Download Increased Security Rating of Overhead Transmission Circuits Using

Increased Security Rating of Overhead
Transmission Circuits Using Compact
Phase Design and High Phase Order
Brian J. Pierre, Student Member, IEEE

Abstract—In this paper the combination of compact phase
design and high phase order (HPO), (e.g., ≥ three phase) is
used to enhance the security ratings of overhead transmission circuits. The advantages of both technologies are used
with the objectives of raising the power transmission capability, reducing right of way requirements, reducing the
phase angle difference between the sending and receiving
end voltages, and reducing the cost of bulk power transmission. Disadvantages of the proposed technology are also
discussed. The main objectives of this paper are to:
 Discus the use of HPO to compact transmission lines
 Calculate HPO sequence reactances in terms of self and
mutual reactances using properties of circulant matrices.
 Determine the increase in security rating for compact
HPO vs. its three phase multicircuit counterpart.
Index Terms—Power transmission, transmission engineering, high phase order, six phase, security rating, compact phase spacing, sequence components, sequence
reactances, circulant matrices.
I. INTRODUCTION
IGH phase order has been proposed for overhead
AC transmission for nearly 40 years. The literature of the field in the area of six-phase technology is copious including (as examples) the economics of
six-phase [1], fault detection and analysis [2, 3], and
electromagnetic impact [4]. An experimental six-phase
line was constructed in the 1990s in Saratoga NY, and
[5] describes results. The general study of HPO for
higher phase order is less voluminous. Perhaps the seminal work on high phase order is that of Barnes [6], and
references [7] and [8] are examples of other literature.
The main advantages of HPO are the reduction of lineline (phase to phase) voltages, decrease of positive sequence reactance (X+), and reduction of electromagnetic
interference of overhead power transmission lines.
The advantage of HPO low phase to phase voltage
is illustrated for the six phase case in which the phase to
phase voltage magnitude is equal to the phase to neutral
H
The authors acknowledge the support of the Power Systems Engineering Research Center (PSerc) which is a Generation III National
Science Foundation Industry University Cooperative Research Center,
awards EEC-0001880, EEC-0968993. The authors also acknowledge
the support of the U.S. Department of Energy for its PSerc future grid
initiative.
The authors are with the School of Electrical, Computer, and Energy Engineering at Arizona State University, Tempe, AZ 85287, and
can be reached at {brian.pierre, heydt}@asu.edu.
G. T. Heydt, Life Fellow, IEEE
voltage magnitude. The lower phase to phase voltage
allows the individual phases to be compacted, i.e., located closer together in space. This will be termed as
compact HPO for purposes of this paper. The ultimate
spacing limitations of the phase conductors are determined by codes (e.g., the National Electrical Safety
Code [9]), consideration of the basic impulse level
(BIL), the spacing required for live line maintenance,
and physical interaction of the phase conductors. The
compacted phases incur advantages such as the increase
in mutual coupling between the phases. This decreases
the X+ of the line. Since the active power level capability of the line for a given terminal voltage phase difference is inversely proportional to the X+ of the line (i.e.,
for „security limited‟ lines), compact HPO lines have
higher security ratings than comparable three phase
lines. To determine the security limit increase in compact HPO over comparable three phase construction, the
X+ shall be evaluated.
It should be noted that comparison of HPO lines
with three phase circuits is complicated by issues of
what parameters are to remain constant in the comparison. These parameters include the phase to phase voltage, phase to ground voltage, conductor size and
ampacity, and cost. For purposes of this paper, voltage
phase to phase and phase to phase spacing are the control parameters that are varied.
The phase compaction is considered to be linearly
related to the decrease in phase to phase voltage. As
indicated above, phase to phase spacing is nominally
limited by code requirements. The approach taken in the
literature has been to examine modest compaction. As
examples, references [10] and [11] relate to phase compaction in transmission engineering.
II. USING HPO LOWER PHASE TO PHASE VOLTAGE TO
COMPACT TRANSMISSION LINES
The phase to phase and phase to neutral voltage
magnitudes, |Vll|, |Vln| and the number of phases are related by,
(1)
(
√ (
where n is the number of phases. The |Vll| / |Vln| vs. the
number of phases is depicted in Fig 1. The lower phase
to phase voltage magnitude at higher phase orders allows for reduced insulation requirements between phases. In this sense, for HPO, a more compact line can be
constructed. For the same phase ampacity in comparison
circuits, a 500 kV double circuit 3φ line will carry the
2
same power as a 288.7 kV 6φ line. In addition, the 6φ
line can be compacted thus decreasing the required right
of way (ROW).
2
1.8
Vll if Vln is held at 1.0 V
1.6
1.4
1.2
ble. The general concept is attributed to Nikola Tesla
[13].
Perhaps the simplest HPO technology is the 6φ
case. Consider a 6φ transmission line on which the
phases are arranged in a regular hexagon as shown in
Fig. 3. Consider the line reactance matrix as a lumped
parameter, lossless 6φ transmission line model,
1
0.8
0.6
(3)
0.4
0.2
0
0
10
20
30
40
Number of phases
50
60
Fig. 1 |Vll| / |Vln| vs. number of phases
III. SECURITY RATING
Compaction decreases the positive sequence reactance which increases the security rating of a transmission line. The security limit of a short, lossless
transmission line is
(
,
7000
Security rating
Thermal rating
Rating (MW)
5000
4000
3000
where the distances are √
less for 6 phase vs. the distances in double circuit 3φ
(2)
where |V1 | and |V2 | are the voltage magnitudes at the
line terminals and δmax is the maximum tolerable voltage
phase angle difference. The security limit is often calculated using 30° as δmax. In (2), only the active power
flow due to the positive sequence voltages and currents
is calculated. Unbalanced operation is not considered. In
(2), a short, lumped, lossless model is used. It is possible to include circuit resistance to capture losses, and it
is also possible to use a long line („hyperbolic‟) model
that is accurate at one frequency (e.g., 60 Hz).
Generally, long lines are limited by security constraints, whereas short lines are limited by thermal constraints, as seen in Fig. 2 (offered as a typical
characteristic for a 3φ 500 kV Drake circuit). Therefore,
HPO compaction can be beneficial for long lines.
6000
[
]
where S is the line self-reactance, and the Mi are mutual
reactances related to di shown in Fig. 3.
500 kV Drake
two bundle at 18 in.
phase spacing 40 ft.
Fig. 3 Configurations and X+ for a double circuit 3φ and 6φ line. The
notation S refers to the self inductive reactance of a given phase, and
M1 is the mutual reactance with an adjacent phase, and M2 and M3 are
the mutual reactances with more distant phases.
The subject of circulant Toeplitz matrices is described in [12], and of special interest is the case of a
symmetrical circulant Toeplitz (SCT) matrix. When any
number of conductors are arranged in a circular symmetric formation (as in Fig. 3), the line impedance matrix is in SCT form, as seen in (3). A circulant matrix
has a unique property that all circulant matrices of size
nxn share the same n eigenvectors, m = 0, 1, … , n-1,
[12],
(
[
]
(
√
These n eigenvectors can be arranged in columns to
form a modal matrix T to diagonalize Xph,
(
The eigenvalues of Xph are calculated using [12],
2000
∑
1000
0
0
50
100
Line length (miles)
150
Fig. 2 Line length vs. security and thermal rating of a lossless line:
exemplary parameters shown for a 3φ Drake 500 kV line
IV. SYMMETRICAL CIRCULANT TOEPLITZ MATRICES
High phase order was initially considered at the inception of AC power generation and transmission.
Three phase designs have a distinct advantage in that
with the addition of a single phase conductor over single
phase counterparts, triple power transmission is possi-
(
where Xph,1,k is the kth entry of row one of the Xph matrix, m is the mth eigenvalue, and n is the number of
phases. Note that λm is the discrete Fourier transform of
the sequence {Xph,1,0, Xph,1,1, …, Xph,1,n-1}.
V. SIX PHASE VS. DOUBLE CIRCUIT THREE PHASE
The 6φ phase to neutral voltages are given by the
vector [1 b5 b4 b3 b2 b]t where b is 1/60o. Note that b is
one of the six complex roots of unity. It is possible to
decouple the 6φ system into six single phase circuits
much like is done for 3φ systems and symmetrical com-
3
ponents [14]. The reactance „sequence components‟ can
be found using (5),
% increase in security rating
14
(7)
[
]
[
]
where „diag‟ refers to making the argument vector into
a 6x6 diagonal matrix. The terminology of the six sequence names, ns, pt, ..., was proposed in reference
[14]. The phase spacing and reactances of any candidate
line are [15],
(
(
(
(
)
)
(
)
)
(
13
12
11
10
9
8
7
0
10
20
30
40
phase spacing distance, d2 3ph, (ft)
50
Fig. 5 The percent increase in security rating for comapct 6φ over
double circuit 3φ is plotted versus phase spacing (distance d2) of the
original double circuit 3φ.
with GMR and dab (in feet). Assume that phase to phase
spacing is linearly related to the phase to phase voltage.
If the 6φ voltage phase to phase is 1/√ times the comparison 3φ phase to phase voltage magnitude, the spacing can be √ times closer in the 6φ line. This will be
termed compact six phase construction. To determine
the increase in security rating for compact 6φ as compared to a double circuit 3φ design, the conductor configuration is shown in Fig. 3. For the configuration in
Fig. 3, each distance will be related to the double circuit
3φ distance, d2. Use the following notation,
Double circuit three phase
√
√
VI. TWELVE PHASE VS. QUADRUPLE THREE PHASE
For further testing of compact HPO, a comparison
will be made between quadruple 3φ and 12φ. The phase
to phase voltage for 12φ is a factor of 0.29886 less than
the 3φ case. For this reason, the phases in 12φ can be
compacted by the same factor. The configurations for
the resultant 12 conductors can be seen in Fig. 6. Using
the configuration in Fig. 6, the line reactance matrix is
the SCT matrix X12ph,
(10)
Compact six phase
√
Using (7)-(9), the positive sequence reactances are
(
(
√
[
)
]
√
√
)
+
Using GMR = 0.0375 ft. corresponding to Drake, the X
vs. phase spacing is found and depicted in Fig. 4. The
percent increase in security rating for 6φ over double
circuit 3φ is depicted in Fig. 5.
Where the distances
will be a factor of
0.29886 less for 12
phase vs. the distances
in quadruple circuit 3
phase.
X+ (Ohm/mile of line length)
1
0.9
Fig. 6 Configurations and X+ for quadruple circuit 3φ and 12φ respectively
0.8
0.7
double circuit 3-phase
Compact 6-phase
0.6
0.5
0.4
0
10
20
30
40
phase spacing distance, d2 3ph, (ft)
50
Fig. 4 Comparison of X+ for double circuit 3φ, and compact 6φ vs.
phase spacing of the original double circuit 3φ (for GMR of 0.0375 ft.
Drake conductor).
Analogous to the 6φ case, the sequence components
for a 12φ system, pictorially shown in [16], is found and
expressed in terms of one of the twelve complex roots
of unity, namely c = 1/30o. The twelve eigenvectors
form the modal matrix T12ph,
4
.
√
[
√
√
√
√
√
√
1.2
1.1
1
Quadruple circuit 3-phase
Compact 12-phase
0.9
0.8
10
20
30
40
phase spacing distance, d1 3ph, (ft)
50
Fig. 8 Comparison of X+ for quadruple circuit 3φ, and compact 12φ
vs. original quadruple circuit 3φ, phase spacing (for GMR of 0.0375
ft. Drake conductor).
17
% increase in security rating
√
1.3
0.7
0
]
Similar to the 6φ case, using (5)-(6), for 12φ the twelve
sequence reactances are,
[
X+ (Ohm/mile of line length)
1.4
]
√
[
]
Note that T12ph is independent of the values of the Mi
and S and this modal matrix is given by the eigenvectors
(4) arranged in columns.
For the configuration in Fig. 6, use the following
notation to relate all the distances to distance d1 of the
quadruple circuit 3φ case. As before,
Quadruple circuit three phase
Twelve phase
Using (8), (9), the 12φ X+ equation, and the distances
above,
[
(
[
(
)]
)]
As an illustration for GMR = 0.0375 ft, Figs. 8 and 9
depict X+ and the increase in security rating in the 12φ
case.
VII. HPO PHASE COMPACTION BENEFITS AND
DISADVANTAGES
Loading of adjacent transmission assets
There is a potential benefit of reducing loading on
critical transmission circuits by phase compaction
through the use of lower reactance parallel paths. The
same advantage is a disadvantage in that some adjacent
circuit assets may experience undesired loading (especially adjacent transformers which may require upgrading).
16
15
14
13
12
11
10
0
10
20
30
40
phase spacing distance, d1 3ph, (ft)
50
Fig. 9 The percent increase in security rating for compact 12φ over
quadruple circuit 3φ is plotted versus phase spacing (distance d1) of
the original quadruple circuit 3φ.
Decreased electric and magnetic field strength
The electric and magnetic fields of an overhead line
may be decreased using phase compaction [5, 10]. Tower height is related to the electric and magnetic field
strengths at ground level. There may be implications of
permissible lower tower height and further reduction of
ROW using phase compaction.
Corona levels
Compaction of conductors makes electric field
strength between conductors higher, and there is simultaneous increase in corona, corona losses, and audible
noise. Note that for high phase order, however, there
may be an advantageous reduction of corona due to reduced phase to phase voltage in some designs.
Decreased ROW
Phase compaction results in obvious reduced ROW.
The disadvantages of reduced phase spacing include
more difficult or preclusion of live line maintenance and
circuit maintenance in general. The decreased phase
spacing may be unacceptable to some operating companies and in some jurisdictions – regardless of the benefits.
Decreased lightning exposure
The smaller cross-section of the transmission circuit in the landscape view results in less lightning exposure.
Increased shunt capacitance
Phase compaction results in higher shunt capacitance. The shunt capacitance is proportional to the in-
5
verse of the logarithm of the spacing and geometric
mean distances of the phase conductors and their images, and therefore compaction results in higher shunt
capacitance. The higher capacitance results in lower
surge impedance, and therefore higher surge impedance
loading (SIL) of the line [10]. Although the higher SIL
may not result in actual operating point change (note
that SIL is simply an index or yardstick of the loadability of the line, and not a measure of the actual operating
point), there may be advantages in long line applications. The increased shunt capacitance will raise the
operating voltage magnitude. In some cases this is an
advantage and in some cases this is a disadvantage. The
increased shunt capacitance causes higher inrush current
when the line is energized.
Probability of flashover
Reports in [10] indicate switching surge flashovers
in an experimental 500 kV compact design were more
prevalent than in conventional designs.
Voltage and current unbalance
Reference [10] reports better charging current balance among the phases for a compact 3φ experimental
500 kV line vs. a traditionally spaced line. This potentially allows lines of hundreds of kilometers to be untransposed.
Use of interphase spacers
Phase compaction results in an obvious increase for
the potential interaction between adjacent phases. The
use of interphase (insulating) spacers may be used to
avoid this difficulty. The design of span length may also
assist in controlling phase spacing.
Protection considerations
Protection of HPO lines is more complex. Many
methods have been proposed, e.g., [2, 3]. One of the
main difficulties is the increased number of possible
faults, along with the increased range of possible fault
current.
Operation with loss of a phase
For very high phase order circuits, it may be possible to trip only one phase of the HPO circuit, thus allowing all the remaining phases to be sound. With a
judicious choice of terminal transformer connections,
the impact of operating with one phase out of service
may be tolerable.
VIII. CONCLUSIONS
High phase order with compaction is a potential alternative for overhead transmission. HPO transmission
lines have lower phase to phase voltage magnitude. The
lower phase to phase voltage allows for compaction of
the phases. This compaction increases the mutual coupling in the circuits and decreases the positive sequence
reactance, thus increasing the security rating of a transmission line.
This paper assesses the increase in security rating
for a 6φ line versus a double circuit 3φ line, and a 12φ
line versus a quadruple circuit 3φ line.
Using a symmetrical conductor configuration results in a symmetrical circulant Toeplitz line reactance
matrix. The sequence reactances for 6φ and 12φ lines in
terms of self and mutual reactances are calculated. Insight into high phase order calculations using circulant
matrices is presented.
IX. REFERENCES
[1] T. Landers, R. Richeda, E. Krizanskas, J. Stewart, R. Brown.
“High phase order economics: constructing a new transmission line,”
IEEE Transactions on Power Delivery, Volume 13, Issue 4, 1998.
[2] N. Bhatt, S. Venkata, W. Guyker, W. Booth, “Six-phase (multiphase) power transmission systems: Fault analysis,” IEEE Transactions on Power Apparatus and Systems, Volume 96, Issue 3, 1977.
[3] E. Badawy, M. El-Sherbiny, A. Ibrahim, M. Farghaly, “A method
of analyzing unsymmetrical faults on six-phase power systems,” IEEE
Transactions on Power Delivery, Volume 6, Issue 3, 1991.
[4] M. Sidik, H. Ahmad, Z. Malek, Z. Buntat, N. Bashir, M. Zarin, Z.
Nawawi, M. Jambak, “Induced voltage on objects under six-phase
transmission line,” Proc. IEEE Region 10 Conference, Bali, Indonesia, 2011.
[5] M. Brown, R. Rebbapragada, T. Dorazio, J. Stewart, “Utility system demonstration of six phase power transmission,” Proc. IEEE
Power Engineering Society, Transmission and Distribution Conference, Dallas, TX, 1991.
[6] H. C. Barnes, L. O. Barthold, "High phase order power transmission", CIGRE SC 32, Electra, No. 24, 1973.
[7] T. Dorazio, “High phase order transmission,” Proc. Southern Tier
Technical Conference, Binghamton, NY, 1990.
[8] C. Fan, L Liu, Y Tian, “A fault-location method for 12-phase
transmission lines based on twelve-sequence-component method,”
IEEE Transactions on Power Delivery, Volume 26, Issue 1, 2011.
[9] IEEE Standards Association, National Electrical Safety Code,
New York, NY, 2012.
[10] X. Gong, H. Wang, Z. Zhang, J. Wang, J. Wang, Y. Yuan, “Tests
on the first 500 kV compact transmission line in China,” Proc.
PowerCon International Conference, Perth, WA, 2000.
[11] A. Clerici, G. Valtorta, L. Paris, “AC and/or DC substantial power upgrading of existing OHTL corridors,” Proc. International Conference on AC and DC Power Transmission, London, 1991.
[12] R. Gray, Toeplitz and Circulant Matrices: A Review, Foundations
and trends in communications and information theory, Now Publishers Inc., Hanover MA, 2006.
[13] N. Tesla, My Inventions, the Autobiography of Nikola Tesla,
SoHo Books, New York, 2012
[14] A. Augugliaro, L. Dusonchet, A. Spataro, “Mixed three-phase
and six-phase power system analysis using symmetrical components
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[15] William H. Kersting, Distribution System Modeling and Analysis,
Taylor & Francis Group, Florida, 2012.
[16] E. Klingshirn, “High phase order induction motors,” IEEE Transactions on Power Apparatus and Systems, Volume PAS-102, Issue 1,
1983.
X. BIOGRAPHIES
Brian Joseph Pierre (StM ‟09) is from Laramie, WY.
Mr. Pierre holds the BSEE from Boise State University,
Boise, ID (2011). He is presently a doctoral student at
Arizona State University, Tempe, AZ.
Gerald Thomas Heydt (StM ‟62, M „64, SM ‟80, F
‟91) is from Las Vegas, NV. He holds the Ph.D. in Electrical Engineering from Purdue University. He is a Regents‟ Professor at Arizona State University.