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PERFORMANCE EVALUATION OF MULTI- PHASE TRANSMISSION LINES
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International Journal of Advances in Engineering Science and Technology
www.sestindia.org/volume-ijaest/ and www.ijaestonline.com
57
ISSN: 2319-1120
PERFORMANCE EVALUATION OF MULTIPHASE TRANSMISSION LINES
Vinay Kumar Tripathi 1, Anil Kumar Bharadwaj 2
Department of Electrical Engineering, SHIATS, Allahabad
Abstract—: There are many problems regarding power flow and stability is an issue of vital
importance at EHV (Extra High Voltage) and UHV (Ultra High Voltage) level because of its
sensitivity with real and reactive power changes. In this paper a multiphase system has been
studied using the techniques of three-phase systems into multi-phase lines and the performance
curves relating to power flow and voltage stability performance of such system is plotted. A
comparison of multiphase phase systems is also presented in the paper, and it can be used for
planning and design of a multiphase transmission network.
Keywords— Transmission lines, Rights-of-way, Multi-phase, Power flow.
I. INTRODUCTION
The contemporary power system network has of load and power flow conditions leading
to problems of line capacity. In this regard multiphase power transmission systems have been
investigated [1]- [9] as potential alternative to increase transmission capacity without increasing
system voltages. The system voltage has already reached extremely high level i.e. EHV and
UHV and it has been found that 4-phase and 12-phase are quite promising. The problems
concerning power flow and stability, particularly voltage stability are of particular interest
because of its sensitivity with changes in real and reactive power. Voltage stability is obtained by
keeping specified voltage magnitude within the set of operating limits under steady state
conditions. The problem has been studied to a great extent in case of three-phase systems [10][12]. However the multiphase system has received little attention and needs similar study. This
paper deals with investigation of these aspects by using techniques of three-phase systems to
multi-phase lines. A number of performance characteristic curves have been obtained relating to
power flow and voltage stability of such system. Considering the multi-phase line as longitudinal
or radial or the one linking to systems on either end, several performance characteristics such as,
(i) reactive power requirements characteristics, (ii) reactive power loss characteristics, (iii)
voltage power characteristics (under loading conditions), (iv) load end real and reactive power
operating contour maps, (v) shunt capacitive support at voltage stability limit using characteristic
of voltage dependant load, and (vi) optimal reactive power at voltage stability limit, loadability
curves can be constructed as done in [12] Employing a sample system a quantitative as well as
qualitative analysis is carried out to highlight relative performances of such systems as compared
to their three phase counterparts. Such performance curves would be highly helpful in planning
and evaluating performance of multi-phase.
The paper is organized as follows: Various performance characteristics for multiphase
transmission system have been derived and graphically analyzed in section III to compare the
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
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PERFORMANCE EVALUATION OF MULTI-PHASE TRANSMISSION LINE
advantages and limitations of multiphase system with conventional three phase system. The
analysis of reactive power requirement for voltage stability of multiphase and three phase system
has also been carried out in section III.
II. BASIC CIRCUIT MODEL AND SAMPLE SYSTEM
Following [2, 6, 12], the basic circuit model with lumped parameters that is used for the analysis
of un-compensated EHV power transmission system can be represented as shown in Fig. 1. Let EA and IA
represent the voltage and current at sending end side. Let EB and IB are the voltage and currents at
receiving end side. In figure 1, YT and YSH represent equivalent series and shunt admittance respectively,
in the case of an equivalent pi-model of the transmission line.
Figure (1) Basic circuit model
For performance evolution three transmission alternatives (3, 4 and 12-phase) with same
number of conductors, same right of way and utilization of
the same air space for power
transmission are considered. Each system is energized at 460 kV line-to ground (L-G) voltages
and has the same thermal rating. The line-parameters are based on assumptions of complete
transposition of conductors are depicted in Table 1.
TABLE I- TEST SYSTEM SPECIFICATION & LINE PARAMETERS
3-Phase line
4-Phase line
12-Phase Line
462 kV (L-G)
462 kV ( L-G)
462 kV (L-G)
SIL = 3270 MW
SIL = 4490 MW
SIL = 5480 MW
Z= (0.0060+j0.390)
Z= (0.0120+j0.4720)
Z= (0 .020+j0.5660)
Ω/mile
Ω/mile
Ω/mile
Y= j 10.630 µS/mile
Y= j 8.9600 µS/mile
Y= j7.480 µS/mile
III. PERFORMANCE CHARACTERISTICS
A. Load End Real and Reactive Power Operating Contour Maps
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
IJAEST, Volume 3, Number 2
Vinay Kumar Tripathi, Anil Kumar Bharadwaj
The load end real and reactive power operating contour maps for the circuit shown in fig.1 can
be described as: [12].
*
*
| S B | −YBB
E B2 | =| eYBB
EB |
(1)
*
The above equation is similar to an equation of a circle. This circle has | YBB
EB2 | as centre
*
and | e*YBB
E B | as its radius. As shown in Fig. 2, all states having the constant amplitudes of e
(=EAYBA/YBB) lie on the circles with these parameters on the S-plane. Each circle (Fig. 2)
represents the locus of |SB|, the receiving end complex power, for a stable value of EB (receiving
end voltage), varying within the range of 0.94 p. u. to 1.0 p. u. that assuming sending end voltage
EA to be constant at 1.0 p.u., the load end real and reactive power operating contour maps, for 3,
4 and 12-phase are constructed for 460 kV and 200 km transmission lines, on p.u. basis, are
shown in Fig. 2. It is evident from the curves in Fig. 2 that for multi-phase transmission system
having more than 3-phases; the power handling capacity is much higher for specified sending
end and receiving end voltages while maintaining the similar set of variations.
Fig.2 Real & reactive power operating contours with same receiving end voltages (EB = 0.94 p.
u.)
Furthermore, Figure 3 (a-c) shows that power handling capacity for 3, 4 and 12-phase
transmission system with 4% increase of receiving end voltage EB1 = 0.94, EB2 = 0.95 and EB3 =
1.0 p.u. maintaining sending end voltage (EA) as it is i.e. EA = 1.0 p.u. It is observed that reactive
and real power handling capacity for 3-phase, 4-phase and 12-phase systems are increased by
10.80 %, 7.30 %, 6.70 % and 4 %, 3.340% %, 3.380 % respectively. As supplement, it can be
seen from Figs. 3(a-c) that increment in real and reactive power capacity for 3-phase, 4-phase
and 12-phase takes place with an increase of 9 % in EB (within voltage stable zone) keeping EA
constant at its previous value i.e. EA=1.0 p.u.. It is observed that the corresponding percentage
increase of in real and reactive power capacity of 3-phase, 4-phase and 12-phase are found to be
9, 8.66, 8.63 and 16.31, 12.77 and 14.30 respectively.
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
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PERFORMANCE EVALUATION OF MULTI-PHASE TRANSMISSION LINE
Fig. 3 (a) Real & reactive power contours of a 3-phase line with EB1 = 0.94, E2 = 0.95 and EB3 =
1.0 p.u.
Fig.3 (b) Real & reactive power contour maps of a 4-phase line with EB1 = 0.94, EB2 = 0.95 and
EB3 = 1.0 p.u
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
IJAEST, Volume 3, Number 2
Vinay Kumar Tripathi, Anil Kumar Bharadwaj
Fig.3 (c) Real & reactive power contour maps of a 12-phase line with EB1 = 0.94, EB2 = 0.95 and
EB3 = 1.0 p.u
It is clear from the above contour maps that the reactive power transfer capacity increases
with the increase of number of phases.
B. Reactive Power Loss Characteristic
The reactive losses (QSL) in an EHV power transmission line are given by
2
 (Q = E B I B ) 
 X
QSL = I X  SL 0
E
B


2
(2)
If a constant power (QSL= EBIB), is assumed that the rate of change of series reactive power
losses with voltage is obtained from (2) as:
dQSL
− 2(QSL 0 ) 2 X
=
dV
EB3
(3)
Hence it can be seen that the rate of change of reactive power loss with respect to
receiving end voltage related to receiving end voltage. It is inversely proportional to the cube of
receiving end voltage. Further, an increase in series reactive power loss that is, dQSL exists if
there is a decline in the transmission voltage in order of EB3. Using equation 3, the curves of
(dQSL /dEB) versus EB (p.u.) can be drawn for the sample cases of 3, 4 and 12-phase lines and
depicted in fig. 4 for a length of 400 km.
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
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PERFORMANCE EVALUATION OF MULTI-PHASE TRANSMISSION LINE
dQSL
dEB
Fig. 4 Reactive power loss characteristics of three transmission alternatives
From the curves in Fig. 4, it is noticed that the series reactive power losses are very small
the losses are smaller in multi-phase transmission lines than the loss in three-phase lines. Hence
it can be assumed that the voltage stability limit of multi-phase transmission systems is
increased. This makes the multi-phase systems very much secured from the voltage stability
view point. Now, equation (2) can be re-written as
 1  ( EB I B ) 2
 =
(4)
QSL = ( EB I A ) 
SIL
 EB / X 
where, SIL is the surge impedance loading and is given by EB2 /X. Based on (4) the results are
shown in the plots of QSL versus SIL vide Fig. 5 for a length of 400 km.
2
Fig. 5 Profile of series reactive power losses (QSL) n verses surge impedance loading (SIL).
ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
IJAEST, Volume 3, Number 2
Vinay Kumar Tripathi, Anil Kumar Bharadwaj
Also from Fig.5 it is seen that the reactive power losses smaller in multi-phase lines. In
view of this, multi-phase systems (employing more phases than three) are more secure from
voltage stability view point.
IV. CONCLUSION
It can be concluded that the multi-phase lines (4-phase and 12-phase) show progressively
increased power handling capacity, reduced reactive power losses, increased power at the
receiving end, reduced reactive power requirement for maintaining stable load voltage, reduced
rating of compensating devices, better voltage stability in case of voltage dependent load and
increased line loadability in uncompensated as well as compensated condition the phase order is
increased the multi-phase lines may be very attractive and beneficial to electric transmission
utility.
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PERFORMANCE EVALUATION OF MULTI-PHASE TRANSMISSION LINE
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ISSN: 2319-1120 /V3N2: 57-69 © IJAEST
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