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CHAPTER I
INTRODUCTION
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Problem Statement and Significance of the Current Investigation
One of the most common concerns of the present day electric utilities is to achieve
higher transmission capabilities with the most efficient utilization of the existing rightsof-way (ROW). This is attributed to the ever increasing power supply requirements
associated with increasing environmental constraints and difficulty of obtaining and
maintaining new rights-of-way (ROW) at any price. Traditionally, the problem has been
tackled by up-grading the voltage level of the existing line; however this option has
become very difficult to adopt because of the aforementioned environmental and
economical constraints. Consequently, a considerable amount of research has been
carried out and several alternatives for the purpose are being considered. One of the
most attractive solutions to the problem is the concept of higher-phase-order (HPO)
transmission that was first proposed by Barthold [1]. In HPO transmission, conventional
three-phase system is converted to six, nine, or twelve phases. By such conversion the
line-to-line voltage between the electrically adjacent phases becomes equal to or less
than the line-to-ground voltage as shown in Fig. (1.1).
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Figure1.1, Line-to-neutral and line-to-line voltages of three, six, and twelve-phase
transmission systems
Therefore, by arranging the physical positions of the phases such that it coincides with
the electrical sequence of the phase's rotation the following fundamental benefits are
attained:
(1) Substantial decrease in the distances required between phases. This in turn
results significant reduction in the structural size hence narrower ROW
compared to the three-phase counterpart.
(2) Substantial decrease in the insulation level between phases
(3) Increase in power transfer capability in a manner that is almost proportional to
the number of phases.
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By these features the upgrade of the power transfer capability of the transmission line is
achieved with the most efficient utilization of the existing ROW.
Since the first introduction of this sparking work, the HPO concept has been receiving
growing interest and several papers and reports investigating different aspects of this
new technology have been published. This considerable amount of research work has
further unfolded many advantages of the HPO concept. Some of these advantages are
shortly highlighted in the following section.
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Highlights on Some Practical Advantages of HPO Transmission Systems
In this section some of the practical advantages that have been verified for the HPO
transmission technology are shortly highlighted. These advantages include:
(1) Higher power transmission loadability over the existing ROW: It has been shown by
many investigations such as [2], [3], and [4] that loadability of the six-phase line
configuration is about two times that of three-phase counterpart and the value becomes
about 4 times for twelve-phase. It is even shown by [2] that from thermal loading limit
point of view the line transfer capability increases proportionally with the number of
phases; therefore for six-phase the capability is increased to 2 PU of the three-phase line
capability while for twelve phases the capability increases to 4 PU and so forth. Surge
impedance loading increases with the number of phases as well, but with lesser rate
(2) Higher power transmission efficiency (low line losses): Investigation of reference
[5] have proven through load flow analysis that system losses are substantially reduced
if three-phase double circuits lines are converted to six-phase. This improvement
increases as the number of converted circuit increases. The improvement of losses
reduces the generated real power. These calculated results were supported by the results
of reference [3] in which actual line of an existing network was investigated
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(3) Lower field gradients at the conductor surface with attendant reduction in corona
losses, radio performance, and audible noise: In reference [2] it has been shown that
about 20 % reduction in the electric field at the surface of the conductor is attained by
converting to six-phase arrangement and about 40% by converting to twelve-phase
arrangement. This indicates that corona related phenomena which are related to the
electric field on the conductor surface become a lesser concern with higher phase order.
In addition, same reference has shown that considerable reduction in the peak radio
noise (about 25 %) has resulted by changing line from three-phase to six-phase
arrangement indicating an improvement in radio noise performance by adopting higherphase order. As for radio noise, high-phase order results in a reduction in audible noise,
and design constraints are reduced.
(4) Better transient performance: In references [3], [6], and [7] different transient
performance advantages of HPO transmission systems were illustrated. In [6], for
example, switching surge comparative analysis has been conducted on representative 6phase and 3-phase systems energized from an equivalent source of 7500 MVA. The
investigations were carried out both with and without surge suppressing resistors in the
operating circuit breakers. The results showed better performance of six-phase system
with and without the suppressing resistors. The same investigation has shown that rate
of rise of recovery voltage during fault clearing is less on high phase order systems than
for three-phase systems with comparable equivalent short circuit MVA. Lightning
performance was proven to be comparable for three and high phase order lines.
(5) Smaller mechanical structure and insulation level compared to three-phase
counterparts: References [2], [6], and [7] provide schematics of three-phase
transmission system and its six- and twelve phase counterparts. Substantial reduction in
mechanical structures and in voltage level for the same power transfer capability is
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noticed. This reduces the overall cost and proves the remarkable efficient utilization of
existing ROW attained by adopting HPO technology.
(6) Better stability margin than three-phase double circuit: Reference [8] concluded by
calculation that transient stability is improved by converting from three-phase double
circuit to six-phase. This conclusion was reinforced by reference [3] in which the
impact of such conversion was investigated on an actual circuit integrated in an actual
system. Reference [9] has shown that six-phase single circuit transfers more power than
three-phase double circuit under faulted conditions, and since power transfer during
faulted conditions plays a significant role in transient stability, the six-phase line has
better stability margin than the three-phase double circuit line.
(7) Compatibility with the existing three-phase system: The conversion of three-phase
double circuit to six-phase circuit can be performed without any abnormal difficulties
weather on the converted line or on the performance of the overall network. This is
illustrated in references [3], [10], and [11]. The six-phase test line constructed for the
investigation of reference [10] was connected to the existing three-phase network
without any difficulties. Even the interfacing transformers required to provide the 60o
phase shifts for the six-phase system can be constructed using a set of two three-phase
transformers as indicated by references [10] and [11].
1-3 Justifications for the Selection of the Six-Phase System as a Sample HPO
Power Transmission System in the Current Investigation
At present, six-phase transmission appears to be the most promising among the other
multi-phase systems for possible realization in near future. It can replace the existing
double circuits of three-phase lines relatively more easily due to similarity in physical
line configuration and simplicity in constructing the interfacing transformers required at
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the ends of the six-phase line by properly connecting two three-phase transformers.
Moreover, the technical feasibility of this phase order has been assessed through three
stages:
(1) Research calculations stage that includes significant amount of investigations
covering almost all steady state and transient aspects
(2) Testing stage through construction of prototype six-phase line investigated in
reference [10]. This stage should have verified or refine the results obtained in
first stage.
(3) Preliminary stage of commercial adoption by demonstrating a project of
conversion of an existing 2.4 Km line belonging to New York State Electric
and Gas Corporation's Goudey-Okdale route. Work is currently underway on
this pilot project [11] [12].
1-4 Literature Review
The literature review of the subject will be ordered in accordance with the aspects that
are covered in the current investigation.
1-4-1 Preliminary and General Feasibility Investigations
It was the CIGRE paper published by L.D.Barthold and H.C.Barnes [1] which sparked
the industry curiosity by suggesting that with a concern over the aesthetic impact of
transmission lines, it seemed timely to review some fundamental principles of overhead
transmission and examine the space efficiency of overhead conductors and one variable
which relates to the efficiency i.e. the number of phases. This paper focused the industry
on the practical aspects that were first explained by Fortseque [13] in 1918 and E.Clarke
[14] in 1943. In addition to the above pioneering reference, general feasibility studies of
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HPO concept are found in references [2], [6], [7], [10] and [15] –[17].
1-4-2 Analysis Technique of HPO Transmission Systems and Basic Line
Parameters Calculations
In general, all investigations dealing with the steady state and the transient aspects of
HPO transmission systems that have been published up to now (some of which are all
references mentioned in the current investigation) utilize three approximation
techniques. The lumped parameters concept, the fully or cyclically-transposed line
model, and the GMR concept with the associated approximations adopted in calculating
the basic line parameters. The first two techniques can be traced in all investigations as
will be seen in the next two sections. A principle example of the third technique is the
work of S.S. Vankata, W.C. Guyker, and N.B. Bhatt [18] who implemented a computer
program that calculates line parameters for six-phase system. Their technique has the
following restrictions:
·
The use of GMR method which can't be trusted in applications where parameters
have to be calculated at high frequencies such as switching transient.
·
The earth return path is taken into account by considering only the first order
correction terms of Carson's infinite series and this give some erroneous results
at high frequencies.
· The program doesn’t calculate the basic parameters for electrically long nontransposed line that are essential when distributed parameters concept is
adopted.
1-4-3 Power Frequency Analysis
In this section the literature in HPO systems modeling and power frequency studies of
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load flow, faults analysis, loadability, and economical dispatch are reviewed.
1-4-3-1 System Modeling and Load Flow Analysis
Six-phase transmission systems, if ever realized will always be integrated in an
otherwise three-phase system, consequently modeling of the six-phase system so that it
can be used in different electric power system analysis is an essential task. Some of the
investigations in this regard preserve the physical identities of the six-phase line in their
modeling while others provide the three-phase equivalent of the six-phase parts. This
was a result of the way intended to be utilized in analyzing such combined networks.
Investigators who preferred to preserve the physical identities of each system
comprising the combined overall system adopted the real six-line model and use phase
coordinates methods in their analysis. Those, on the other hand, who prefer unified
system approach adopt the three-phase equivalent model of the six-phase parts and use
the conventional three-phase analysis tools to analyze the combined system. However,
both groups utilize the aforementioned three simplification techniques. J.L. Whillems
[19] provided model for three-phase to six – phase converting transformers without
considering the leakage impedances of the windings. He derived, as well, models for the
six-phase transmission line by its ABCD parameters. Tiwari and Singh [5] presented a
model incorporating the leakage impedance and admittance of the three to six-phase
converting transformer. These authors introduced as well a further modified model
considering the off-nominal tapings on one of the windings. In addition, they derived
the nominal π-representation of the six-phase line assuming full transposition case.
They provided as well the single and three–phase equivalents of the six-phase
transmission line model to be used in studies involving three and six-phase parts.
However this model assumes full transposition and short line model by representing the
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line in terms of its series impedance only. They devoted part of their work to a
demonstrative load flow analysis carried out on composite three and six-phase system
using unified system approach. N. B. Bhatt and others [20] provided models of the sixphase line by its phase impedance matrices. Zafer Demir, Osman Klic, and Serafetin
Ozbey [21] applied phase-coordinate method to the load flow analysis of mixed three,
six and twelve-phase systems.
The modeling part in current investigation derives all types of models ranging from
exact model for long non-transposed configuration to the short transposed line model. In
addition, the three-phase equivalent of six-phase transmission system is also provided.
Regarding the choice between the actual and equivalent models, the approach adopted
in the current investigation is as follows. In analysis such as load flow and economical
dispatch where generalized system characteristics are detected the unified system
technique will be used; hence the equivalent model will be utilized. In the studies which
require the detection of the response in every conductor of the six-phase line such as
fault and transient analyses the actual line configuration is utilized.
1-4-3-2 Economical Dispatch Analysis
Up to the knowledge of the author of the current work, the impact of the six-phase
conversion on the economical dispatch of electric power system has not been detected
yet. Therefore the current work will be the first contribution in this aspect.
Mathematical models utilizing the available techniques used in such analysis for pure
three-phase network are developed to study network consisting of six- and three-phase
parts. The developed models in the current investigation are capable of analyzing large
network containing any number of six-phase lines