Download Distribution High Impedance Fault Location Using Localized Voltage

Distribution High Impedance Fault Location Using
Localized Voltage Magnitude Measurements
Shamina Hossain, Hao Zhu, and Thomas Overbye
Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois 61801
Email: {shossai2, haozhu, overbye}@illinois.edu
Abstract—The detection and location of high impedance faults
has historically been a difficult endeavor due to the low currents
produced. However, the recent advent of distributed voltage
monitoring devices, enabling access to fast-sampled, expansive
voltage measurements throughout a distribution network, can
ease this task. This paper considers the potential to use these
distribution level devices to detect and locate such faults. A
simulation-based method is proposed that compares a measured
voltage profile, obtained from the devices, and simulated voltage
profiles at various locations using a power system simulation
software. The simulation locations are intelligently selected using
the Golden section search and possible fault impedance values
are iterated through for each location. The L1-norm is used to
compare the two profiles, with the lowest error norm representing
the best match – the most likely fault location and impedance.
Index Terms—high impedance fault, fault location, voltage
sags, distributed monitoring devices
I. I NTRODUCTION
Vast and complex, the electric power grid is central to modern society. The interconnected system’s most critical function
is to maintain continuous delivery of electric power to serve
all loads. However, inevitable interruptions can occur due to
sudden changes in load demand, external circumstances such
as weather, equipment failure, and various other disturbances.
When an event arises that interferes with the normal flow of
current in the power system, a fault has occurred. A number of
different faults can occur in a power system including singlephase and multi-phase faults [1]. The majority of faults result
in currents that can reach very high magnitudes, in comparison
to normal system current levels, and cause severe damage to
power system equipment. It is pertinent to locate and clear
these faults promptly with the use of protective equipment.
However, about 5 − 20% of faults in distribution systems are
high impedance faults which produce low currents and can
escape detection from conventional protective devices.
A high impedance fault (HIF) occurs when there is a
downed, energized primary conductor in contact with the
ground or when the conductor comes in contact with quasiinsulating objects such as trees, poles, or other equipment.
These types of faults are difficult to detect using conventional
protective devices that are triggered by overcurrents. Although
the low currents cause little damage to network components,
HIFs can pose a severe threat to public safety. The downed,
energized lines could be lethal to humans and risk igniting
978-1-4799-5904-4/14/$31.00 ©2014 IEEE
fires due to arcing and flashing at the point of contact [1].
Such faults in distribution systems affect more residential and
commercial areas and are the focus of this work. To avoid
such dangerous situations, quick and accurate fault detection
and location techniques must be employed.
Previously, methods have been explored measuring the third
harmonic current phase angle with respect to the fundamental
phase voltage and comparing it with stored values. Another
approach performs system pattern recognition on harmonic
current energy levels in the arcing fault. The loss of voltage
due to a downed line could also be utilized to detect the fault
as well [2]. Nonetheless, this technique is limited by the lack
of available measurements. The distribution system is usually
only monitored at the substation end of lines, not offering
much information on the remaining parts of the network.
The advent of distributed voltage monitoring devices allow
for the collection of voltage magnitude, angle, and frequency
data all across the network and can collect these measurements in near real-time. Operating at the distribution level,
they can be placed anywhere along the line, not limited
to substation-ends. Frequency Monitoring Network (FNET)
sensors are examples of such devices, developed at Virginia
Tech in 2003 [3]. The wide-area measurement system utilizes
a type of phasor measurement unit, a Frequency Disturbance
Recorder (FDR), to obtain the measurements. Thus, with such
distributed voltage sensors, access to expansive, fast-sampled
data from the distribution system can be achieved.
With access to these extensive voltage measurements, a
novel distribution HIF location algorithm is motivated. As
the low currents are difficult to use to detect and locate the
fault, a method using voltage measurements is favorable. The
occurrence of the HIF in the network impacts the voltage levels
more significantly than the current levels. By studying the
characteristic voltage sags in the distribution system after a
HIF, the location and fault impedance can be determined.
Therefore, an algorithm can be developed using only the
voltage magnitude measurements collected from the sensors.
The monitoring devices are economical in comparison to
traditional substation devices because they are installed and
maintained at distribution level. A fault location method using
these devices would not only use the cost-effective sensors
to their fullest capabilities but also process less parameters
as only voltage is studied. There exists a need for fault
location algorithms for HIFs due to their hazardous nature
yet difficult detection. Although not the most common fault,
such occurrences can be highly detrimental to public safety.
In this paper, a distribution HIF location algorithm is proposed using voltage magnitude measurements obtained from
distributed voltage monitoring devices. Measured and simulated voltage profiles are compared from a known network,
given fault type and phase, and the method determines the fault
location and associated impedance. The simulation locations
are intelligently selected using the Golden section search.
The following section provides background on existing
fault location algorithms based on voltage sags and related
topics. Next, the method details and formulation are presented.
The algorithm is demonstrated using a case study and the
subsequent results are discussed. Lastly, conclusions and plans
of future work are given.
closer to the actual fault location. Therefore, depending on
where the fault occurred, a unique voltage profile of the system
will arise. A radially configured distribution system provides
discernible profiles for the different fault locations. This is due
to the fact that such a system consists of one power source for
a group of customers; a disturbance at one point will affect
the whole system.
The distributed voltage monitoring devices allow access to
extensive voltage data throughout the system, allowing the
construction of a characteristic voltage profile. An example
profile after a fault is shown in Fig. 1, where a fault has
occurred at Bus 4 with an impedance of 5Ω.
Balanced Three−Phase Fault at Bus 4 with Impedance 5 ohms
0.92
0.91
To augment the development of the method, background
information on the tools and concepts utilized is presented
next.
A. Voltage Sag Algorithms
Fault location methods that study voltage sags, or the reduction of system voltages after a fault has occurred, typically
rely on both voltage and current measurements. Lotfifard et al.
[4] describe an approach based on data gathered from meters
installed at some points along a feeder, such as power quality
meters. Knowledge of pre- and during-fault voltage and current
phasors at the root node as well as information about the
fault phase and type are required in this method. After the
load models are updated using the pre-fault measurements, the
during-fault current and voltage data is utilized to discover
the fault location. Using the measured voltage sag data, a
comparison is made with calculated voltage sags of faults at
each node from a modeled network in a power flow program.
The highest similarity is presumed to be the location of the
fault.
Li et al. [5] also present an algorithm for distribution
systems using voltage sag measurements. This approach involves a power flow and fault analysis program, a database
search method, and a pattern recognition technique to identify
the fault section automatically. However, information about
fault current is still needed. With the distributed voltage
monitoring devices only collecting voltage information and the
low magnitude of currents from HIFs, the algorithm proposed
in this paper utilizes only voltage data. Current measurements
after a HIF are not significantly different from pre-fault data.
Thus, the availability of extensive voltage data from anywhere
along the line, all across the distribution system, enables the
development of a fault location algorithm using solely voltage.
B. Voltage Profiles
As previously mentioned, the occurrence of a fault in the
distribution system, such as a HIF, results in characteristic
voltage sags. These voltage sags are “deeper” or more severe
Phase Voltage (p.u.)
II. BACKGROUND
0.9
0.89
0.88
0.87
0.86
1
2
3
4
5
6
7
Bus #
Fig. 1: Voltage profile after a balanced three-phase fault at Bus
4 with an impedance of 5 Ω occurred in a 7-bus radial system.
C. Cost Function
For voltage profiles or any two vectors to be numerically
compared, cost functions are often employed. A cost function
is a real number measure that intuitively represents a “cost”
between one or more variables after some event [6]. In this
case, if the cost function between two voltage profiles is the
difference, we seek to minimize it to find the best match.
Therefore, a suitable cost function is the L1- or One norm.
Given two voltage profiles, the L1-norm is the the sum of the
absolute values of the columns between them [6].
Mathematically, this is written as:
y = [y1 y2 ...yn ]T
T
ŷ = [ŷ1 ŷ2 ...ŷn ]
n
|yi − ŷi |
d = ||y− ŷ||1 =
(1)
(2)
(3)
i=1
The variable d is the result of the evaluation of the L1-norm
between two vectors or profiles, y and ŷ. In this manner, the
smallest difference between two vectors can be found and used
to determine the best match.
D. Golden Section Search
B. Formulation
The Golden section search is a technique for finding a minimum or maximum by successively narrowing down a range in
which it is known to exist [6]. After establishing the start and
end point of a range, it determines
probing points according
√
to the golden ratio, φ = 1+2 5 = 1.618033... Using the
evaluations of the function at these probing points, the range
is narrowed down in each iteration. The technique derives its
name from the fact that it maintains the function values for a
triplet of points whose distances form the golden ratio. This
search algorithm only works with strictly unimodal functions
where the function f (x), for some value m, is monotonically
decreasing for x ≤ m and monotonically increasing for x
≥ m, or vice versa. A typical stopping criterion, using a set
tolerance, is when given range start and end points x1 and x3
and probing points x2 and x4 :
Given a fault of known type and phase has occurred in the
distribution system, a voltage profile of the network is received
from the distributed monitoring devices. The measured voltage
profile, along with the fault type and phase, are inputs for the
fault location algorithm. The model of the distribution system
is also available.
The algorithm subsequently obtains the voltage profiles for
the initial locations as selected by the Golden section search.
The fault at the initial bus locations are iterated through with
all possible impedance values. Each combination’s resulting
voltage profile is compared with the measured voltage profile
using the L1-norm, the cost function. For each of the initial bus
locations, the impedance that provides the minimum L1-norm
is chosen as the most likely combination for that particular
bus location.
The four resulting bus location and best match impedance
results are then compared against one another using the
conditions of the Golden section search. Thus, if convergence
or satisfaction of the stopping criteria is not achieved, new bus
locations are selected and the process is repeated. If convergence is obtained, the best match fault location including bus
number and fault impedance has been found.
Essentially, the algorithm will behave as follows:
1) Obtain measured voltage profile from system.
2) Apply the Golden section search to select the range
and probe locations according to L1-norm error values
between selected and measured voltage profiles.
• Call power simulation software to simulate faults at
selected locations with range of impedance values.
• In a computation platform, calculate the L1-norm
error between the measured and each of the simulated profiles. Apply search routine according to
least error – the bus location and impedance value
combinations that output the minimum L1-norm
error are found.
3) Search routine converges on the best match fault bus
location and impedance or terminates when norm is
lower than specified threshold value.
|x3 − x1 | < τ (|x2 | + |x4 |)
(4)
Some of the benefits in using this search routine are that
it is robust and can handle any unimodal function. After
the initial iteration, only one new probing point needs to be
calculated every iteration– reducing the amount of evaluations
needed. The amount of iterations required only depends on
the tolerance value, not the scale of the problem.
Disadvantages include that two initial guesses are required
when beginning the algorithm and that it does not have as
fast convergence rate as other existing search algorithms.
However, implementation is relatively straightforward, making
the Golden section search a favorable tool for the initial
development of a comparison-based fault location algorithm.
III. M ETHOD
The developed distribution HIF fault location algorithm
compares a measured voltage profile, as obtained from distributed monitoring devices, with calculated voltage profiles
achieved through simulations at possible locations with a range
of fault impedances. The profile locations are selected intelligently using the Golden section search so that every location
does not need to be simulated. The resulting simulated and
measured voltage profiles are compared using the L1-norm.
The best match between the profiles, or lowest error norm
result, provides the best estimate for the actual fault location
and associated impedance. The details and formulation of the
algorithm are given in the following sections.
A. Triggering
The algorithm would be triggered when a sudden, sustained
change in voltage is detected along the feeder in the given
distribution system. Measurements at feeder nodes that do not
correspond to loads would be of particular interest, as the
change from the normal condition would be more obvious.
A node with a large load, such as an induction motor, can
have sudden but momentary drops in voltage when starting.
However, if that drop is sustained, it is apparent that an
abnormal event has occurred in the system, such as a fault.
IV. C ASE S TUDY
A. Setup
To demonstrate the use of the method, a 13-bus PowerWorld
case, in Figure 2, is utilized. The feeder system is comprised
of 13 buses and 10 loads that are classified as either primarily
commercial, industrial, or residential [7]. As can be seen
from the one-line diagram, the breaker between Bus 7 and
Bus 8 is open and, therefore, two separate radial systems
are represented. For testing the algorithm, the radial system
composed of Buses 1 − 7 is used.
PowerWorld, a power system software, is employed for
simulating the faults and obtaining voltage profiles. For the
computational processing of the measured and simulated profiles, Matlab is utilized. SimAuto, the COM automation server
Impedance(ohms)
Fault on Bus 5, Impedance 1 Ohms
20
1
18
0.9
16
0.8
14
0.7
12
0.6
10
0.5
8
0.4
0.3
6
0.2
4
Fig. 2: Feeder system in which Buses 1 − 7 form a radial
configuration.
of PowerWorld, is also used to streamline the algorithm and
eliminate manual retrieval and storage steps.
For the initial development of this algorithm, balanced threephase faults are studied. Since all phases are affected equally
in such a fault, they are the easiest to analyze. In the future,
realistic HIFs and other fault types will be tested.
B. Parameters
Since the model of the distribution system is known, the
maximum impedance, threshold, and tolerance values are derived from an initial study. By studying typical fault currents,
the maximum impedance of the system is calculated to be
60Ω. A conventional tolerance value of 0.01 is applied for
terminating the algorithm if the best match is converged upon
with the Golden section search conditions. If the error norm
calculated in an iteration is already less than the threshold
value, the best match has been found and the time required
to check convergence can be avoided. The threshold value is
derived from the study of contour plots of the error norms for
a particular fault compared against all possible combinations
of fault location and impedance, as shown in Figure 3 and
Figure 4. The darkest color represents the area with the least
norm error value.
By studying the contour plots and the average error norm of
the correct bus location and impedance, accounting for noise,
the threshold value is set to be 0.03; meaning, if the error
norm is less than 0.03, the associated bus location and fault
impedance is the most likely actual combination.
Another insight to be gained from the contour plots is
that the nature of the fault location problem is unimodal, as
required by the Golden section search. This is more apparent
in Figure 4, the surface contour plot, where the cost function
decreases until the correct combination (the dip at Bus 5,
Impedance 1Ω) and increases immediately after. This behavior
allows the use of the Golden section search in finding the
lowest L1-norm error, as to correctly locate the faulted bus
and fault impedance.
0.1
2
1
2
3
4
5
6
7
Bus(#)
Fig. 3: Simulated balanced three-phase fault on Bus 5 with
Impedance 1 Ω compared with measured voltage profiles of
every location and impedance combination.
Fault on Bus 5, Impedance 1 Ohms
1
1.4
0.9
1.2
0.8
1
0.7
0.8
0.6
0.6
0.5
0.4
0.4
0.2
0.3
0
0
0.2
2
20
15
4
10
6
Bus(#)
8
0.1
5
0
Impedance(ohms)
Fig. 4: Surface contour plot of balanced three-phase fault on
Bus 5 with Impedance 1 Ω compared with measured voltage
profiles of every location and impedance combination.
C. Pseudo-Measured Voltage Data
To emulate the measured voltage data obtained from the
distribution network after a fault, a pseudo-measured voltage
profile was created. A specific fault was simulated in PowerWorld and was subsequently processed in Matlab for the
addition of noise. This noise was to mimic the highest measurement accuracy noise of the distributed voltage monitoring
devices, which is usually 0.005 or 0.5%.
Thus, random noise was generated using Matlab’s command
for normally distributed pseudorandom numbers. If m is the
final measured data, s is the simulated, and n is the set of
random noise, the final measured data is achieved as follows:
m = s + 0.005 · n
(5)
In this manner, the measured voltage data encompasses the
effect of measurement noise, imitating the realistic data from
distributed devices. For this case study, the random noise set
is kept constant as to pinpoint differences with different faults
incurred not associated to noise.
The fault location method was tested with an array of faults
occurring in the 7-bus radial distribution system, including
those listed in Table I. Pseudo-measured voltage data was
created for the listed combinations of fault location and fault
impedance. Subsequently, it was inputted into the algorithm
with known fault type and phase, as well as distribution
model in PowerWorld. The fault type was balanced threephase, affecting all phases equally. As observed in the table,
the method was successfully able to find all the faults within 1
or 2 iterations. The maximum variation was 5Ω for impedance,
which is within range of reasonable difference. Figures 5-7
display the visual comparison of the actual and found fault
voltage profiles, illustrating that the results were very closely
matched. The maximum norm error difference between these
profiles was 0.0219.
Measured Profile
Simulated Profile
0.9
Phase Voltage (p.u.)
D. Results
Balanced Three−Phase Fault at Bus 4 with Impedance 5 ohms
0.91
0.89
0.88
0.87
0.86
0.85
1
2
3
4
Bus #
5
6
Fig. 6: Comparison of best match calculated and measured
profiles for a balanced three-phase fault at Bus 4 with
Impedance of 5 Ω.
Balanced Three−Phase Fault at Bus 7 with Impedance 18 ohms
1.025
Measured Profile
Simulated Profile
1.02
TABLE I: Results of algorithm after various balanced threephase faults have occurred in 7-bus radial system.
Algorithm Result
Bus 1, 18 Ω
Bus 3, 10 Ω
Bus 4, 5 Ω
Bus 6, 5 Ω
Bus 7, 19 Ω
1.015
Phase Voltage (p.u.)
Actual Fault
Bus 1, 13 Ω
Bus 3, 10 Ω
Bus 4, 5 Ω
Bus 6, 5 Ω
Bus 7, 18 Ω
Final Error
0.007
0.0219
0.0219
0.0219
0.0082
7
1.01
1.005
1
0.995
0.99
0.985
Balanced Three−Phase Fault at Bus 1 with Impedance 13 ohms
1.06
0.98
Measured Profile
Simulated Profile
1.05
0.975
Phase Voltage (p.u.)
1.04
1
2
3
4
Bus #
5
6
7
Fig. 7: Comparison of best match calculated and measured
profiles for a balanced three-phase fault at Bus 7 with
Impedance of 18 Ω.
1.03
1.02
1.01
variation as demonstrated by the Bus 1, 13Ω fault and also
reducing the run-time even further. It will be pertinent to test
larger systems and observe if the run-time and iteration number
still remains low.
1
0.99
0.98
1
2
3
4
Bus #
5
6
7
Fig. 5: Comparison of best match calculated and measured
profiles for a balanced three-phase fault at Bus 1 with
Impedance of 13 Ω.
All in all, the algorithm worked quite well in intelligently
comparing the measured and simulated voltage profiles to
obtain the best match fault location. The results indicate that
future work can be done in perhaps reducing the impedance
V. C ONCLUSIONS AND F UTURE W ORK
With the advent of distributed voltage monitoring devices,
access to fast-sampled, expansive voltage data across the
distribution network is enabled. This availability motivates
a distribution HIF location algorithm utilizing the provided
voltage magnitude data, as presented in this paper. The results
indicate that the method worked successfully, with close
accuracy and few iterations.
Presently, the algorithm can pinpoint which bus and with
what impedance the fault was incurred, given the fault type
and phase for a small case. In the future, the method will
also be tested with larger systems and different fault types
to investigate if the Golden section search remains effective
in reducing the number of simulations. OpenDSS, an open
source electric power Distribution System Simulator (DSS),
will be used to test the larger networks. The method will also
continue to be improved to reduce impedance variation and
achieve greater accuracy.
ACKNOWLEDGMENTS
The authors would like to thank the Illinois Center for
a Smarter Electric Grid (ICSEG) for their support in this
research.
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