Department of Electrical EngineeringUniversity of Washington
Seattle, Washington
W.C. Guyker, Senior MemberW.H. Booth, Senior Member
Allegheny Power Service CorporationGreensburg, Pennsylvania
J. Kondragunta, Student MemberDepartment of Electrical Engineering
University of MissouriColumbia, Missouri
N.K. Saini, MemberAmerican Electric Power Service Corporat
Columbus, Ohio
Abstract - In the past decade, transmission plan-ners and researchers have been keenly investigating thefeasibility of six-phase concept as a planning alterna-tive. The concept, if proved feasible, would alleviatethe problem of acquiring additional rights-of-way tomeet the increase in electric power and energy demand.Allegheny Power System (APS) has been investigating theconversion of some of their 138-kV three-phase double-circuit lines to 138-kV six-phase lines. The latter isan alternate option to 230-kV three-phase upgrading ofthe line.
This paper addresses one aspect of the APS inves-tigation, namely, fault analysis. It first discussesthe greater variety of fault types that could arise ona six-phase line. It is then followed by the descrip-tion of a technique for evaluating source impedances atthe two ends of the line. The fault analysis by thephase coordinate method is delineated for one type ofunfamiliar fault in the following section of the paper.The analytical results are presented for all types ofsignificant faults that could occur on a six-phaseline. Summary and results conclude the paper. The en-tire paper is developed by focusing the attention on aspecific line in the APS territory. The contents of thepaper should be of direct benefit to utility engi-neers.
1. INTRODUCTION
Allegheny Power System (APS) has several hundredcircuit miles of 138-kV three-phase double-circuitlines. In order to increase the power transfer capa-bility of these transmission line corridors without ma-jor rebuilding, at least two alternatives can be con-sidered. One is to upgrade the towers to 230-kV opera-tion. The number of insulators, conductor sizes, andtower spacings of the existing 138-kV three-phasedouble-circuit lines suggest that an upgrading of theselines to 230-kV double-circuit may be possible. Thesecond is to consider conversion to 138-kV six-phaselines.
The use of six-phase (and other higher orderphases) for transmission was proposed in 1972 as onealternative to use electrical rights-of-way more ef-fectively and efficiently [1-2]. Since that time, theconcept of six-phase has been described in the litera-ture in several papers and reports [3-17]. Some ofthese publications are products of a joint Allegheny
61 SM 485-2 A paper recommended and approved by theIEEE Transmission and Distribution Committee of theIEEE Power Engineering Society for presentation atthe IEEE PES Summer Meeting, Portland, Oregon, July26-31, 1981. Manuscript submitted February 2, 1981;made available for printing May 13, 1981.
E.K. Stanek, Senior MemberDepartment of Electrical Engineering
Power System (APS)-West Virginia University (WVU) studyof the feasibility of 138-kV six-phase conversion as analternative to 230-kV three-phase double-circuit con-version which study had been undertaken during 1976-79[4-14].
This work had been pursued in order to explorethe potential for increased power transmission capabil-ity of existing rights-of-way and the 138-kV double-circuit lines which exist on these rights-of-way. Up-grading these lines to 230-kV double-circuit or 138-kVsix-phase is technically feasible. In either case,with existing conductor thermal limits, at least a 73%increase in power transmission capability is feasibleover these lines.
The 138-kV six-phase line may have the followingadvantages over a 230-kV double-circuit line: reducedconductor gradients, potentially better public accept-ance since nominally it will remain a 138-kV system,stability characteristics and potentially lower audiblenoise levels, radio interference levels, etc. The dis-advantages of a 138-kV six-phase line compared with a230-kV double-circuit line are: substation and tap-point equipment changes, central system changes, thelack of experience in operating and maintaining a six-phase system, higher ground gradients, some possiblereliability penalties, and problems in coordinationwith three-phase lines and systems.
It appears from the study that there are poten-tial benefits that could accrue from the six-phase op-tion. It becomes more attractive as right-of-way util-ization and acquisition problems continue to grow andtransmission capacity and economy increase in import-ance. However, there are some problems that need to besolved before adopting the six-phase concept for 138-kVthree-phase double-circuit line conversion. It shouldbe emphasized that the six-phase alternative is beingdeveloped as an option available to transmission plan-ning engineers.
One of the important items in applying six-phasealternative in transmission planning is the design ofan adequate protective scheme. This requires a detail-ed and realistic fault analysis which is the main themeof this paper. The different fault types that exist onsix-phase systems and the number of significant faulttypes are discussed in Section 2. In order to conducta realistic fault analysis, one needs to evaluate theequivalent source impedance on both sides of a givdnsix-phase line. The calculations of such source imped-ances as applied to a proposed line is described inSection 3. In an earlier paper [8], the authors intro-duced the theory of six-phase symmetrical componentsand the analysis of important fault types with this im-portant tool. During the course of this work it wasrealized that all significant faults that could occuron a six-phase line are not amenable to symmetricalcomponent analysis. The superiority of the phase coor-dinate method over the symmetrical component methodlies in the fact that all such faults could be easilyanalyzed with its aid. Section 4 is devoted to thesix-phase fault analysis by the phase coordinate meth-
od. Section 5 summarizes the paper and draws conclu-sions based on the numerical results obtained. The en-tire development of the paper focuses on a specific138-kV three-phase double-circuit line in the APS ter-ritory which has the potential to operate as a six-phase line.
2. SIX-PHASE FAULT TYPES
The complexity of fault analysis in a six-phasesystem is much greater than in three-phase systems.The fact that there are six phases, each subjected to adifferent voltage, and a neutral in a six-phase systemmakes the number of fault types much greater for thesix-phase system. The numbers of phase-to-phase andphase-to-phase-to-neutral fault combinations are tabu-lated in Table I for both six-phase and three-phasesystems. Out of the 120 possible combinations in asix-phase system, there are 23 combinations with dis-tinct fault levels and phase interconnections.
Consider line-to-line faults that do not involveground. The current magnitude and circuit asymmetryfor a fault on phases a and b is the same as that on band c, and so on. Therefore, the 15 two-phase faultcombinations reduce to three significant combinations.These are:
(1) faults between phases 60 degrees apart, e.g.a to b,
(2) faults between phases 120 degrees apart,e.g. a to c,
(3) faults between phases 180 degrees apart,e.g. a to d.
Similarly, the analysis for all faults can beconfined to the 23 significant combinations mentionedabove. For a three-phase system there are only fivesignificant fault types as can be observed from TableI.
3. EVALUATION OF SIX-PHASE SOURCE IMPEDANCE
Figure 1 shows the Springdale-McCalmont 138-kVthree-phase double-circuit line in the Allegheny PowerSystem. The line will be considered as an example inthis paper since it has the potential to operate as a138-kV six-phase line. In order to obtain the appro-priate values of source impedances on both sides of theline, it is necessary to have the results of the line-to-ground fault study on the existing line in thethree-phase mode. These results are shown in TablesII(a) and (b).
The following assumptions were made for obtainingthe source impedances.
(1) While ZsL, the self-impedance of a transpos-ed line, remains the same whether it operates in athree-phase or six-phase mode, ZmL, the mutual imped-ance between phases, is assumed to be the same in bothmodes of operation, though there is noticeable but in-significant difference between them. In fact, for thisline operating with WP 8 configuration [7] carrying six1024.5 kcmil ACAR conductors and two No. 6 Alumoweldground wires,
Z L = 0.2925 + j-1.236 ohms/mile
and Z L = 0.1921 + j 0.5001 ohms/mile (three-phase)
= 0.1921 + j 0.4624 ohms/mile (six-phase).
These parameters were evaluated using a computer pro-gram entitled "Electrical Parameters and PerformanceCharacteristics" developed during the research work todocument six-phase line design. The capabilities ofthis general program will be discussed in a separatepaper [171.'
Table I
Types of Faults on Six Phase Systems and the Numberof Phase and/or Neutral Combinations
Fault Total Significant Faulted PhasesType Number of Number of for Significant
(2) Each of the i lines terminating on busses atits two ends is represented as an equivalent balancedvoltage source in series with its Thevenin-impedance asshown in Figure 2.
3.1 Source Impedance at Springdale Bus
Step 1: Calculate positive- and zero-sequence current,Ili and Ioi, contributions from each of the existingthree-phase lines using the values listed in columns(3) and (4) of Table II(a).Step 2: Convert the sequence currents obtained in Step(1) into their respective per unit values based on 100MVA and 147.7 kV nominal values (based in APS experi-ence 147.7 kV is chosen as base instead of 138 kV).
1205
Step 3: Find the positive- and zero-sequence currentsflowing into the Springdale bus from:
t-6I = E I p.U.
i=1
IOs = Z Ioi p.u.i=1
(1)
(2)
(Note: t = 6 stands for the 6 lines terminating on the
Springdale bus)Step 4: Find the positive-sequence source impedanice at
the Springdale bus from:
E1s = 1. /Q 7 (I1S) (Z1S)or
1.0 /00 - EisZ = p.u.'s is
The per unit value of E IS is shown in
Similarly an equivalent (three-phase)source impedance at the Springdale bus
from
(3)
Table II(a).zero-sequence
can be found
s= OpuO
Table II(a)
Lire-to-Ground Short Circuit Results at Springdale Bus
EiS(P*u) EOs(p.u)-- No Lines Out
0.718 0.435Springdale 138 kV 0.04 -0.14
Line 1 phase-ground faultDesig- (I+ 1nation --Contributions-- (2 i1 Oi) o
The per unit value of EOS is given in Table lI(a).
Step 5: Calculate self- and mutual-impedances, ZsS ard
ZmS, of the source impedance from
2ZIs + ZOs
Os ssS 3 p.u.
and S 1 p.u.
(5)
(6)
since ZS = ZsS ZmS and ZOS = ZsS + 2ZmS for a trans-
posed three-phase line.
Step 6: Convert ZsS and ZmS, calculated in Step (5),into their ohmic values using the selected bases given
in Step (2). The values of ZsS and Zns thus calculated
are valid for both three-phase and six-phase operating
conditions due to the assumption (1) made earlier in
this section.The following results were obtained using the
data given in Table II(a).
Z Ss 2.03 + j 9.04 ohms
Z = 1.08 + j 2.94 ohms
Table II (b)
Line-to-Ground Short Circuit Results at McCalmont Bus
E (p) EM(p u)iN O-- No Lines Out --
0.815 0.631McCalmont -1.79 -4.63
Line 1 phase-ground fault.Desig- (2I1.+T) 31nation --Contributions-- (1i Di)
Line Name (kA) (kA)(1) (2) (3) (4)
1 McCalmont - 4.733 5.741Kilgo -76.73 -78.46
Legend: The numbers are in polar form
i.e., Z where Z is the magnitude
6 is the angle
(7)
(8) 4. THE PHASE COORDINATE METHOD
3.2 Source Impedance at lIcCalmont Bus
The self and mutual impedances, ZsMI and Z m>, atthie McCalmont bus can be calculated in a similar mannerusing the procedure given in section 3.1 and thei nformationi provided in Table II(b).
The numerical values for the impedances obtainedwere:
ZNM 4.0 + j 17.94 ohms
mM1.66 + j 3.64 ohms
4.1 Assumptions
Besides the usual assumptions made for fault
studies, two additional ones made were:
1) Let E = [Ea, Eb, Ec, Ed, Ee, EfIT be the balanced
set of open-circuit six-phase source voltages. With
the six-phase operator 'b' defined as Ej60, Eb = b5Ea,
EC = b4E . and E = bE.. This assupmtion impliesthat the phase sequence is 'abcdef.'
T
2) Let V [Va, ,V , Vd, Ve, V f] be the bus
voltage under fault condition.
and
1206
4.2 Fault Analysis Procedure
Figure 3 shows the model of the Springdale-McCal-mont six-phase line mentioned in Section 2, with sourceimpedances included at its ends. The fault analysis ofsuch a line entails carrying out the following twosteps for each fault type.Step 1: Evaluate Total Fault Current on the faultedphases stemming from both sources and the voltages ofthe unfaulted phases. In order to obtain the faultcurrent contribution from either side of the line,solve equation (9) with appropriate boundary condi-tions, representing the fault, incorporated in it.
E - va a
E - v
E - Vc c
E - vd d
E - Ve e
Ef - VfE-v
z
Z\\/mE m
Ia
IbIe
If
Substituting equations (11) - (13) in (9) yields
E - va a
b E - 0a
b4E - 0a
b3E - Va d
b2E - Va e
a Vf
0
Ib
c
0
0
(14)
[o_JEquation (14) represents six simultaneous equa-
tions in six unknowns; namely, the two fault currentsIb and Ic and the four unfaulted phase voltages Va, Vd,Ve, and Vf. The solution yields,
(9)
In using equation (9), care should be exercisedin interpreting Zs and 7m properly as explained in thelatter part of this section.Step 2: Evaluate Voltages at Unfaulted Buses
To obtain the voltages at any bus other than thefaulted bus, solve the set of equations (10) for Va,Vb, . * * Vf.
V E Ia a a
Vb E b111 b
d Eb I
[V c (10)Vd EdId
[.7f Ef mLIfJwhere Ia . . ., If are the fault current contributionsfrom this particular bus to the fault point.
Zs and 7m are (Thevenin) self and mutual imped-ances at that bus looking into the source.
Before proceeding further, the procedure indicat-ed in Step I of this section will be illustrated forone of the significant fault types.
4.3 Phase b - Phase c - Neutral Fault Analysis
This type of fault represents a fault on twophases of a six-phase line which are 60 electrical de-grees apart. Since there is no pair of phases 600apart which when faulted yields a symmetrical systemwith respect to phase 'a', assuhie the faulted phases tobe 'b' and 'c.' Experience has indicated that is isdifficult and cumbersome to analyze this particularfault by the symmetrical component method, whereas theanalysis is simpler by the phase coordinate method, asexplained below. Figure 4 depicts this type of faultfor which the relevant boundary conditions are
I + Ic = In (neutral or ground current) (11)
Ia = Id = Ie If = 0 (12)
Vb = V =0 (with zero fault impedance) (13)
Ea 5 3VZmIb= z - z + z
s m s m
Ea 4 jVTZI = (b + )c Z - Z +Zs m 5 m
(15)
(16)
Then from equation (11),
E (b5+b4)I =an Z + Z
s m
-j 3EaZ +Zs m
(17)
Proceeding further,
V = E - Z Ia a m n
V =b3E - Z Id a m n
V = b2E - Z Ie a m n
and Vf =b Ea ZmIn
(18)
(19)
(20)
(21)
All other fault types could be analyzed in asimilar way. Table III lists the fault current expres-sions for all the 23 significant fault types.
5. APPLICATION
Referring to Figure 3, for a fault on the McCal-mont bus, the total fault current is the sum of currentcontributions from the Springdale and lIcCalmont sides.The current contribution from the Springdale side canbe found using equation (9), for which case,
Zs Zs + ZsL = 7.72 + j 32.63 ohms
Z = Z + Z = 5.07 + j 12.21 ohmsm mS mL
(22)
(23)
ZsS, Zm,S ZsL, and EmL are defined in Section 3.The numerical values for these impedances are alsolisted in the same section. The current contributionfrom McCalmont side can also be found in a similar wayusing equation (9) again. In this case, Z s = ZsM andZm = Zel, the source impedances at that bus. At thisstage, the solution also yields the voltages at the un-faulted phases of this particular faulted bus. Thiscompletes Step 1 of the fault analysis described inSection 4. The voltages at the Springdale bus can nowbe found using equation (10), which is Step 2 of theanalysis.
1207
Table III
Analytical Expressions of PhaseCurrents for Significant Fault Types
Fault Type Faulted Phases1.
Table III Continiuo-d.~~~~~~~~~~
Phase Fault Currents
Ea b5ESix-Phase a-b-c-d-e-f I = a_ a
a z -z tb Z-Zs m s m
b4E b3E-I = a ac Z -Z' d Z -Z'
s m s m
b2E bEa if a
e Z -Z zf -Zs m s. m
E b5ESix-Phase a-b-c-d-e-f-n I = a -
Z ato Neutral a Z -Z b Z -Z
b 4E b3Ea 1= a
c zs m Zs m
b2E bEa ae z-Z f Z -Z
s m s m
Five-Phase
Five-Phase-to-Neutral
b-c-d-e-fI|- (5b +1) E1I ab 5(Z -Z )'s m
3(5b +l)E
d 5(Z-Z )'s m
(5b+l) EI af 5a -Z )s m
b-c-d-e-f-n
b4+l) Eac 5 (Z -Z )
s m
2(5b +l) Ea
e 5(Z -Z ) 'sin
E ZI= a (b+ m
Z-Z Z +4Z5 in 5 in
E ZI = zaz (b + ),c z-Z~ Z +4Z 's m s m:
E Za 3 in
Id = z Z (b + 4Z 'Is m s m
E ZI a
(b + in InIe =z -Z (b+ 4- )'Ii s m s. m
E ZI a i
i = z a (b+ m )s m
z+4zSin S in
a-b-d-f-n
t ~~~~54b5E b4EFour-Phase lb-c-e-f I a-I ~ ~ - tZ -Z'I
s m :s m
2bE 6Ea
Ie -z-Z f Z -Z.s i sin
Ia = z _ (1 + ;a Z -Z (1 4 )
s m
Eab = z-Z (b +4
s in
Ea 4 j,fI = Z (b + )
s m
Id =Z--Z_ b I4
Eaa (11- )nz ( 4s m
a 5 -
E= _z (b _ w)
s mEa 3= Z(b _w
(b - -)
b5%z -Z 's -m
4b4EI =. ac Z -Z X
S T
E ij /3 Za mZ -Z ~iZ + 3Zs. m s m
Ea
z -Zs m
Ea
z -Zs m
Ea
z -zs m
EI aa Z -Z
5 in
EI = ab Z -Z
s m
EI - ad Z -Zi s m
j /3 Z(b +z + 3Z
s m
4 j inzsb4 m )(b+3+3Z
5 n
j TZ3 in3(b3 + mm)b + 3Z
5 in
z(1- m
z +Sz5 in
z(b 3Z +3Z
in
b3 Zms. m
z(b- m
Z +3ZS in
Table
Three-Phase
Three-Phase-to-Neutral
III Continued
ib-d-fb5E b3E
a I ab Z -Z ' d Z -Z '
s m s m
bEI = af Z -Z
s m
Table III Continued
lb-f
E.a(1
b5a-b-d I = (1-)
a Z -Z 3s m
Ea 5 b5ab= z(b b-b z3Z
s m
E (3-b'I sa (b - )
I d ZZ.
a-b-f
b-d-f-n
EEa 2
a= z z (1-
s m
Ea 5 2I = (b - )Z -Z 3s m
E
E=a 2if =z Z (b- 3)s m
b5Ea
Ib Z -Zs m
b-c
Two-phase- a-d-nto-neutral
b3EI = ad Z -Z
s m
bEI a
f Z -Zs m
E b5Za-b-d-n I = a (1 - +2Z )'a Z -Z Z +2Z
s m s m
5E b z1= a (b5 m)
bs m s +Zm
E b5ZI
a b3 -
mid= z (b Z +2Zs m s m
a-b-f-n
Two-phase
EI a (a Z -Z
s m
Eaa(b -b)b 2(Z -Z ) '
snm
Ea(b-b )
f 2(Z =Z )Snm
Ib =
c=C
Ea
2(Z -z )
Ea
2(Z -z )
EI
a
a Z -Zs m
E
=, I =-az -z
m
Ea 5 Zm
b-f-n Ib = a Z (b + z
S. m s m
E ___If, = ;a m(b + Z +z )
.~~~~~~~~.I I~~~~~~I~~~~~~~
b-c-nEa 5)
a-Z (b + Z +ZmS m
Ea 4 j ZmI =- (b + )c Zs-Zm Z +Z
s m
S±.gl}- a-n I = a
phase-to- sneutral
2 Zm
Z + 2 Zs m
E 2Za 5
I = (b-b Z -Z Z +2Zs m s m
E 2ZI =a, (b-Zmf Z -Z +2Z
s m s m
EI = aa Z -Z '
s m
EI = _ a
d Z -Zs m
1208
i._
a-d
6. RESULTS AND CONCLUSIONS
The results of the fault analysis for Springdale-McCalmont line operating as a 138-kV six-phase line arepresented in Tables IV to VI. Table IV presents thetotal fault current for the 23 significant fault typesat the McCalmont bus. It can be observed from thistable that the a-b-d-f fault is the most severe one.The maximum current in phase 'd' under this fault con-dition is 19.6 kA.
Even though the possibility of a four-phase fault(such as a-b-d-f) is quite remote,it cannot be neglectedif one wants to provide 100% protection for the line.
One can observe from this table that the leastsevere fault is the a-b-f fault and the value of theminimuim current is 5.2 kA and it occurs on phase a.Thus the range of fault currents vary from 5.2 kA to19.6 kA for the particular line under consideration.
Tables V and VI show the complex voltages at theSpringdale and lIcCalmont busses, respectively under thefault corditions mentioned above. From Table V it canbe seen that the maximum phase voltage of 160 kV (1.16p.u.) occurs on phase If' for the 'b-c-n' fault. The
1209
minimum voltage occurs on phase 'b' under the 'b-c-d-e-f' fault condition and it is equal to 110.2 kV (0.75p.u.) on the Springdale bus. In a similar manner itcan be observed from Table VI that the voltages on theMcCalmont bus vary from 29.5 kV (0.21 p.u.) to 191.4 kV(1.39 p.u.).
7. SUMMARY
The primary objective of this paper is to presentthe fault analysis of a 138-kV six-phase line. Thefault types that could arise in a six-phase system arediscussed in Section 2. Section 3 presents a step-by-step procedure to evaluate source or Thevenin impedanceat each end of the six-phase line from the existingshort-circuit study results. The fault analysis isdescribed for an uncommon fault type by the method ofphase coordinates in Section 4. Section 5 deals withthe application of the analysis to an existing double-circuit line which has the potential to operate as asix-phase line. Results, conclusions and summary bringout the salient features of the analysis. The entirepaper has been documented for direct use by utilityengineers.
FIGURES REFERRED TO IN TEXT
McCalmont
Kilgore
Figure 1. One Line Diagram of 138-kVSpringdale-McCalmont, Line
McCalmont
G0 pu(
1.0 pu .N'"a
Sprin dale
Allegheny Ld. #4
Fed. St 138
Shaff. Corner
---White Valley
Wycoff Junction
Huntingdon 138
Three-Phase Double-Circuit,
- Springdale 1.0 pu
Figure 2. Representation of Three-Phase Double-Circuit Line forSource Impedance Calculations.
Figuire 3. Springdale-McCrnlmont Line With Six-Phlase Sources(This represents equivalent six-phase case of theline shown in Figure 1. Three-phase/six-phaseinterface transformers' impedances are neglec.ed.
a'1
,a. 4
b
c E.~~~~~Id c
f
Figure 4. Schenatic for Phase 'b'-Phase 'c'-
Ground Fault on a Six-Phase Line.
1210
1211
Table IV
Fault Currents For All The Significant Faults on McCalmont Bus
[1] L.O. Barthold--Optimization of Open-Wire Trans-mission Lines," U.S. Patent 3,249,773. May 3,1966.
[2] L.O. Barthold and H.C. Barnes, "High Phase OrderPower Transmission," CIGRE Study Committee No. 31Report, 1972 and ELECTRA, No. 24, pp. 139-153,1973.
[3] H.C. Barnes, "Energy Transfer I - Overhead Trans-mission Systems," Keynote Address - Conference on
Research for the Electric Power Industry, Wash-ington, D.C., December 11-14, 1972.
[4] S.S. Venkata, "Reliability and Economic Analysesof Higher-Phase-Order Electric Transmission Sys-tem," Final Report on Grant No. 74 ENGR 10400submitted to NSF, July 1977.
[5] , "Feasibility Studies of Higher-Order Phase Electrical Transmission Systems(Phase I)," Final Report to Allegheny Power Sys-tem, Greensburg, Pennsylvania, 1976-77.
[6] , "Feasibility Studies of Higher-Order Phase Electrical Transmission Systems(Phase II)," Final Report to Allegheny PowerSystem, Greensburg, Pennsylvania, 1977-78.
[7 ] , "Feasibility Studies of Higher-Order Phase Electrical Transmission Systems(Phase III)," Final Report to Allegheny PowerSystem, Greensburg, Pennsylvania, 1978-79.
[8] N.B. Bhatt, S.S. Venkata, W.C. Guyker, W.H.Booth, "Six-Phase (Multi-Phase) Power Transmis-sion Systems: Fault Analysis," IEEE Transactionson Power Apparatus and Systems, Vol. PAS-96, No.3, May/June 1977, pp. 758-767.
[9] S.S. Venkata, N.B. Bhatt, W.C. Guyker, "Six-Phase(Multi-Phase) Power Transmission System: Conceptand Reliability Aspects," Paper No. A 76 504-1,presented at the 1976 IEEE Summer Power Meeting,
-Portland, Oregon, July 18-23, 1976.
[101 W.C. Guyker, W.H. Booth, M.A. Jansen, S.S.Venkata, E.K. Stanek, N.B. Bhatt, "138-kV, Six-Phase Transmission System Feasibility," Proceed-ings of the 1978 American Power Conference,Chicago, Illinois, April 25, 1978, pp. 1293-1305.
[11] W.C. Guyker, W.H. Booth, S.S. Venkata, "138-kV,Six-Phase Power Transmission Feasibility: AnOverview," presented at the Pennsylvania ElectricAssociation's Planning Committee Meeting, ValleyForge, Pennsylvania, Mlay 1-2, 1979.
[12] W.C. Guyker, W.H. Booth, J.R. Kondragunta, E.K.Stanek, and S.S. Venkata, "Protection of 138-kV,Six-Phase Transmission System," presented at thePennsylvania Electric Association's Electric Re-lay Committee Meeting, Tamiment, Pennsylvania,October 12, 1979.
[13] W.C. Guyker, W.H. Booth, and S.S. Venkata, "138-kV Six-Phase Power Transmission Feasibility,"Transmission and Distribution, October 1, 1979,pp. 78-79.
[14] M. Chinnarao and S.S. Venkata, "A Six-PhaseTransmission Line Simulator," presented at the1979 Mid-West Power Symposium, The Ohio StateUniversity, Columbus, Ohio, October 11-12, 1979.
[15] lIarstad Associates, Inc., "Skagit Loss Reductionand Transmission Uprate Study," Report for Cityof Seattle, Department of Lighting, Seattle,Washington, October 1977.
[16] J.R. Stewart and D.D. Wilson, "Report on Feasi-bility of High Phase Order Transmissions," (ERDAContract E(49-18)2066), United State Energy Re-search and Development Administration, February1977.
[17] S.S. Venkata, W.C. Guyker, W.H. Booth, et. al.,"EPPC--A Software for Six-Phase Line Design," tobe submitted to 1981 IEEE Transmission and Dis-tribution Conference, Minneapolis, Minnesota,October 1981.
DiscussionsF. R. Bergseth (University of Washington, Seattle, WA): The authorshave presented a significant addition to the pioneering work on six-phase systems reported earlier by some of these same authors.(8)*
In this paper, as in the previous paper, the authors have used theassumption of complete transposition of the line. This assumptionresults in equality of all the off-diagonal terms, Zm, of the impedancematrix. In turn, as a further consequence, the phase-coordinate methodof fault current calculations as presented in the paper is valid. It may beof interest to illustrate the consequences of something less than com-plete transposition in some sample fault calculations.
In a study made of converting an existing 230 kV double-circuit linein the Pacific Northwest to six-phase operation(l 5) a differenttransposition pattern was assumed. By simply "rolling" the six conduc-tors one space at a time fewer transpositions were required than for the"complete" transposition which requires many interchanges of conduc-tor positions. Furthermore the line-to-line voltage between adjacentconductors remains fixed whereas with complete transposition twicenormal voltage would appear between adjacent conductors (a-d, for ex-ample) at certain points in the transposition sequence.With the rolled type of transposition the off-diagonal terms, Zm, of
the impedance matrix are no longer identical. The symmetrical compo-nent impedance matrix remains diagonal however, and thereforebalanced (positive-phase-sequence) currents cause only balancedvoltage drops, which is necessary for satisfactory operation of thesystem. The symmetrical component impedances, Z1 through Z5 are nolonger all equal, however, and this fact precludes the use of the authors'"phase coordinates" for fault computation. Table I, following, il-lustrates typical values for the several impedances for the line mention-ed above which had a common configuration of two lines on a singletower forming an almost hexagonal spacing pattern.The authors' approach greatly simplifies fault current computations
if the "complete" transposition assumption may be used as an approx-imation for the "rolled" case. To gain some insight into the errors in-volved with this approach some sample fault current computations weremade using symmetrical components for the rolled line and phase coor-dinates of the paper for the completely transposed assumption. Faultsat the end of a 100 mile section of the line with parameters as in Table Iwere considered. An infinite 230 kV bus was assumed at the sendingend.
For the sample faults selected the symmetrical component relationsproceed as follows:
Six-phase Fault:
11 = E/Zl
If- I1
One-Line-to-Neutral:
Ek Z0 + Z1 +
k = 0 5If = 6I1
Line-to-Line (Adjacent lines, b-c):2E
13 =
Z2 +Z3 Z4 Z5
1 + 3Z2 + 4Z3 + 3Z4 + 5
If = 313
Line-to-Line (Diametrical, a-d):E
1+ Z: + Z5113
If =31i1
Table II summarizes the fault currents calculated for the hypotheticalline section chosen. It will be noted that the error involved in using thesimplifying assumption is small, approximately 13 per-cent in the worstcase. The one-line-to-neutral case, which is perhaps the most commonlyexperienced fault, is exactly the same for -both methods as a conse-
1215
quence of the usual assumption neglecting the conductor height incalculating depth of return. If ground wires were present over the phaseconductors there would probably be a small difference in the calculatedvalues by the two methods. It would be of further interest to learn ofany errors introduced by the phase-coordinate method for faults closeto a rotating machine where Zl # Z2 (in terms of three-phase sym-metrical components).
*Numerical superscripts refer to the references of the original paper.
J. R. Stewart and D. D. Wilson (Power Technologies, Inc., Schenec-tady, NY): One of the technical areas which is important to the successof the high phase order concept is that of system protection. This papermakes a contribution in the assessment of fault types and currents andtheir effect on relay settings.The method is that of the establishment of a Thevenin equivalent of
the entire system at the fault location and the application of terminalconditions representing the fault. By treating the fault as if the systemhad a set of external terminals at the fault point, any fault can be ex-amined without constraints imposed by sequence network interconnec-tions.The discussors have several questions on the development of theanalysis:
1. The calculation of equivalent impedances in this paper assumes afully transposed line where the phase impedance matrix has onlytwo distinct terms, the self and the mutual term. The primarybenefits of six phase accrue because of the reduced voltages be-tween the adjacent conductors due to the sixty degree electricalangle. If complete conductor transposition is used, these benefitsare lost. Therefore, if the advantages of high phase order are to beexploited, the best which can be accomplished is a roll transposi-tion where each phase retains its relationship to all others. For asix phase line this results in a circulant matrix of four distinctterms, the self and three distinct mutuals. This roll transpositiondoes diagonalize the symmetrical component impedance matrix sothat the system is balanced. Do the authors know how much erroris introduced in their calculation by the assumption of fulltransposition? If this error is insignificant then a worthwhile sav-ings in computation may be made by assuming full transpositioneven though it is not practical.
2. The discussors have duplicated equations 11 through 21 and agreethat this is a proper method. However, it is unclear if the properapplication is made of these equations in Section 5. The fault con-ditions must be applied to a Thevenin equivalent of the full systemat the fault point. Once the voltages on the six conductors at thefault point and the current leaving the six conductors are deter-mined, these results can be applied back to the original system toget the contributions from various parts of the system. It is incor-rect to assume the lines on both sides of the fault can be treatedseparately and then to sum the results, as the wording would seemto imply. The superposition theorem does not allow tamperingwith the network. Would the authors please elaborate on theirprocedure for applying equations 18-21 for this specific exampleto clarify this point.
3. The implication of Figure 3 is that the six phase line in question isthe only link between the two segments of the system. Normallythere are many parallel paths and the 138 kV six phase line may ac-tually be one of the weaker of these. Thus, these parallel pathsmay be important in a fault study because of the relative contribu-
Z4 Z5
1216
tions from different parts of the system. The method proposed inthe paper correctly accounts for these parallel paths if an overallThevenin eqivalent of the system is taken at the fault location andthe resulting fault current is injected into the whole system. Havethe authors considered the impact of the assumption that the twosides can be separated on the accuracy of the results? How muchof the system can be treated using the phase coordinate methodbecause of the need for handing 6 x 6 matrices for all the lines?
4. Table IV gives calculated fault currents. The discussors attemptedto duplicate the b-c-n case by another calculation method to verifythe results. While the angles agreed, the currents were high,although in the proper ratio. Also, the McCalmont bus voltagesdid not match the values of Table VI. By assuming the network tobe severed on both sides of the fault and computing the two sidesseparately (as discussed above) the McCalmont voltages matchTable VI but the currents still do not. There are several possibleexplanations: Was Table IV calculated using a source voltage of147.7 kV as Section 3.1 would indicate? The presence of 147.7 en-tries in Tables V and VI would indicate that it was. Were the im-pedances of equations 22 and 23 and the McCalmont source im-pedance of Section 3.2 used for the computation of these tables?One possibility is that the computations were carried out byseparating the network at the fault point. As a small point,sometimes the use of an odd base voltage causes more ultimateconfusion than it saves. It may be preferable to use a 138 kV baseand to allow the voltage to be greater than 1 per unit.
5. The neutral shift in Tables V and VI is interesting as this is impor-tant in surge arrester application. Have authors investigated thequestion of neutral shift in terms of realistic systems and im-pedances and have they any conclusions?
6. With full transposition there should be symmetry between thephases. Do the authors know of a physical reason why the cur-rents to ground from phases- b and c should be different? Theydo calculate that way but what is the physical reason?
7. Six phase transmission certainly appears to be practical and maybe especially useful in uprating double circuit three phase lines asthis paper suggests. Based on PTI experience with constructionand operation of a short six phase test line and construction of ashort twelve phase test line, it appears to us that twelve phase mayalso be practical and perhaps even more useful than six phase as asubstitute for three phase at the highest transmission voltages [1].Economic studies are currently assessing the potential of twelvephase. Protective relaying will be even more detailed with the in-crease of possible fault combinations. Have the authors anyobservations on the practicality of relaying of a twelve phase line?
The discussors thank the authors for a stimulating contribution to thecontinuing discussion of high phase order.
REFERENCE
[1] J. R. Stewart and I. S. Grant, "High Phase Order--Ready for Ap-plication," IEEE Paper 81 TD 675-8 to be presented at the IEEETransmission and Distribution Conference, Minneapolis,September, 1981.
Manuscript received August 17, 1981.
therefore, the relaying scheme will be much more complex if conven-tional relaying schemes using distance relays are used. Will it not beworthwhile to consider a microcomputer for coping up with such aproblem.4. It may be worthwhile to evolve a generalized fault analysis for-mula taking into account the frequency dependence of lineparameters for inclusion into a transient response program for faultsurges, recovery voltages, etc.5. A recent paper on a similar subject increases the power transfer bycreating a phase shift in the second circuit. In what way the six phasescheme will be more economical than that?.
Finally, I would like to congratulate the authors for their research ef-forts and encourage them to perform transient fault studies on the Six-phase systems and develop a comprehensive relaying scheme for protec-tion of such systems.
Manuscript received August 18, 1981.
J. L. Willems (University of Gent, Belgium): In this interesting paperthe authors show that the analysis of short-circuit currents in six-phasepower systems is not really more complicated than in t-hree-phasedouble-circuit transmission systems and that it does not require addi-tional data. I want to comment on the authors' statement that the phasecoordinate method is superior to the symmetrical component techni-ques for the computation of short circuits in six-phase systems. It is myfeeling that the main reason why this is true is the assumption madethroughout this paper that the six-phase power system is completelytransposed [11; the phase coordinate method leads to a much more com-plicated analysis for transmission lines which are only cyclicallytransposed than for completely transposed lines. The former case alsooccurs as the six-phase equivalent of a three-phase element connected toa six-phase line through a three-phase-to-six-phase transformer [2l.For completely transposed power systems other component schemes
can be developed which yield a simpler analysis than the symmetricalcomponent technique and are certainly competitive to phase coor-dinates. Consider the impedance matrix of a completely transposed six-phase element:
Zs Zm Zm Zm Zm Zm
Zm s m m zm %m
L
zm zm zs zm zm zmz z z z zinz Zm Z s Im 7mz z z .z zZm zmi m Z m
z z z z zin in in i
mzmzmz
The phase sequence is denoted by "abcdef". Let the phase currentsand voltages be transformed to the difference and sum components;e.g. for the currents this yields the components
2 aI Id), 5- 2(Ic- f, 2 e b
P. K. Dash (Regional Engineering College, Rourkela, India): Theauthors are commended for an interesting and timely paper on "SixPhase Transmission Systems". The paper is very useful to utilityengineers, system designers and engineering educators dealing withtransmission systems planning. The discussor would very much ap-preciate the authors commenting on the following specific questions:
I. The fault analysis presented in the papers considers nearly 23 typesof faults, but mostly the shunt faults through zero impedance. Boththe series faults and faults through impedance have not been treatedin the paper. In some cases a combination of series and shunt faultcan occur or simultaneous shunt faults on the different phases of theSix-phase system. In such cases how do the authors intend to modifytheir results?2. It seems to the discussor that the determination of self and mutualimpedances of the transmission system will be affected if the six-phase system is untransposed. Would the authors please comment?.3. In the six-phase system, the fault types considered are 23, whereasfor a 3-phase system the fault types are 5. For the six-phase system,
I4 =2 (Ia+Id), I5 = 2 ( f 6 2 e b
Then the transformed impedance matrix is
LAZt =
]
where the matrix A is diagonal with equal elements (Zs-Zm) on thediagonal; the matrix B is a symmetrical circulant matrix with equalelements (Zs+Zm) on the diagonal and equal elements (2Zm) else-where. This matrix B can then be diagonalized by means of the three-phase Clarke components. Note that the sum components of a balancedset of source voltages are zero; this may lead to considerable simplica-tion. Some fault types are very easily analysed by means of this ap-proach.
REFERENCES
[1] J. L. Willems, "Fault Analysis and Component Schemes for Poly-phase Power Systems," Electrical Power and Energy Systems, Vol.2, No. 1, January 1980, pp. 43-48.
[2] J. L. Willems, "The Analysis of Interconnected Three-Phase andPolyphase Power Systems", 1979 IEEE PES Summer Meeting,Vancouver, B.C., Paper A 79 504-2, July 1979.
Manuscript received September 16, 1981.
S. S. Venkata, W. C. Guyker, W. H. Booth, J. Kondragunta, N. K.Saini and E. K. Stanek: The authors are grateful to all the discussors fortheir interesting and thought-provoking observations and questions.1. Each of them raised an issue on the validity of assuming a six-phaseline to be "completely" transposed. We, the authors, decided that thiswould be the most desirable and practical approach considering the factthere were 23 significant faults to be analyzed. As Professor Bergsethcorrectly pointed out in his discussion, that our assumption wasreasonable and justifiable on the basis that at most 13% error would oc-cur if the line were treated to be totally transposed, instead of,"cyclically" transposed. We feel more confidently now that it is indeedthe best way to proceed with the fault analysis. We also suggest that ifthere are any critical cases, then those could be re-analyzed by treatingthe line to be either untransposed or "roll" transposed, since themethod we presented in the paper is general and only [Z] matrix of theline need to be appropriately re-defined. Since the entire idea oftransposition of a six-phase line is not a familiar topic, we list below,the different series impedance matrix of the six-phase line under thevarious conditions discussed above.
(a) For an untransposed line:8
0 0@ Z.aa ab ac ad Zae Laf
<;) ÆZ\Dr bbc dd be bf
\CC cd ce cf[iL
CSymimetric %dd de df
'ZeeZef
'Zff
(A.1)
(b) For a "roll" transposed line with a conductor configuration withvertical symmetry and with six barrels of transposition: 15, A.1, A.2
LZI =
) -Zs Zml Zm2Zm3 Zm2 Zml-Zs ml Zm2 m3 m2
Zs Zml Zm2 Zrn3Zs Zml zm2
i) Zs Zml(e) Lzs-
(A.2)
In equation (A.2), Zml is the mutual impedance resulting from theaverage distance between all adjacent conductors. Zm2 is the mutualimpedance arising due to the mean distance between all alternate con-ductors and Zm3 results due to the mean distance between oppositeconductors. In other words, for a cyclically transposed line, one selfand three different mutual elements would occur. As shown by Pro-fessor Bergsethl5 and others A.1, A.2 that when equation (A.2) istransformed into its sequence form using the symmetrical transforma-tion matrix [T]8, the resulting matrix is still a diagonal one. In this case,four different self sequence impedance elements would result. Theseare:
z0 = zs + 2Zml + 2ZLm2 +L311 z55 = ZS + Zml Zm2 Z
~~m3
Z22 Z44 Zs Zml Zm2 Zm3
Z33 = ZS 2Zml + 2Z 2 )Z3
(A.3)
1217
(c) Finally for a completely transposed line with 15 barrels oftransposition, the [Z] matrix is given in equations (9) and (10) of thepaper. As correctly observed by the discussors, it is practically difficult,if not impossible, to achieve this.2. We regret if the application of the Thevenin's theorem as presentedin Section 5 of the paper was not clear. What we aimed at, was to obtaina 2-port equivalent at each end of the subject line as depicted in FiguresA. I and A.2. We did not either tamper with or tear the network asMessrs Stewart and Wilson imply. Once we obtained the equivalentsource impedances Zs and Zm at each terminal bus as shown in FigureA.2, we then applied the Superposition Theorem in the very classicalsense by considering one voltage source at a time and shorting the othervoltage source.3. In view of the comments made in 2. above, we are certain that the ef-fect of any parallel path for fault current flow is already taken into ac-count. Our method should work whether any fault impedance is presentor not. On the question of how much of the system needs accurate 6 x6 representation, we suggest, based on our experience, that only thesubject line be modelled that way. The remaining system can be treatedas totally balanced. We will investigate this aspect further and reportour findings at a later time.4. We regret the numerical errors in equations (22) and (23). Theyshould read as
What were incorrectly reported are indeed ZsL and ZmL for the26.4-mile test line. Therefore, it was no wonder that Messrs Stewart andWilson could not repeat the results we reported. Using the above cor-rected values for Zs and Zm, we did obtain the results as presented inTables IV to VI of the paper.As they correctly observed, we did use 147.7 kV (1.07 p.u.) as the
system open-circuit voltage as per APS engineers recommendation. Wecould not elaborate on many points such as this due to the space limita-tion.At this point, we would also like to report a few additional
typographical errors in the paper. There are:a) In Table 11 (b), "Kilgo" should read "Kilgore"b) In Legend under Table 11 (b), 0 is in degreesc) In Table III, for a-b-d-f-n fault, the expression for lb should read
a m
s s nJ3Z
d) In Table III, for b-f fault, the expression for If should be
E (b-b5)2 (Zs zm
5. We are thankful to Messers Stewart and Wilson for observing theneutral shift in Tables V and VI for voltages. We are yet to investigatethis shift in terms of realistic systems and impedances.6. We strongly feel that lb and Ic for b-c-n fault are different becauseof the phase sequence. This aspect is not peculiar to six-phase lines. Itcan easily be shownA.3 that the two phase currents, for a double-line-to-ground fault in a three-phase system, get interchanged if the phasesequence is reversed.7. We are studying practical ways to relay a six-phase line. It hasrecently been brought to our attention that Auburn University is alsoinvestigating this important problem under a Electric Power ResearchInstitute contractA.4. In our opinion, relaying a twelve-phase line is achallenging task. It is our conjecture, that a microprocessor-basedsystem is the answer. This observation was also correctly made by Pro-fessor Dash.8. We will look into the errors introduced by our method for faultsclose to a rotating machine as per Professor Bergseth's suggestion.9. In our detailed investigation, we found that all the 23 significantfaults are not easily amenable to the symmetrical component method ofanalysis even when the sequence impedance matrix of the line ifdiagonal. However, the phase coordinate method allows such analysiswhether the line is completely transposed or cyclically transposed. Wedo admit, as Professor Willems points out, that the analysis is more dif-ficult in the latter case than in the former case. He has presented a newand interesting transformation which he claims is simpler. He also con-
1218
tends that only some fault types are easily analyzed by this approach.Can all the 23 significant faults be analyzed with his approach?10. In regard to Professor Dash's other comments, we have alreadyanalyzed all fault types with fault impedances included. For lack ofspace, we could not report them in this paper. We will make every effortto report these along with other related results soon. We do not feel,from a practical stand point, that it is desirable to consider fault casesinvolving a combination of series and shunt faults. We will investigatethis aspect only if such work is warrented.11. We concur with Professor Dash on the need to develop an analysisto take switching surges into effect. To date only PTI has successfullysolved this problem using TNA approach and reported recently bythemA.5 .12. Professor Dash refers to "a recent paper on a similar subject...".We would like to receive more information on that.
In summary, it is gratifying to note that the interest on this subject isgrowing day by day. We sincerely hope that the multi-phase or high-phase-order concept becomes a reality due to the combined efforts ofall the researchers involved. We are once again thankful to all thediscussors for their valuable contributions.
McCal mont Spri ngdal e
Zsm,Z mmM ZsL'ZmL ZsS' ZmS_ i _~
*'1MoM
E1MEOM.C.
138-kV SIX- I sPHASE LINE Io
Os
EisE
Figure A.1: One-Line Diagram of A 138-kV Six-Phase Line as anIntegral Part of A Three-Phase System.
REFERENCES
[A. 1] J. L. Willems, "The Analysis of Interconnected Three-Phase andPolyphase Power Systems," Presented in 1979 IEEE PES Sum-mer Meeting, Vancouber, B.C., Paper A79-504-2, July 1979.
[A.2] M. M. Hassan, Ph.D. Comprehensive Examination, WestVirginia University, Morgantown, WV, 1979.
[A.3] Personal Communication with Professor Bergseth, Summer1981.
[A.4] Personal Communication with EPRI, Palo Alto, California,Summer 1981.
[A.5] I. S. Grant, J. R. Stewart, D. D. Wilson, T. F. Garrity, "HighPhase Order Transmission Line Research," CIGRE Symposium22-81, Paper No. 220-02, Stockholm, 1981.
Figure A.2: One-Line Thevenin Equivalent of the Six-Phase LineShown in Figure A. 1. Manuscript received October 27, 1981.
