Multiphase power transmission research—A survey

Electric Power Systems Research, 24 (1992) 207-215

207

Multiphase power transmission research

a survey

S. N. Tiwari and G. K. Singh Department of Electrical Engineering, MNR Engineering College, Allahabad 211004 (India)

A. S. Bin Saroor Department of Electrical Engineering, University of Aden (Republic of Yemen)

(Received March 7, 1992)

Abstract With the continual growth in power generation, trends towards large unit plant capacity and remote siting of power plants, and the necessity of interconnection, transmission systems have assumed greater importance than ever before. Conventionally, increasingly higher voltages have been the main technological drive for enhancing the power transfer capability of overhead AC lines. This has brought about the transmission of electrical power at the UHV level. However, because of the several drawbacks and technological problems associated with such extremely high voltages, research has been underway for the last two decades to investigate transmission of power by multiphase (also referred to as high phase order or polyphase) lines employing more than three phases as a potential alternative to the conventional three-phase systems. This paper reviews the progress made in multiphase transmission research and development since its inception. Attempts are made to highlight the current and future issues involved for the development of this transmission technology for future applications.

1. I n t r o d u c t i o n Owing to ever-increasing power supply demands, electrical utilities all over the world are facing the pressing need to increase their transmission capacity in the next few years. The transmission of bulk power is receiving ever greater attention because of remotely located major generating and load centres as well as the necessity of interconnection. The most common technological drive to increase transmission capacity by increasing the system voltages of AC overhead lines has led to UHV levels in several parts of the world. However, the transmission of power at such extremely high voltages has the drawbacks of introducing strong electric fields at ground level with the possibility of biological effects, audible and radio noise, visual pollution, increased demands for rights of way, etc. The problem of acquiring a right of way (ROW) is now becoming more and more difficult because of public opposition and awareness of these effects, the growing importance of forests and the high cost of land. Multiphase transmission (MPT) employing more than three phases [1] is a unique approach to the problem of increasing transmission 0378-7796/92/$5.00

capability of overhead lines and alleviating certain problems that have developed for the conventional three-phase systems in recent years. Since the inception of the concept, MPT research has made rapid strides, beginning with the investigation of basic feasibility [2-9], and going on to the construction and testing of experimental lines for six and twelve phases, substations, etc. [10-12]. This paper deals with a state-of-the-art discussion of MPT research and development, highlighting analytical, technical and economical considerations as well as various issues addressed in the litarature towards the practical realization of this new transmission technology in the near future.

2. Concept, benefits a n d v o l t a g e nomenclature

2.1. Concept and feasibility studies The concept of multiphase transmission emerged, for the first time, in 1972 at a CIGRE meeting, where Barthold and Barnes [1] presented calculations of the power density of open © 1992

Elsevier Sequoia. All rights reserved

208

wire transmission systems. It was shown that the ultimate power density capability is about 12 000 MW/m", which is several times higher than achieved by the usual three-phase lines. Thus, the idea of a more efficient utilization of the right-of-way corridor came into being, with the use of a higher number of phases (more than three) as one of the options permitting increased power without increased space requirements. Detailed computations involving phases from 3 to 36 were made to examine the initial feasibility of multiphase transmission. Since then the development of multiphase systems has taken place mainly along the following lines: completely new designs for six-phase and twelve-phase lines; uprating of existing transmission facilities with or without reconductoring.

2.2. Benefits The potential benefits of a multiphase system result from the smaller phase angle between the phases, leading to lower adjacent phase to phase voltages. The most significant advantages include: increased power transfer capability with efficient utilization of rights of way, reduced electrical evironment effects, compact structures, reduced imbalance due to the possibility of having symmetrical conductor arrangements, and compatibility with existing systems.

2.3. System voltage nomenclature In contrast to three-phase systems, there are several line voltages having different magnitudes in a multiphase system. The adjacent phase to phase voltage, which is used to describe a threephase system, decreases with the phase order (being 1.732, 1, 0.517 and 0.261 for systems having 3, 6, 12 and 24 phases, respectively) and does not provide a convenient system voltage nomenclature. Efforts have been made to unify the definition of system voltages in the USA [4] and the phase to ground voltage has been favoured to describe a multiphase system. Table 1 shows the relative picture of the phase to ground and phase to phase voltages (for a circular configuration of conductors) for 3 to 24 phases.

T A B L E 1. Phase to ground and I)hasc t() plmsc (:lcli~l<<,l~i voltages P h a s e to g r o u n d v o l t a g e (kV)

P h a s e to p h a s e ( a d j a c e n t ) v o l t a g e (kV)

76 127 231 442

3"0

6-~

12@

24 (I)

132 220 400 765

76 127

3,4 67 120 229

20 35 (;0 l 15

231

142

reference to the 462 kV (phase to ground) 3-, 6and 12-phase lines [14] depicted in Fig. 1 and employing the same number of conductors, right of way, air space and thermal ratings, loadability (sending-end power expressed in p.u. of SIL) the curves shown in Fig. 2 are obtained. Based on the findings of the study, it is found that MPT lines offer more power transfer for the same performance criteria (voltage drop and stability margin) the benefit in terms of line loadability increases with phase order;

/

/

X

\

\

t

t

, (a)

(b)

2-

%

(c)

Fig. l. C o n d u c t o r c o n f i g u r a t i o n s for a 462 kV p h a s e to g r o u n d line (24.1.762 in. Bluebird c o n d u c t o r s , 50 ft d i a m e t e r circle, 50 fl m i n i m u m g r o u n d clearance). (a) 3-40 l i n e ( S l l , = 3275 M W ) z - (0.0063 + j0.398) L / m i l e y j 10.638 ~ls

j 6 th

(b) 6-6 l i n e ( S I I , = 1494 M W ) z (0.0126 ~ j0,4726) ~)/mile y = j8.9606 ~ts

(c) 12-,~) l i n e ( S I L = 5485 M W ) z (0.025 + j0.5667) t l ! m i l e y - j7.4830 i~s

462 KV(L-G)3-q~{ine,SIL=3275 MW 462 KV(L-G) 6-~ line,SIL-/~,@4 MW KV(L-G)12 C~line SIL= 5 / . 8 5 M W

~ 4 6 2

._c >-Z,

i3 -1 2

3. L o a d a b i l i t y c h a r a c t e r i s t i c s In a recent study [13] the loadability of MPT lines has been investigated both qualitatively and quantitatively under various system performance and operating criteria. With specific

100

200

300

4 0

500

600

Line length in miles

Fig. 2. G e n e r a l i z e d 462 kV lines.

loadability

c u r v e s for t h r e e a l t e r n a t i v e

209

- an increase in system strength, series compensation and voltage drop limitation yields an increase in line loadability with phase-order increase, whereas a decrease in the stability margin results in increased line loadability with phase order; - a six-phase uprating of a double-circuit threephase line yields around 75% benefit in line loadability; - MPT lines have better voltage performance and maintain a better stability margin, especially during heavy loading, than their three-phase counterparts; - the requirements of minimum VAR reserves for MPT lines are progressively lower than for three-phase lines at all loading levels.

4. C o m p o n e n t t r a n s f o r m a t i o n m a t r i c e s

The methods of symmetrical and Clarke's component transformations are well established for the analysis of three-phase systems for unbalanced conditions and faults. There has been a considerable amount of work on the derivation of such transformations for multiphase systems, particularly the six-phase and .twelve-phase systems [4, 15-27]. However, the symmetrical component transformation for six phases by Bhatt et al. [15] and twelve phases by Stewart and Wilson [4], the power invariant symmetrical and Clarke's component transformations by Singh et al. [16, 17] and those by Willems [18 20, 23] and Augugliaro et al. [22] are worthy of mention here.

5. L i n e p a r a m e t e r s

The basic electrical parameters on an MPT line are resistance R, inductance L, capacitance C and conductance G. The procedure for calculating R and G is similar to that for conventional threephase lines. The expressions for L and C, whose values depend upon the conductor configuration and line geometry, have been reported in several works [2 4, 28-31] for transposed and untransposed conditions. The significant findings of these studies may be summarized as follows: - MPT lines possess higher inductive and capacitive reactance than their three-phase counterparts; - the effectiveness of transposition (only cyclic) on MPT lines is only slight and hence it is not needed;

- MPT lines are characterized by higher and stronger positive-sequence parameters; the Xo/X1 ratios for MPT lines are higher than their lower phase order counterparts. 6. E l e c t r i c a l a n d m e c h a n i c a l c h a r a c t e r i s t i c s

The steady-state characteristics of six- and twelve-phase lines have formed the subject of investigation of several studies [3-5,10-12, 14, 32]. Takasaki et al. [32] have carried out a detailed investigation of the voltage gradient on the conductor surface, the electric field intensity at ground level and the phase distribution of the energy, etc. of a six-phase line. The investigation contains a comparative study between a doublecircuit three-phase line and a six-phase line with different phase arrangements. Grant and Stewart [14] have carried out an extensive study of the mechanical and electrical characteristics of EHV multiphase lines. In the study, 462 kV six- and twelve-phase lines with power transfer capability similar to a 1200 kV three-phase line were compared. Furthermore, the study provides details of the design of support structures and insulators based on clearances and phase spacings. 7. T e s t l i n e s a n d h a r d w a r e d e v e l o p m e n t

The construction and testing of experimental six- and twelve-phase lines have been carried by Power Technologies Inc., USA. Adequate data and experimental results, design criteria for MPT lines, substations, insulators, etc. are described in several contributions [10-12]. Earlier, Allegheny Power Company, in association with West Virginia University, USA, conducted studies on converting 138 kV double-circuit threephase lines to six-phase lines and the findings were reported [3, 33]. In view of these developments, the Central Power Research Institute (CPRI) Bangalore, India, has undertaken certain preliminary studies which examine a 462 kV sixphase transmission line as an alternative to an 800 kV double-circuit three-phase transmission line, as well as the conversion of certain existing 220 and 400 kV double-circuit three-phase lines to six-phase operation [6]. 8. E c o n o m i c v i a b i l i t y a n a l y s i s

An economic optimization study has been carried out by Stewart et al. [34] considering five

210

alternative MPT schemes under the assumptions of specific technical and economic parameters. The study clearly demonstrates the economic viability of MPT schemes and concludes that the overall cost reduces with multiphase systems. Kallaur and Grant [35], found the six-phase line to be an economic uprating tool for double-circuit three-phase lines.

9. Transformers for multiphase conversions The transformers associated with MPT systems are basically required to obtain high phase order (6, 9, 12, etc) conversion from three phase. A three-phase to six-phase conversion is relatively easy and a variety of connection schemes, namely, wye star, d e l t a - s t a r , wye--hexagon, d e l t a - h e x a g o n , etc. have been considered and discussed extensively in the literature [3, 36-42]. However, higher phase order conversions require specially built units, although such conversions have been employed earlier [43-46] in synchronous converters and valves. Among the schemes to derive twelve-phase conversion from three phase, those worthy of mention are: doublechord connection, simple double-chord connection, interconnected-star or zig-zag twelve-phase connection [44] and the wye wye delta phase shifting transformer [12].

multiphase transformers was developed for unbalanced network analysis [37 40]. The transformer equivalent circuits showing correspondence between multiphase sequences and threephase sequences on the multiphase and threephase sides, respectively, were developed by Willems [36] for six-phase and by the present authors for twelve-phase conversion. 10.1.2. Transmission lines MPT lines have been modelled by the phase impedance matrix [15, 16, 36], ABCD parameters [36 39] and the three-phase equivalent of a sixphase line, including the interfacing three-phase/ six-phase transformers at either end, in a composite three-phase and six-phase network [36 39]. Six-phase line models suitable for load flow studies have also been discussed by Venkata et al. [47]. Some of these approaches have been generalized to 12-phase and N-phase systems [41, 42]. 10.1.3. Loads Loads on an MPT system have been represented by constant impedances/admittances under balanced as well as unbalanced conditions [36 39]. Loads in the form of multiphase machines have been modelled and their three-phase equivalent representation employing six-phase/ three-phase interfacing transformers connected to a three-phase bus was also obtained [39, 41].

10. Analytical techniques and studies

10.2. Analysis

Mathematical models for transformers, lines and loads and analytical techniques for a variety of system studies on MPT systems covering steady states and transient states have been developed. Those developments addressed in the literature are briefly summarized in this section.

10.2.1. Mixed three-phase~six-phase network analysis One of the essential features of a multiphase system analysis has been the development of' analytical tools for a mixed three-phase/six-phase (or higher phase order) network. It is believed that an MPT line, whenever realized, will always be integrated with a three-phase network via interfacing three-phase/multiphase transformers at either end. The analytical methods towards this have relied on representing: (i) a multiphase network by its equivalent three-phase network [36 39], as depicted in Fig. 3; (ii) a network containing mixed phase order elements in phase coordinates [39] similar to that shown in Fig. 4; and (iii) a network represented solely in terms of a multiphase network by replacing the three-phase network by its multiphase equivalent [39], as depicted in Fig. 5.

10.1. Mathematical models of M P T elements 10.1.1. Transformers Three-phase/six-phase transformers have been modelled as ideal transformers [36] and as ideal transformers in series with leakage impedances/ admittances of windings including off-nominal tappings [37-39]. Similar representations for three-phase/twelve-phase transformers as well as the same generalized to N-phase conversion followed next [41, 42]. An alternative model for three-phase/six-phase transformers employing the symmetrical lattice equivalent of singlephase units representing parallel windings of

211

Equivolent3-phase ndwork i- . . . . . . . . . . . . . . . . . I

C. I____

:e

I~

L1

6-¢'ine

16

3C

'

T2

. . . . . . LI~ . . . . . .

Fig. 3. Single-line diagram of a sample system. T~ = 3-<~/6-~> transformer; Te = 6-~>/3-<~ transformer.

Other important developments in this area are contained in several recent contributions [1820, 22-24, 48, 49]. 10.2.2. Load flow analysis A load flow study was carried out earlier by Guyker et al. [3] for several cases with a line operating alternatively as three-phase and sixphase. V e n k a t a et al. [2] carried out such studies on double-circuit three-phase and six-phase lines. A generalized formulation of the load flow problem and extensive investigation on a composite three-phase/six-phase system were carried out by Tiwari and Singh [50]. Various alternative schemes for power flow studies, depending on the network of interest, that is, three-phase, sixphase or both, have been presented, for balanced as well as unbalanced situations. Several case studies including the impact of converting double-circuit three-phase lines to six-phase lines have been carried out [2, 38, 47, 50]. 10.2.3. Fault analysis One of the basic requirements of a transmission planning exercise is an effective and comprehensive protection scheme. This often necessitates a series of fault analyses to obtain the status of the symmetrical and phase components of the current and voltage in all predictable fault situations. The types of faults and

~24 ..31

~2~o21

T1

~1~ LI

=s!

41

Io,

71 I

131 I

61

12L

sl

I,I

"

L~

their combinations increase rapidly with the phase order, as can be seen from Table 2. As a result, fault analysis of a multiphase system is often complex and needs a more powerful technique t h a n its three-phase counterpart. A considerable a m o u n t of research work has been directed towards the analysis of shunt faults employing transformation techniques [19, 21, 22, 24, 26, 27, 30, 33, 51 54], phase coordinate methods [25, 34, 42, 47, 51] and generalized t r e a t m e n t [51, 55-57] involving both these approaches. Since, an MPT system employs several conductors, even at lower voltage levels, the probability of open-conductor or series faults is much higher t h a n in a three-phase system. In view of this, the analysis of series faults on MPT systems has been the subject of some recent investigations [58, 59]. In addition to the analysis of sustained faults, that of sequential faults on MPT systems, particularly the six-phase system, has been carried out [60]. With these developments a substantial a m o u n t of information on faults and their characteristics is now available. However, much more effort is still needed to explore this important aspect fully. 10.2.4. Stability analysis Two categories of stability, namely, steadystate and transient, are of importance in comparing the performance of an MPT system with a three-phase system at EHV levels. In the case of steady-state stability, the synchronous reactance is used in computing the voltages and the total value of the reactance, X, for obtaining the familiar p o w e r - a n g l e diagram. The corresponding Pmax (Fig. 6) is called the steady-state stability limit. Considering the EHV transmission alternatives of Fig. 1 for a specific line length, the values of /)max are depicted in Fig. 6. As is evident from Fig. 6, higher steady-state limits are

,

/ l O S

]

Tz

IIV'

Fig. 4. Schematic diagram of the network of Fig. 3 showing bus numbering sequence for phase coordinate load flow and fault analysis.

212 l

F ..........

,

6- @ LINE

[ i

F.

~¢

~c

..........

. . . . . . . . . . . . . . .

! I i

L..... EQUIVALENT 6-PHASE NETWORK

Fig. 5. S c h e m a t i c r e p r e s e n t a t i o n of a m i x e d 3-d? a n d 6-(~ n e t w o r k for a n a l y s i s a s a n e q u i v a l e n t 6-d~ n e t w o r k . T A B L E 2. C o m p a r a t i v e s u m m a r y o f t o t a l a n d s i g n i f i c a n t c o m b i n a t i o n s of s h u n t f a u l t [47, 51, 52] Fault combination

System type

T o t a l no. of f a u l t combinations T o t a l no. of s i g n i f i c a n t fault combinations

3-~

6-~

12-~

I1

120

8178

5

23

425

©

G p: El.x E 2 Sin812

45

[2, 48, 61 63] and the h y p o t h e t i c a l n e t w o r k s e(mtaining three-phase and multiphase n(,tw()rks [62, 641. 10.2.5. Network simulator and switching transient studies Several t r a n s i e n t n e t w o r k analyser studies on six- and twelve-phase systems have been carried out by Wilson et a l [10, 14,65]. The studies summarized the specific system configurations analysed, maximum surge m a g n i t u d e s observed and the effect of variations of p a r a m e t e r s (i.e. phase to ground R M S voltage, line length. surge impedance, switching operation and circuit b r e a k e r pre-insertion resistors). Further, the t r a n s i e n t recovery voltages associated with cap a c i t a n c e switching on 138kV six-phase transmission lines have been studied by R a m a s w a m i (,t al. [66]. A recent study [67] has i b r m u l a t e d the problem of M P T line transients as an extension of the three-phase technique developed by U r a m and Miller [68]. Several cases of line terminations including faults have been studied. The other significant work carried out earlier on sixphase lines is reported in refs. 69 and 70.

~O Vbase= ,',62 k V ( L - N )

~

30

5base: 100(3MVA( per phase)

c

x 5

OI

i

20

I

20

610 80

i

,

t

100 120 1/-0 1;0 180

Angle disNacernenl (deg)

Fig. 6. P o w e r

a n g l e c u r v e for a l i n e o f l e n g t h 100 m i l e s .

a s s o c i a t e d with m u l t i p h a s e lines as compared to their lower phase order counterparts. Analysis of t r a n s i e n t stability can often be performed by applying the p o w e r angle curve to a simplified system model r e d u c e d to two machines. In performing such an analysis it is imp o r t a n t to recognize t h a t the post-contingency p o w e r a n g l e curve has a lower peak value t h a n the system's normal curve, indicating t h a t the loss of a line results in lower power transfer capability. An investigation shows t h a t the effect on the stability of losing an M P T line is more critical t h a n w h e n a lower phase order or threephase line is lost. A n u m b e r of investigations have been directed to examine this aspect for a six-phase line

10.2.6 Line protection The problem of protection of a 138 kV sixphase line against faults and o v e r v o l t a g e s was studied by G u y k e r et al. [33]. It was reported that twenty-one distance relays are needed to completely protect a six-phase line. The connection for a p e r c e n t a g e differential relay for a delta star, three-phase/six-phase transformer was shown. C h a n d r a and Singh [71] have proposed an ultra high speed relaying scheme based on the concept of travelling waves in which the frequency domain technique for modelling the six-phase line was employed.

11.

Related

developments--multiphase

machines

B e c a u s e of the potential benefits resulting fl'om the use of a phase order higher than three in transmission, some interest has also grown in the area of multiphase machines. Halley and Willyong [72] and H a n n a et al. [73, 74] have described the use of a six-phase g e n e r a t o r and its associated transformer for high power applications. Schiferl and Ong [75, 76] analysed six-phase s y n c h r o n o u s machines with AC and DC stator connections for equivalent-circuit steady-state analysis, harmonic analysis and u n i n t e r r u p t i b l e

213

power supply schemes. The characteristics of several high phase order induction motors were examined by Klingshirn [77, 78]. Other contributions in the area of mathematical modelling for steady-state analysis, dynamic stability and transient stability, Park's transformation and the inherent symmetries of a six-phase generator have also been reported [79 82]. Conclusions The investigations spread over the last two decades indicate the technical and economic viability of using a number of phases higher than three in overhead electrical power transmission. The technology of multiphase power transmission, once developed to the stage of practical application, has many advantages to offer over conventional systems. Some of these advantages include the efficient utilization of rights of way, increased power capability at much lower voltages, compact, smaller and more pleasing structures. Furthermore, multiphase transmission is an economic circuit uprating tool. Substantial progress has been made in multiphase transmission line research covering analysis, simulation, hardware development and testing. However, many problems and issues, especially those related to the development of protection schemes, transformers for multiphase conversion, efficient fault analysis tools, etc., still need to be addressed to brighten the prospects for the early application of this new transmission technology. References 1 H. C. Barnes and L. O. Barthold, High phase order power transmission, Electra, (24) (1973) 139-153. 2 S. S. Venkata, N. B. Bhatt and W. C. Guyker, Six-phase (multi-phase) power transmission: concept and reliability aspects, I E E E P E S Summer Meeting, Portland, OR, USA, 1976, Paper No. A 76 504-1. 3 W. C. Guyker, W. H. Booth, M. A. Jansen, S. S. Venkata, E. K. Stanek and N. B. Bhatt, 138 kV six-phase transmission system feasibility, Proc. Am. Power Conf. Chicago, IL , USA, 1978, pp. 1293 1305. 4 J. R. Stewart and D. D. Wilson, High phase order transmission a feasibility analysis, Part I. Steady state considerations, I E E E Trans., PAS-97 (1978) 2300 2307. 5 J. R. Stewart and D. D. Wilson, High phase order transmission a feasibility analysis, Part II. Overvoltages and insulation requirements, I E E E Trans., PAS-97 (1978) 2308 2317. 6 S. Subhas, M. K. Kumari and S. Parameswaran, Feasibility studies on multi-phase transmission systems, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India), pp. 7 19.

7 B. M. Weedy, Electric Power Systems, Wiley, Chichester, UK, 1979, pp. 68-69. 8 R. D. Begamudre, Extra High Voltage A C Transmission Engineering, Wiley Eastern, New Delhi, 1986. 9 L. P. Singh, Advanced Power System Analysis and Dynamics, Wiley Eastern, New Delhi, 2nd edn., 1986, pp. 369 398. 10 I. S. Grant, J. R. Stewart and D. D. Wilson, High phase order transmission line research, Symp. Transmission Lines and the Environment, Stockholm, Sweden, 1981, Paper No. 220-2. 11 J. R. Stewart and I. S. Grant, High phase order ready for application, IEEE Trans., PAS-I01 (1982) 1757 1767. 12 J. R. Stewart, 138 kV twelve-phase transmission line research, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India), pp. 1 7. 13 S. N. Tiwari and A. S. Bin Saroor, An investigation into loadability characteristics of EHV high phase order transmission lines, IEEE P E S Winter Meeting, New York, USA, 1991, Paper No. 91 WM 269-1 PWRS. 14 I. S. G r a n t and J. R. Stewart, Mechanical and electrical characteristics of EHV high phase order transmission, IEEE Trans., PAS-103 (1984) 3380 3385. 15 N. B. Bhatt, S. S. Venkata, W. C. Guyker and W. H. Booth, Six-phase (multi-phase) power transmission system: fault analysis, IEEE Trans., PAS-96 (1977) 758 764. 16 L. P. Singh and V. P. Sinha, Steady state analysis of multiphase power system network using group theoretic techniques, Proc. I F A C Symp. Computer Applications in Large Scale Systems, New Delhi, India, 1979, Vol. II, pp. 160 167. 17 L. P. Singh, A. C. Chaubey and V. P. Sinha, Generalized Clarke's component transformations for grounded n-port network, J. Inst. Eng. (India), Part EL, 60 (1980) 291 292. 18 J. L. Willems, Generalized Clarke's components for polyphase networks, IEEE Proc. Educ., E-12 (1969)69-71. 19 J. L. Willems, Fault analysis and component schemes for polyphase systems, Electr. Power Energy Syst., 2(1980) 43 48. 20 J. L. Willems, Symmetrical and Clarke's components for six-phase and polyphase systems, Proc. Univ. Power Engineering Conf. (UPEC), Leicester, UK, 1980. 21 S. M. Peeran, M. A. Neema and H. |. Zynal, Six-phase transmission systems: alpha beta zero components and fault analysis, IEEE P E S Summer Meeting, Vancouver, BC, Canada, 1979, Paper No. A 79 536-4. 22 A. Augugliaro, L. Dusonchent and S. Nuccio, Mixed threephase and six-phase power system analysis using symmetrical component method, Electr. Power Energy Syst., 9 (1987) 233240. 23 J. L. Willems, A new approach to the analysis of mixed three-phase and six-phase power systems, Electr. Power Energy Syst., 11 (1989) 115 121. 24 Y. Onogi and Y. Okumoto, A method of fault analysis and suppression of fault current in six-phase power transmission systems, Electr. Eng. Jpn., 99 (1979) 50 58. 25 K. Ramar, M. Krishnamurthy and T. Minipaul, A new generalized approach to fault analysis of high phase order transmission systems, Electr. Mach. Power Syst., 15 (1988) 49 62. 26 P. K. Shukla, A. Chandra and L. P. Singh, Fault analysis of multi-phase (9-phase) systems, All India Seminar on Multi. phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India), pp. 68 86. 27 U. Pal and L. P. Singh, Feasibility and fault analysis of multi-phase (twelve-phase) systems, J. Inst. Eng. (India), Part EL, 65 (1985) 138 146. 28 S. S. Venkata, W. C. Guyker, J. K. Kondragunta and N. B. Bhatt, E P P C - - a computer program for six-phase transmission line design, I E E E Trans., PAS-101 (1982) 1859-1869.

214 29 A. S. Bin Saroor and S. N. Tiwari, Six-phase power transmission: evaluation of line parameters, Symp. E H V U H V AC, H V D C Transmission Systems, Bangalore, India, 1987, Central Board of Irrigation and Power Publ., New Delhi, pp. SV17 21. 30 A. S. Bin Saroor and S. N. Tiwari, Evaluation of twelvephase (multiphase) transmission line parameters, Electr. Power Syst. Res., 15 (1988) 63 76. 31 A. S. Bin Saroor and S. N. Tiwari, Line parameters of a 500 kV six-phase transmission and its double circuit three phase counterpart, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, pp. 87 98. 32 M. Takasaki, Y. Sagisaka and K. Neri, Steady state charaeteristics of six-phase transmission system, Electr. Eng. Jpn., 102 (1982) 235 242. 33 W. C. Guyker, W. H. Booth, J. R. Kondragunta, E. K. Stanek and S. S. Venkata, Protection of 138 kV six-phase transmission system, Pennsylvania Electr. Assoc. Electric Relay Committee Meeting, Tamiment, PA, USA, 1979. 34 J. R. Stewart, E. Kallaur and I. S. Grant, Economics of high phase order transmission, IEEE Trans., PAS-103 (1984) 3386 3392. 35 E. Kallaur and I. S. Grant, Uprating without reconductoring the potential of six-phase, Canad. Communication Energy Conf., Montreal, Canada, 1982, IEEE Publ. 82 CH 1825-9, p. 120. 36 J. L. Willems, The analysis of interconnected three phase and polyphase power systems, I E E E P E S Summer Meeting, Vancouver, BC, USA, 1979, Paper No. A 79 502-2. 37 S. N. Tiwari and L. P. Singh, Steady state modelling of six-phase (multi-phase) transmission systems, Electr. Power Energy Syst., 4 (1983) 120 128. 38 S. N. Tiwari and L. P. Singh, Mathematical modelling and analysis of multi-phase systems, I E E E Trans., PAS-101 (1982) 1784 1793. 39 S. N. Tiwari and L. P. Singh, Six-phase (multiphase) power systems: some aspects of modelling and fault analysis, Electr. Power Syst. Res., 6 (1983) 193 202. 40 A. O. M. Saleh, M. A. Laughton and G. T. Stone, M-to-N phase transformer models in phase coordinates, Proc. Inst. Electr. Eng., Part C, 132 (1985) 41 48. 41 M. M. Choudhary and L. P. Singh, Generalized mathematical modelling of n-phase power system, Electr. Mach. Power Syst., 10 (1985) 367 378. 42 S. Swaroop and L. P. Singh, Generalized mathematical modelling of multi-phase (six-phase and twelve-phase) power system network for analysis in phase coordinates. J. Inst. Eng. (India), Part EL, 66 (1986) 188--195. 43 Massachusetts Inst. Technol., Electrical Engineering Dep., Magnetic Circuits and Transformers. MIT Press, Cambridge, MA, 1943. 44 R. R. Lawrence and H. E. Richards, Principles of Alternating Current Machinery, McGraw-Hill, New York, 4th edn., 1953. 45 D. G. Fink and H. W. Beaty (eds.), Standard Handbook for Electrical Engineers, McGraw-Hill, New York, 12th edn., 1987. 46 W. N. Kennedy, J. P. MacDonald and W. J. McNutt, Developments in converter transformer design, Electr. Forum (General Electric Company), 9 (3) (1984). 47 S. S. Venkata, W. C. Guyker, W. H. Booth and N. K. Saini, Six-phase line models for load flow studies in interconnected three-phase/six-phase systems in electric power problems, The Mathematical Challenge, SIAM, Philadelphia, PA, 1980. 48 S. N. Tiwari, Analysis of six-phase (multi-phase) systems integrated into a three-phase network, Nat. Power Systems

Conf., Trivandrum, India, 1983, System Soc. India, N~,~ Delhi. 49 S. N. Tiwari and L. P. Singh, Modelling of six-phase (multi phase) power transmission systems for phase coordinatt: analysis, Annu. Convention and Exhibition, India Council o¢' IEEE, New Delhi, Nov. 9 12, 1981. 50 S. N. Tiwari and L. P. Singh, Six-phase (multiphase) transmission systems: a generalized investigation of the load flow problem. Eleetr. Power ~'~vst. Res.. 5 (1982) 285 297. 51 A. S. Bin Saroor and S. N. Tiwari, A generalized formulation and analysis of shunt, faults in multi-phase transmission systems, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India. 1989. Inst. Eng. (Italia), pp. 49 67. 52 A. S. Bin Saroor, S. N. Tiwari and C. P. Gupta, An analysis of ground faults in multi-phase transmission systems, Fifth Nat. Power Systems Conf., Bangalore, India. 1988, CPRI. Bangalore, pp. 173 177. 53 S. P. Nanda, S. N. Tiwari and L. P. Siugh, Fault analysis o[' six-phase systems, Eleetr. Power Syst. Res., 4 (1981) 20l 211. 54 Y. Onogi, K. Isaka. A. Chiba and Y. Okumoto, A method of suppressing fault currents and improving the ground level electric field in a novel six-phase transmission system, IEEE Trans., PAS-102 (1983) 870 880. 55 R. D. Sharma and B. K. Bhat, Generalized treatment of ground faults in six-phase power systems, J. Inst. E'ng. (India), Part EL, 68 (1987) 12 29. 56 B. K. Bhat and R. D. Sharma, A general treatment of phase faults on a six phase generator, Eleetr. Power Energ.'/Syst.. 10 (1987) 247 252. 57 B. K. Bhat and R. D. Sharma, Analysis of sinmltaneous ground and phase faults nn a six-phase power system, IEEE Trans.. PWRD-4 (1989) 1610 1616. 58 C. Grande-Moran, Series faults in six-phase electric power systems, Electr. Power Syst. Res., I3 (1987) 109 117. 59 A. S. Bin Saroor and S. N. Tiwari, An investigation into analysis of series faults in multiphase transmission systems, Electr. Power Syst. Res., 19 (1990) 85 93. 60 B. K. Bhat, The analysis of sequential ground faults on a six-phase power system in phase coordinates, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 198,9, Inst. Eng. (India). 61 A. Augugliaro, L. Dusonchet, and A. Spataro, Transient analysis for symmetrical and unsymmetrical faults in mixed three-phase and six-phase power systems, Electr. Power EnergLv Syst., 11 (1989) 9 18. 62 S. N. Tiwari and L. P. Singh, Six-phase (multiphase) power systems: transient stability analysis, Electr. Power Syst. Res., 9 (1985) 273 281. 63 A. Chandra Sekaran, S. Elangovan and P. S. Subrahamanian. Stability aspect of' a six-phase transmission system, I E E E Trans., PWRS-1 (1986) 108 112. 64 M. M. Choudhary and L. P. Singh, Transient stability analysis of a six-phase (multi-phase) power system network. All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India). 65 D. D. Wilson and J. R. Stewart, Switching surge characteristics n f a six-phase transmission line. I E E E Trans., PAS-103 (1984) 3393 3401. 66 R. Ramaswami, S. S. Venkata and M. A. EI-Sharkawi, Sixphase transmission system: capacitance switching, lEEE Trans., PAS-103 (1984) 3681 3687. 67 A. S. Bin Saroor and S. N. Tiwari, Modelling and analysis of multiphase (twelve-phase) line transients, Electr. Power Syst. Res., 20 (1991) 49 62.

215 68 R. U r a m and R. W. Miller, Mathematical analysis and solution of transmission line transients, IEEE Trans., PAS-83 (1964) 1116-1134. 69 A. S. Bin Saroor, A. H. Ghorashi and S. N. Tiwari, Sixphase power transmission; analysis and solution of line transient, Nat. Power Systems Conf., Kurukshetra, India, 1987, System Soc. India, New Delhi. 70 M. Chinnarao and S. S. Venkata, A six-phase transmission line simulator, IEEE Midwest Power Symp., Columbus, OH, USA, 1979. 71 A. Chandra and L. P. Singh, Fault studies in six-phase systems and proposed ultra high speed relaying scheme, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1983, Inst. Eng. (India), pp. 124 134. 72 C. H. Holley and D. M. Willyong, Stator winding systems with reduced vibrating forces for large turbine generators, IEEE Trans., PAS-89 (1970) 1922-1934. 73 R. A. Hanna, D. C. MacDonald and P. G. H. Allen, The six-phase generator and its associated transformer, Proc. 4th Univ. Power Engineering Conf. (UPEC), Loughborough, UK, 1978, Paper No. 5A5. 74 R. A. H a n n a and D. C. MacDonald, The six-phase generator and transformer into a three-phase power system, IEEE Trans., PAS-102 (1983) 2600 2607. 75 R. F. Schiferl and C. M. Ong, Six-phase synchronous machine with AC and DC stator connections, Part I. Equivalent

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circuit representation and steady state analysis, IEEE Trans., PAS-102 (1983) 2685-2693. R. F. Schiferl and C. M. Ong, Six-phase synchronous machine with AC and DC stator connections, Part II. Harmonic analysis and proposed uninterruptible power supply scheme, IEEE Trans., PAS-102 (1983) 2694 2701. E. A. Klingshirn, High phase order induction motors, Part I. Description and theoretical considerations, IEEE Trans., PAS-102 (1983) 47 53. E. A. Klingshirn, High phase order induction motors, Part II. Experimental results, IEEE Trans., PAS-102 (1983) 54 59. M. M. Choudhary and L. P. Singh, Operating point stability analysis of a six-phase synchronous machine, IFAC Syrup., Bangalore, India, 1987. M. M. Choudhary and L. P. Singh, Mathematical modelling of a six-phase (multi-phase) synchronous machine for transient stability analysis, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India), pp. 135-149. A. Z. Gaber and L. P. Singh, Investigation of symmetries inherent in synchronous machines and development of a generalized Park's transformation based solely upon symmetries, Electr. Power Syst. Res., 15 (1988) 203 213. A. Z. Gaber and L. P. Singh, Symmetries in six-phase synchronous generator and its consequences, All India Seminar on Multi-phase (High Phase Order) Systems, Kanpur, India, 1989, Inst. Eng. (India), pp. 195 213.