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Abstract—This research presents the development and implementation
in a computational routine of algorithms for fault location
in multiterminal transmission lines. These algorithms are part
of a fault-location system, which is capable of correctly identifying
the fault point based on voltage and current phasor quantities, calculated
by using measurements of voltage and current signals from
intelligent electronic devices, located on the transmission-line terminals.
The algorithms have access to the electrical parameters of
the transmission lines and to information about the transformers
loading and their connection type. This paper also presents the development
of phase component models for the power system elements
used by the fault-location algorithms.
INTRODUCTION
TRANSMISSION lines, responsible for connecting generation
plants to consumers, are classified according to their
voltage level. Usually, high-voltage transmission lines have only
two terminals. However, subtransmission lines may have lateral
branches connected to tap points along their main branch, terminating
at distribution substations.
When a permanent fault occurs in these lines, maintenance
crews usually spend more time to locate the fault point, since
there is no indication of the line section where the fault occurred.
Therefore, maintenance costs may increase while the reliability
of the system diminishes.
The deregulation process contributed to increasing the complexity
of the problem. Normally, the substations connected to
the line branches do not belong to the company responsible
for operating the transmission line and, due to commercial reasons,
the information available at these substations (voltage and
current measurements), which might improve the fault-location
process, is not shared with the transmission company.
A. Transmission System
Multiterminal transmission networks may use single- or
double-circuit lines. As a result, the main branch may use a
single transmission line or a double-circuit line (both circuits at
the same towers, circuits at different towers and at the same corridor,
or circuits at different towers and at different corridors).
Fig. 1 illustrates a typical multiterminal transmission network.
The main branch connects two terminals ( and ). Along
the main branch, there are tap points ( to ) where lateral
branches are connected. These lateral branches terminate at
distribution or industrial substations (terminals to ).
IEDs installed at and are responsible for recording
voltage and current signals. These records may or may not be
available at other terminals ( to ). Nonetheless, the proposed
system is capable of correctly identifying the fault point
based only on the signals recorded at and , with or without
time synchronization. In addition, if the records are available at
other terminals, the proposed system uses them in order to improve
the accuracy of the results.
Although voltage and current records may not be available
at one or more terminals ( to ), the proposed system is
capable of correctly estimating the load connected to them in
order to proceed with the fault location. In addition, it is important
to point out that the transformers connected to these terminals
may have a grounded-wye/delta/grounded-wye connection
type. As a result, a significant part of the fault current may flow
through the primary winding of these transformers, for faults
involving the ground. This scenario increases the complexity of
the problem and since voltage and current records may not be
available at these terminals, the mathematical model used to represent
the transformers must implicitly consider the current flow
through the primary winding.
Fault-Location Methods
Several algorithms for fault location in three terminal transmission
lines have been proposed [1]–[6]. However, due to the
complexity of the problem, only a few algorithms for fault location
in multiterminal transmission lines have been proposed
[7]–[10]. In addition, these algorithms do not address all of the
requirements described in Section II.
References [7] and [8] present fault-location algorithms
for multiterminal single-circuit transmission lines. These
algorithms are based on synchronized voltage and current measurements
at all terminals and on the short transmission-line
model. As a result, these algorithms may present accuracy
errors when handling medium and long multiterminal transmission
lines.
References [9] and [10] present fault-location algorithms for
multiterminal double-circuit transmission lines. These algorithms
are also based on voltage and current measurements at all
terminals and on the short transmission-line model; therefore,
both algorithms may present accuracy errors when handling
medium and long multiterminal transmission lines. The first
one presents two different approaches based on synchronized
voltage and current phasor quantities at all line terminals.
The second one was developed according to certain unusual
assumptions, which are difficult to verify, and it is not clear if
it depends on time synchronization.
Due to these reasons, the main goal of the fault-location
method proposed in this paper is to address all of the problems
described before in order to present an accurate solution for
fault location in multiterminal transmission lines.
II. SYSTEM MODELING
The fault-location method proposed in this paper is based on
voltage and current phase components. In order to improve the
accuracy of the results, it was necessary to develop precise mathematical
models for transmission lines, loads, and transformers.
The following sections describe these models.
Transmission Line
Fig. 2 illustrates the three-phase pi-model of a single-circuit
transmission line, whose line length is . The transmission-line
series impedance and shunt admittance matrices, per unit length,
are and , respectively. Equation (1) describes the
mathematical relation of the voltage and current phasors at local
and remote ends
Postfault Processing
The postfault processing stage consists of calculating two
sets of postfault voltage and current phasor quantities at all tap
points. One of them using postfault voltage and current phasor
quantities at terminals and the other using postfault voltage
and current phasor quantities at terminal . This stage is based
on (1) and (11). It depends on the load impedances at terminals
and and on the postfault voltage and current phasor
quantities at terminal . It also considers that the system is
not faulted in order to perform the calculations.
Using this approach, it is possible to determine whether the
fault occurred at any lateral branch or at the main branch. In
other words:
• if the fault has occurred at a lateral branch, the postfault
voltage phasor quantities at the respective tap point, from
both sets, must be equal. In this case, the fault-location
system investigates only the respective lateral branch;
• otherwise, the fault occurred at the main branch and all line
sections belonging to it must be investigated.
Two algorithms were developed in order to estimate the fault
location. The first one is based on the postfault voltage and current
phasor quantities at both ends (Section III-D). Hence, it is
used to locate faults at line sections from the main branch or
lateral branches where voltage and phasor quantities are available
at the respective substation terminals. The second one is
based on the postfault voltage and current phasor quantities at
one end (Section III-E). Thus, it is used to locate faults at lateral
branches where voltage and current phasor quantities are available
only at the tap point.
D. Fault-Location Algorithm—Voltage and Current at Both
Ends
The algorithm proposed in this section is used to locate faults
at line sections where voltage and current phasor quantities are
available at both ends [15].
As an example, consider the line section depicted in Fig. 8,
which is part of the system illustrated in Fig. 6. This line section
is delimited by tap points and , has a length of , and
the fault point is located at an unknown distance from .
From (1) and (11), it is possible to calculate the postfault voltage
and current phasor quantities at and by using the postfault
voltage and current phasor quantities at terminals and ,