak torques arising from various faults. It can be concluded
that based on the same power capability, such a low voltage
six-phase system is more prone to suppress turbine-generator
torsional torques. On average the reduction ratios (depicted
from the last rows of Table 4) in shafts and blades are about
36% and 43% respectively, as compared with a three-phase
system.
Figure 8. The average peak-to-peak torque (Tpp) following the fault types
tabulated in Table 3 (a)three-phase double-circuit system (345kV) (b)sixphase system (345kV)
Table 4. The average of the average peak-to-peak torque for the main shafts
and blades subjected to 23 significant types of short-time line faults
LP1RLP2RShaft/Blade section
B2F
B2R
LP2F
GEN
3-phase double-circuit
3.5315
5.0136
0.2140
0.2076
system(345kV)
6-phase system (345kV)
3.2281
4.3896
0.1583
0.1565
6-phase system (199kV)
2.3153
3.0755
0.1205
0.1192
Figure 9. As for Figs. 7 and 8, but for six-phase system (199kV).
B. Fault Tripping and Auto-Reclosing
B.1 Transient Stability Comparison
In this section, the following six-phase protection scheme
has been adopted in the Goudey-Okadal Project [2]. The main
criterion is to perform a traditional single pole switching
scheme from the respective transformer. As referred to Figure
3, one conventional three-phase step distance relay monitors
phase a-b-c, and the other monitors phase a’-b’-c’. The
following switching criteria are assigned [2, 3]:
Figure 7. Generator armature current, E/M torque, torsional torque, and rotor
angle responses due to a three-phase-to-ground (abc-G) fault from 0.1 sec to
0.19 sec (a) three-phase double-circuit system (345kV) (b)six-phase system
(345kV)
(1) For single line-to-ground faults, the faulted single pole trip
and one shot high-speed autoreclose. When encountering
unsuccessful reclosure, corresponding triple pole tripping with
no further reclosure permitted.
(2) For line-to-line or double line-to-ground fault on any
adjacent (a-b’ or a-c’) or opposite (a-a’) phase conductors, the
faulted pole trip and one shot high-speed autoreclose.
(3) Three phase trip of all phases from one transformer (a-b-c
or a’-b’-c’) for multi-phase faults from that transformer. No
autoreclose would be attempted for fear of damaging turbinegenerator shaft or blades.
Since a single line-to-ground fault has the largest
occurrence probability among power line accidents, the
2964
transient responses involving with armature current during
worst-case unsuccessful reclosing of a 5.4-60-5.4 cycle’s single
line-to-ground fault occurred are indicated in Figure 10(a) for
the three-phase system, in Figure 10(b) for the six-phase
system with the same line-to-line voltage, and Figure 10(c) for
the six-phase system with the same phase voltage. As can be
anticipated, the 345kV six-phase system possesses the best
stability performance and stability margin. Even after a threepole tripping during unsuccessful reclosing (>1.29 sec), the 345
kV six-phase system becomes the original three-phase singlecircuit system. However, at this instant, the 199 kV six-phase
system becomes a 199kV three-phase single-circuit system and
leads to a rapid rotor acceleration because of the effect of
double transmission impedance. Converting a system with less
right-of-way consideration is against system stability margin.
B.2 Torsional Torque Level Comparison
As a result of the effective reduction for the single line-toground fault current as evidenced by armature current in
Figures 10(b) and 10(c), there are smaller induced
abovementioned three components of E/M torque. Thereby, the
shafts and blades suffer inconsiderable vibrations especially for
the 199kV six-phase system. Besides, during the dead time
between single-pole tripping and line reclosing, the negative
sequence current gives rise to the E/M torque with the double
system frequency component which may stimulate turbine
blades [8]. In the figures, they reveal that, during the dead time,
the six-phase system injects more negative sequence currents to
the generators as the voltages decreases. But fortunately, the
onerous supersynchronous oscillation in turbine blades is not
induced since the vibration modes stay away from the
forbidden band of double system frequency. The effectiveness
of restricting blade vibrations is still guaranteed.
V.
[4]
L. J. Oppel and E. Krizauskas, “Evaluation and testing of a single
terminal step distance scheme for use on a six phase transmission
system,” IEEE Trans. Power Delivery, vol. 13, No. 4, pp. 1527-1529,
October 1998.
[5] A. K. Mishra, A. Chandrasekaran, S. S. Venkata, “Estimation of errors
in the fault analysis of six phase transmission lines using transposed
models,” IEEE Trans. Power Delivery, vol. 10, pp. 1401-1407, 1995.
[6] S. O. Faried and T. S. Sidhu, ”A new method for fault analysis of sixphase transmission systems,” Electric Power Systems Research, vol. 53,
pp. 157–163, 2000.
[7] The Mathworks Inc., "Power System Blockset for Use with Simulink
User's Guide", June 2001.
[8] C. H. Lin and T. P. Tsao, “Suppress vibrations on turbine blades by high
temperature super-conductive fault current limiter,” IEE Proc.
Generation, Transmission and Distribution, Vol. 148, No. 2, pp. 97-103,
March 2001.
[9] E. H. Badawy , M. K. El-sherbiny, A. A. Ibrahim, “A method of
analyzing unsymmetrical faults on six-phase power systems,” IEEE
Trans. Power Delivery, vol. 6, no. 3, July 1991.
[10] T. J. Hammons, "Stressing of large turbine-generators at shaft couplings
and LP turbine final-stage blade roots following clearance of grid system
faults and faulty synchronization," IEEE Trans. Power Apparatus and
Systems, vol. 99, no. 4, pp. 1652-1662, 1980.
[11] Arthur R. Bergen, Vijay Vittal, Power System Analysis, USA, PrenticeHill, 2000.
CONCLUSIONS
1. Under the assumption of identical line-to-line voltage, there
are a 25% torque reduction for the turbine blades on average
following various line faults and considerable stability
improvement in the six-phase system. Under the assumption of
identical transmission capability, there is up to 40% torque
decrement on turbine shafts and blades.
2. For the most frequent fault of the single line-to-ground fault,
the six-phase system induces more significant negativesequence current during the dead time and stability margin
reduction problem under single-circuit line tripping. However,
the torsional torque suppression on either blades or shafts is
still effective and satisfying.
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[2]
[3]
T. L. Landers, R. J. Richeda, E. Krizauskas, J. R. Stewart, and R. A.
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A. P. Apostolov and R. G. Raffensperger, “Relay protection for faults on
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vol. 11, pp. 191–196, 1996.
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2965
Figure 10. Transient responses during unsuccessful reclosing of a 5.4-60-5.4
cycles single line-to-ground fault (a) three-phase double-circuit system
(345kV) (b)six-phase system (345kV) (c)six-phase system (199kV).