ISSN: 2319-5967
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International Journal of Engineering Science and Innovative Technology (IJESIT)
Volume 3, Issue 3, May 2014
Transient Stability Analysis of Three-Phase and
Six-Phase Transmission Lines for SLG Fault
1
T.Charan Singh, 2K. Raghu Ram, 3B.V. Sankar Ram
Swarna Bharathi Institute of Science & Technology, Khammam – 507002 A.P., India
2
Laqshya Institute of Science & Technology, Tanikella, Khammam-507305, A.P., India
3
Jawaharlal Nehru Technological University, Kukatpally, Hyderabad A.P., India
1
Abstract— Transmission lines of present power systems are becoming increasingly popular because of growing demand
and limitations on constructing new lines. One of the problems associated with such a system is the risk of losing stability
following a disturbance. For meeting the ever increasing power demand, not only production of additional power but also
transferability of more power plays an important role. The six-phase or integrated three-phase/six-phase transmission line
received significant attention in recent times as an alternative to the three-phase double circuit transmission line since it
possesses several advantages, mainly √3 times power transfer. In this paper the transient stability of three-phase double
circuit transmission line is compared with integrated three-phase/six-phase transmission line. An SLG fault with single
pole and three pole switching is considered with 9-bus system having one slack bus, two generator buses and six load buses.
For the system considered necessary input values are given in p.u. and using Gauss Siedel’s iterative method load flow
analysis and using modified Euler’s method transient stability analysis are performed at different circuit breaker opening
times from the time of fault occurrence. The swing curve results are obtained by different graphs for different fault clearing
times from witch critical clearing time as well as critical clearing angle is found. From these results by comparison of
three-phase double circuit line and that of six-phase line, it is concluded that three-phase/six-phase transmission line
exhibits more transient stability and “c++” computer language is used for the analysis of this stability
Index Terms— Power Transfer Capability, transient stability, three-phase Double circuit AC transmission line,
six-phase transmission line, Modified Euler’s method, Gauss Siedel’s method, SLG Fault.
I. INTRODUCTION
Power system stability is the ability of an electric power system for a given initial operating condition, to regain a
state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded
so that practically the entire system remains intact[1-2]. Due to the complexity and vastness of this problem, it has
been divided to smaller areas including rotor angle, frequency, and voltage stabilities. Rotor angle stability refers
to the ability of synchronous machines of an interconnected power system to remain in synchronism after being
subjected to a disturbance. Rotor angle stability is divided in to two subcategories, small signal and transients
abilities [2-4].Traditionally, the need for increasing power transmission capability and more efficient use of
right-of way space has been accomplished by the use of successively higher system voltages. Constraints on the
availability of land and planning permission for overhead transmission lines have renewed interest in techniques
to increase the power carrying capacity of existing transmission lines using same available right –of-way. High
phase Order (HPO) transmission is the use of more than the conventional three phases to transmission corridor.
The increased interest in HPO Electric Power Transmission over past thirty years can be traced on a CIRGE paper
published by L. D. Barthold and H. C. Barnes [5]. Among the HPO, six-phase transmission appears to be the most
promising solution to the need to increase the capability of existing transmission lines and at the same time,
respond to the concerns related to electromagnetic fields [5], [6]. One of the main advantages of six-phase
transmission is that a six-phase line can carry up to73% more electric power than a double circuit three-phase line
in the same right-of-way [8].Since that time, the concept of HPO transmission has been described in the literature
in several papers and report [6]-[16]. The other alternative to increase the power transmission capability is HVDC
transmission. However, a major drawback of HVDC transmission is the huge capital required for installation and
operation. And it is economically only if the transmission distance is more than the break even distance. So
six-phase is better option [17].
II. SYSTEM CONSIDERED
A simple three-phase consisting of two generators, five transformers including one regulating transformer and
five transmission lines resulting in a 9 bus system shown in fig 1. is considered. Different SLG fault at Bus five
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are assumed and the transient stability of the system is analyzed with three phase double circuit lines and the
equivalent are converted six-phase lines of that system.
Fig. 1: 9 bus single line diagram with one slack bus,
and 6 load buses.
Fig. 2: Zero sequence diagrams of the given 9 2 generator buses
bus system
Bus number 1 = slack bus
Bus number 2 & 3 = Generator buses
Bus number from 4 to 9 = Load buses
III. METHOD OF ANALYSIS FOR SLG FAULT
The solution of transient state stability problem for Single line to ground (SLG) with single and 3 pole switching..
Since they Single line to ground fault, the positive, negative and zero sequence networks are to be used and based
on the type of fault these 3 sequence networks must be interconnected during the fault analysis.
So the 9 bus problem is now converted into 18 bus or 27 bus problem based on how many sequence networks that
are used. Totally 4 cases with each case having 4 sub cases are considered and results are found.
A. Before fault: Using the matrices Gauss-Seidel’s procedure is followed and are implemented to obtain Y load
matrices for 3 phase and 6 phase cases separately of order (9 9). Then in these matrices 3rd row and 1st row, 3rd
column and 1st column are interchanged. This Y load matrices are reduced to (2 2) by nodal elimination method
since 2 generators are considered for transient stability analysis. From this (2 2) matrices the transfer
reactance (X23) is calculated for finding initial (starting) angle (  0).
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……………1
Where X23bf = X23 before fault =
1
of the (2 2) matrix from the above equation  0can be found.
Y12
B. During Fault: During the SLG fault, the sequence networks will be interconnected. If all 3 sequence
networks are present there will be totally (9  3) =27 nodes for a 9 bus system. Some common nodes can be
ignored for ease of analysis. Thus Y bus matrix of order (27 27) or less can be found which is reduced to
(99for Gauss-Seidel's procedure. Then it is reduced to (2 2) as there are 2 generator buses under
consideration. From this reduced (2 2) matrices and for three-phase and six-phase cases and using the
corresponding value of the electrical power output during fault Pe2 for any generator can be found as follows.
…………. 2
Where X23df = X23during fault condition. In equation 2 the value of X23df is obtained from the reduced Ybus matrices
during fault and  will be known during the modified Euler’s method calculations. So Pe2 can be found at each
value of  for each increment of time in modified Euler’s procedure.
C. After Fault: During the after fault period from t = t1second to t = t2 second: since the circuit breakers of the
faulty section are opened, if it is single pole switching off it is and the unbalanced operation. So positive, negative
and zero sequence networks are to be interconnected showing open circuit at the fault point. From this network
by reducing the Ybus using nodal circuit elimination method the transfer reactance (X23) can be known. In case of
3- pole switching off the circuit breakers since it is a balanced operation of the power system there is no need for
3 sequence networks. So using positive sequence 9 -bus system and (9  9) Ybus matrix, reduced Ybus can be
found from which transfer reactance X23 can be found. This X23 in 1-pole (or) 3 pole switching is known as X23 of
(X23 value during after fault condition). Using this X 23 the electrical power output during after fault condition
(Pe3) is found.
During the “after fault” period.
……………….3
D. Reclosing Period: From t = t2 second to the final time t = tf seconds assuming the restoring of healthy
conditions, circuit breakers are reclosed. During this period, the before fault circuit conditions will provail. So
the same equations 1 for the electrical power out (Pe4) can be used as follows.
…………..4
In equation 4, the X23bF is obtained from the reduced Y load for three-phase/six-phase. In this reclosing period
Gauss-Seidel’s procedure makes use of matrix of order (9  9) and modified Euler’s procedure is performed using
X23bF and equation 4 for finding  and Pe4 step by step.
In the system considered it assumed that an SLG fault occurs at bus 5, on one circuit of the three-phase double
circuit line and on one phase of the six-phase transmission line. The interconnection of three sequence networks
for SLG fault is shown in fig.5The common nodes are merged into a single node. Using this interconnected
network with reduced nodes the shunt and series admittance values are fed to the computer from which the Y Bus
during fault is formed. This YBus is reduced to(2 2) matrix and corresponding elements are used for finding
electrical output (G2,G3) of generators at nodes 2and 3. Using these values of G2 and G3 modified Euler’s
method is continued up to t = t1 i.e. “switching off’ time of the circuit breakers. From t = t1up to t = t2 that period is
considered as after fault period. During after fault period two Cases are considered as follows:
Case 1: “single pole switching” of the circuit breakers.
Case 2:” three poles switching” of the circuit breakers.
Case 1: in this case only one pole or one phase of the three phases of one circuit of the three phase double circuit
line is opened. All remaining five lines will be closed. Then the three sequence networks are interconnected during
“single pole switching off “for the system considered is shown in fig: 2. F1, F2and F3 are fault points in the
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positive, negative and zero sequence networks. Since only one phase is open circuit during the “switching off”
period, the open circuit is considered at F1, F2and F0 in above figure by considering three more points F1I,F2I and
F0I. Now F1 F2and F0are joined together. Similarly F1I, F2I and F0I. are also joined together as shown. Thus after
fault condition of” single pole switching off” is implemented in the interconnected sequence diagram due to
unsymmetrical behavior of the system. Same procedure is followed for six-phase line. Since F1, F2, and F0 are
common nodes they are considered as one node only while feeding the series and shunt admittance values to the
computer, after fault. Thus during after fault situation a total of 29 nodes are obtained in six-phase case. With this
type of network YBus of (29) is formed for six-phase case. These metrics are reduced to (9) For Gauss- Seidel’s
procedure and (2 2) for modified Euler’s procedure of transient stability analysis, since two generators at nodes
2 and 3 are under the transient stability analysis.
Case 2: This is the case of “three pole switching off “the three phase circuit breaker after fault. So in three –phase
double circuit line, only one circuit will be present in the 9 bus system. Correspondingly the three-phase and
six-phase networks are designed using positive sequence networks only due to symmetrical opening of the
three-phase circuit breaker and balanced operation of the system. The remaining analysis is done as explained in
case 1.
Fig.3: Interconnection of sequence networks in admittance form for 3-phase/6-phase system, for an SLG fault at bus 5
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Fig.4: Interconnection of sequence networks in p.u for an SLG fault at bus 5 consisting of a 3-phase double circuit line
At t = o an SLG fault occurs on one phase of the 6-phase line at the beginning. Until the circuit breakers of that
single line open that period is treated as during fault period. Since it is an unsymmetrical fault it is analyzed using
the 3 sequence networks. For convenience the star (Y) network of 6-phasecircuit is converted into  circuit
between nodes (4) & (7) assuming 2 nodes (24) & (25).
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Fig.5: Equivalent circuit showing the interconnection of sequence networks during single pole switching
IV. RESULTS
Table.1 Results showing tcr, cr & (cr -for SLG fault cases. whare initial load angle
S.No
Fault
Type of
Switching
Generator
Line
tcr sec’s
cr
Ele.Deg
(cr- o)
Ele.Deg
1
SLG
Single pole
G2
Three-phase
0.25
83.6
24.6
2
SLG
Single pole
G2
Three/Six-phase
0.32
90.8
35.8(more)
3
SLG
Single pole
G3
Three-phase
0.28
86.4
30.4
4
SLG
Single pole
G3
Three/Six-phase
0.35
93.6
41.6(more)
5
SLG
Three pole
G2
Three-phase
0.22
76.8
17.8
6
SLG
Three pole
G2
Three/Six-phase
0.31
88.4
33.4(more)
7
SLG
Three pole
G3
Three-phase
0.26
80.8
24.8
8
SLG
Three pole
G3
Three/Six-phase
0.34
92.4
40.4(more)
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Fig.6: comparison graph between 3-phase line and 3-phase/6-phase line for 1-line conversion, clearing
0.27sec
time
Fig.7: comparison graph between 3-phase line and 3-phase/6-phase line for 1-line of  of generator- 2 for 1-line
conversion for critical clearing time 0.22sec
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Fig.8: comparison graph between 3-phase line and 3-phase/6-phase line for 1-line of  of generator- 3 for 1-line
conversion for critical clearing time 0.17sec
Table.2: Results from the above table are compared and analyzed as follows
S.No
Comparison Between
3-phase and 6-phase for
different cases
3-phaseline and 6-phase for
any fault.
Salient Features
Reason
Starting angle is less for 6-phase line
compared to that of the 3-phase line.
6-phaseline.Indicating more stability.
The reactance offered by a 6-phase
line is less compared to that of a
3-phaseline
Single pole switching exhibits more tcr,
,cr and (cr-o) compared to 3 pole
switching, indicating more transient
stability, for 6-phase line
The reactance offered by single pole
switch off is less than that of 3 pole
switch off.
1
2
Single Pole Switching and
Three Pole switching of
SLG fault
V. CONCLUSION
In this paper method of analyzing the SLG fault is explained and analyzed during 4 different periods i.e. before
fault, during fault, after fault and re-closing periods. Then the implementation of modified Euler’s method is
explained and different cases are considered for transient stability analysis. Each case is discussed in detail,
computer program in c++ language is written and results are obtained. The results revealed aspects that the starting
angles are less for six-phase line compared to that of a three-phase double circuit line and more values of critical
clearing time (tcr), critical clearing angle (cr) and permissible angular swing for six-phase line.This indicates the
greater transient stability of a six-phase line or 3-phase/6-phase integrated transmission line compared to that of a
normal three-phase double circuit line. it is well know that SLG fault will be occurring more probably in a
transmission line, to improve the stability of the system in addition to 6-phase line, smart grid technology can also
be implemented with FACTS devices, so that the overall stability of the system can be improved.
ACKNOWLEDGMENT
The authors would like to acknowledge the help of Dr P.S Subrahmanian for his valuable suggestions and advise
for the information and guidance in this research in 3-phase6-phasetransmission linesand thank the
Management, Directors , Principal , HOD and the members of the Department of Electrical & Electronics
Engineering (EEE) of Swarna Bharathi Institute of Science and Technology (SBIT), Laqshya Institute of Science
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& Technology,(LITS) Tanikella, Khammam for their support in executing this work in the Department.
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AUTHOR BIOGRAPHY
T. Charan Singh he obtained his B.Tech in Electrical and Electronics Engineering from JNTU, Hyderabad in 2001.
He obtained M.Tech in Energy Systems in 2006 from JNTU college engineering Hyderabad and pursuing Ph.D at
JNTU, Hyderabad. He has teaching experience of 11 years and guided more than 20 UG projects and 7 PG projects.
He has four International Journal publications to his credit. At present he is working in Swarna Bharathi Institute of
Science & Technology, Khammam, Andhra Pradesh-5007002,India as Associate Professor in department of
Electrical and Electronics Engineering and his areas of interest include 6-Phase system , Power Systems stability,
FACTS and Smart Grid .
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Dr.K.Raghu Ram obtained his B.Tech in Electrical and Electronics Engineering in the year 1979, M.Tech in Power
Systems in 1983, Ph.D in 2004 from JNTU, Hyderabad, Andhra Pradesh, India. He has 12 technical papers to his
credit in various international and national journals and conferences. He is guiding 6 research scholars for Ph.D and
guided more than 70 M.Tech Projects. His areas of interest include Multi Phase Transmission System, FACTS,
Power Systems stability and Multi Phase Machines. He received “Best Teacher” award twice from Sathyabhama
Deemed University, Chennai, India. Also he got sanctioned Rs: 3, 00,000/- AICTE, New Delhi research Project
on“3phase/6 phase transmission line simulator” while working in sathyabama Deemed University Chennai, India
during 2003. Presently he is the Principal of Laqshya Institute of Technology& Sciences, Tanikella (V), Konijerla
(M),khammam (Dt) – 507 305, Andhra Pradesh, India.
Dr.B.V.Sanker Ram obtained his B.E in Electrical Engineering in the year 1982 from OU college of Engineering
and Obtained M.Tech in Power Systems in 1984 from OU College of Engineering and Ph.D in 2003 from JNTU.
He joined in JNTU in 1985 and worked in various Capacities. He was the head of the Department from 2006-2008.
As Head of the department he has established Power Electronic controlled drives lab, which is unique in the state of
A.P. He has 72 technical papers to his credit in various international and national journals and conferences. He has
guided 16 research scholars for Ph.D and 6 candidates are still pursuing their research. He guided more than 100
M.Tech Projects. His areas of interest include FACTS, Power Electronic Applications to Power Systems, Power
Systems Reliability. Presently he is the Chairman of Board of Studies in Electrical & Electronics Engineering
JNTU, Kuatpally, Hyderabad-500085, Andhra Pradesh, India.
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