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1226 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 2, MAY 2013

Detection of High Impedance Faultin Power Distribution Systems Using

Mathematical MorphologySuresh Gautam , Student Member, IEEE , and Sukumar M. Brahma , Senior Member, IEEE

Abstract— A high impedance fault (HIF) is characterized bya small, nonlinear, random, unstable, and widely varying faultcurrent in a power distribution system. HIFs draw very low fault

currents, and hence are not always effectively cleared by conven-

tional overcurrent relays. Various schemes are proposed to detectsuch faults. This paper presents a method to detect HIFs usinga tool based on mathematical morphology (MM). The methodis implemented alongside the conventional overcurrent relay atthe substation to improve the performance of this relay in de-

tecting HIFs. It is rigorously tested on standard test systems using

PSCAD/EMTDC® to generate test waveforms, and Matlab® toimplement the method. Simulation results show that the proposedmethod is fast, secure, and dependable.

IndexTerms— High impedance fault, mathematical morphology,power distribution system, power system protection.

I. I NTRODUCTION

H IGH impedance faults (HIFs) cannot be detected or cleared by conventional overcurrent relays due to verylow fault current. Such faults occur either when a tree limb or

other high impedance objects make contact with the primarydistribution conductor and the ground, or when a conductor

breaks and touches the earth’s surface such as asphalt, con-

crete, grass, sod, sand, etc. These surfaces impose very high

impedances and limit the fault currents to very low values. HIF

studies are reported by the Power System Relaying Committee

(PSRC) working group, which indicates less than 20% success

rate using conventional protection schemes [1]. The undetected

HIFs are hazardous to the public as they leave an energized

conductor exposed and uncleared.

HIF has been a topic of interest since the 1970s with research

focused on investigation of distinguishing characteristics in cur-

rent and voltage waveforms [1]. HIFs typically occur at voltage

levels of 15 kV and below [1], [2]. They are characterized, in

addition to low values of fault currents, by “random behavior

with unstable and wide fluctuation in current” [1]. HIF currents

are found to be composed of harmonics and high frequency

components. During the initial phase, the researchers were pri-

marily engaged with laboratory models and staged fault studies.

Manuscript received January 18, 2012; revised June 01, 2012; accepted Au-gust 14, 2012. Date of publication September 24, 2012; date of current versionApril 18, 2013. Paper no. TPWRS-00056-2012.

The authors are with Klipsch School of Electrical and Computer Engi-neering, New Mexico State University, Las Cruces, NM 88003 USA (e-mail:[email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2012.2215630

However, with a better understanding of the nature and charac-

teristics of HIF and the advancements in simulation software,

the trend has shifted more towards simulation studies. The HIF

models used for simulation studies are discussed in Section II.

Researchers, from both academia and utilities, have proposed

different methods comprising of single or multiple algorithms

to detect HIFs in a distribution system. Majority of the studies

in this area were reported in 1980s and 1990s, but the sim-

ulation and detection methods are still being developed andrefined. An extensive literature sur vey of HIF can be found in

[3]. The HIF detection methods can be broadly classified into

frequency domain algorithms, time domain algorithms, hybrid

algorithms, and expert systems. Statistical techniques using

sequence components and their harmonics [4], third harmonics

[5], second-fourth-sixth harmonics [6], and high frequency

components (2–10 kHZ) [7] are some of the methods based

on the frequency domain. Other frequency domain algorithms

include the use of burst noise signal [8], improvements over the

use of third harmonic based algorithms [9], [10] and a combi-

nation of current magnitude with the magnitude and phase of its

harmonics [11]. Time domain algorithms include proportionalrelaying [12], ratio ground relay [13], randomness algorithm

[14], use of current flicker [15], fractal techniques [16], and

signal superposition [17]. Frequency and time domain hybrid

methods such as discrete wavelet transform [18]–[24] have

also been proposed by researchers. Because of the random-

ness of HIFs, expert methods using combinations of multiple

algorithms [25]–[28], multiple tools [29]–[31], Kalman filter

[32], [33] as well as training based methods such as decision

tree [34], artificial neural networks [35]–[38], and neuro-fuzzy

method [39] based on genetic algorithm [40] are proposed.

Another expert method [41] uses neural networks with features

extracted using mathematical morphology for the detection of

HIF.

These prior studies and proposed algorithms have helped re-

veal many hidden properties of the HIF, but they are not ca-

pable of detecting all HIFs. These studies also do not report

the detection delay except for [16] and [27], where the detec-

tion delays are reported as 4 s and approximately 1 min, respec-

tively. This paper proposes a superior method that tracks the

shape of the voltage waveforms to detect an HIF with excellent

reliability and speed, using a tool based on mathematical mor-

phology (MM). No training or learning is required.

MM is a nonlinear time domain signal processing tool that

transforms the shape of signals [42], [43]. The transformation

is based on set theory and integral geometry, and was originally

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the current waveform, magnitude of the current drawn, and the

frequency content.

Several models have been proposed in the past for the pur-

pose of time domain simulation. A fixed resistance at the point

of fault [2] is the simplest model which was later modified

by including nonlinear impedances [11] to incorporate the

nonlinearity of the fault current. Inclusion of two anti-parallel

dc-sources connected via two diodes [9] modeled the asym-

metric nature of the fault current, as well as the intermediate

arc extinction around current zero. This model was further

modified by adding one [34] or two [20], [33], [37], [39], [50]

variable resistances in series with the dc sources to model

the randomness of the effective impedance and thus the ran-

domness of the resulting fault current. Other models used for

the analysis of HIF are TACS (transient analysis of control

systems) controlled switch to connect and disconnect the fault

[18] or randomly vary the effective HIF resistance [51], and

differential equation based models [21], [22], [38].

This paper uses an HIF model shown in Fig. 3, connected

between phase and ground, being the phasor value of the phase voltage. It is structurally similar to the source-diode-re-

sistance model described in the previous paragraph using cita-

tions; the parameters are tuned to suit the system voltage. The

model is simple, yet captures all the characteristics of HIF cur-

rent. The two dc sources and are connected to two diodes

and , respectively. The dc sources are of unequal magni-

tude, and their valuesrandomly vary around and every 0.1

ms. This arrangement models the asymmetric nature of the fault

current and intermediate arc extinction. The values of and

depend upon the voltage of the system for which the simula-

tion is performed and the amount of asymmetry to be modeled.

When the instantaneous value , current flows towardsground, and reverses when . During the period when

, no current flows. Changing values of and

also add randomness to the amount of asymmetry and the

duration of arc extinction. Two variable resistances and

are also connected in series with the diodes. These resistances

vary independently and randomly every 0.1 ms, and model the

randomly varying arc resistance. To test the robustness of the

proposed algorithm, the range of variation of the resistances is

restricted such that the fault current always lies below 10% of

the full load current of the feeder. Below are the model param-

eters used for HIF simulation with the IEEE 13-node feeder:

%

%

–

–

Fig. 4 shows voltage and current waveforms during a high

impedance fault modeled on the IEEE 13-node test feeder using

the HIF model discussed in the previous paragraph. The current

in Fig. 4(b) is random and asymmetric with unequal positive and

negative peaks. The interruptions around zero crossings repre-

sent temporary arc extinctions. Fig. 5 shows the charac-

teristics of this HIF. The current waveform [Fig. 4(b)] and the

characteristics (Fig. 5) are similar to those obtained from a

staged fault [15], from a lab setup [9], [22] and from other high-

Fig. 3. HIF model.

Fig. 4. Arc voltage and current waveforms during HIF.

impedance arc models [21], [22]. Moreover, the fast Fourier

transform (FFT) analysis of the HIF current waveform yields an

average second harmonic content of 4.8%, and third harmonic

content of 11.8%. These numbers are within the observed range

of similar harmonics during the staged fault reported in [15].

Hence the HIF model in Fig. 3 faithfully represents the nonlin-

earity, randomness and asymmetry in the fault current, as well

as the arc dynamics and intermediate arc extinctions.

C. Selection of Waveform for HIF Detection

The methods proposed for HIF detection either process only

the current waveforms, or both current and voltage waveforms

to obtain signatures that characterize HIFs. However, it should

be kept in mind that the waveform shown in Fig. 4(b) is the

actual fault current, not the current flowing at the substation

source. The current waveform at the substation will be much

less distorted, because the system still draws sinusoidal load cur-

rent. In our case, in order to test our method against the worst

cases, we have limited our HIF current to less than 10% of the

load current. This means the irregularities of the HIF current

may well be masked substantially at the substation. In order to

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GAUTAM AND BRAHMA: DETECTION OF HIGH IMPEDANCE FAULT IN POWER DISTRIBUTION SYSTEMS 1229

Fig. 5. V-I characteristics during HIF.

Fig. 6. V-I characteristics during HIF.

examine this, Fig. 6(b) shows the current drawn from the sub-

station during the same HIF. As suspected, this current hardly

shows any traces of the irregularities of the actual HIF current.

The strength of MM based tools lies in the fact that they can

detect and distinguish between very small (seemingly insignif-

icant) changes to a wave-shape. Fig. 4(a) shows the voltagewaveform across theHIF. A zoomed view shows there is a slight

distortion in the waveform. This slight distortion is obviously

also reflected at the substation, as seen in Fig. 6(a). It is possible

that the current waveform at the substation would also contains

a slight disturbance, but the extent of such distortion may vary

for different pre-fault conditions. In contrast, the distortion in

the voltage waveform does not depend on the pre-fault currents,

and is more likely to provide a more consistent signature when

processed by MM. Due to the unique property of MM based

tools to detect very small distortions, and the better likelihood

of the voltage waveforms providing a more consistent signature

when processed by such tools, the voltage waveform is chosen

for processing. The results documented in Sections III and IV

further confirm the validity of this choice.

III. DEVELOPING THE BASIS FOR HIF DETECTION USING MM

A. MM Operations

As mentioned in Section I, MM is composed of two elemen-

tary transformations—dilation and erosion. Based on these two,

several other transformations are defined [52]. Opening and

closing are other commonly used transformations for one-di-mensional signals. These four transformations are defined now.

Equation (1) defines the dilation of a signal by :

(1)

Similarly, (2) defines the erosion of a signal by :

(2)

In these equations, is the signal to be transformed, de-

fined in domain , and is the struc-turing element, defined in domain , and

and are integers such that .

Based on these two elementary transformations, opening and

closing are defined by (3) and (4):

(3)

(4)

It can be observed from (1)–(4) that these transformations

require only addition and comparison. So, they impose a very

low computation burden, which is a great advantage for real

time applications.

The structuring elements are the foundation of all MM trans-

formations, and are used as probes for feature extraction. They

may have different lengths and can be linear, sinusoidal, square,

circular, or other geometrical shapes [52]. The frequency of in-

terest plays a major role in the selection of a structuring element

for a particular application, though the choice is influenced by

other factors such as the type of signal, frequency spectrum, and

the sampling rate. The optimal choice would be such that it cap-

tures the feature of interest while suppressing other features.

Equation (5) defines a Closing Opening Difference Opera-

tion (CODO) [48]. This operation is very effective in detecting

any disturbance in waveforms. The application proposed in this

paper uses the CODO operation to detect and classify HIFs. Alow sampling rate of 3840 Hz (64 samples per cycle) is chosen

so that the computation burden is low, while still preserving the

ability to capture the disturbance signature:

(5)

Gautam and Brahma [53] present a detailed analysis that

leads to some guidelines in selecting an optimal structuring

element to detect disturbances in power system. Based on these

guidelines, samples of voltage waveforms from the secondary

of voltage transformer (VT) are selected to be treated with

CODO. The waveforms are normalized by the peak value of

their rated value prior to the treatment with CODO to make

the application general and applicable at all voltage levels.

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Fig. 7. Phase A voltage waveform and the CODO output for High ImpedanceFault.

Since the waveforms are normalized, the height (magnitude) of

each element of the structuring element is set at 0.01 [53]. The

guidelines also recommend structuring elements with shorter

length for disturbance detection. So, an iterative process was

adopted to determine an optimal length. Structuring elements

with lengths 2 to 5 were implemented and performance was

observed. It was found that all the structuring elements were

capable of detecting the HIFs, but the shortest one resulted in

the least delay. Therefore, a structuring element of length 2 was

selected for this application.

B. Deriving Unique HIF Signature From the CODO Output Simulations were carried out for high impedance faults and

other disturbances at different locations indicated in Fig. 1. The

legends in the location boxes denote the number of the simula-

tion case with letter prefixes. The prefixes H, C, and L denote

HIF, capacitor switching, and load switching, respectively. For

example, H-2 denotes the second simulation case of HIF. The

voltage waveforms are sampled from the secondary side of VT,

and normalized by the peak value of the rated secondary voltage.

The normalized voltage is then treated with the CODO opera-

tion defined by (5), with the structuring element of length 2 and

height 0.01, selected as described in Section III-A.

Figs. 7–9 show the normalized voltage waveforms and thecorresponding CODO output for three different disturbances.

Since the disturbances in the voltage waveforms are very small,

zoomed parts of the waveforms are inserted to clearly show the

disturbances.

Fig. 7 shows phase A voltage waveform, and the corre-

sponding CODO output for a phase A to Ground HIF simulated

at 6.817 s at location H-4 (Fig. 1). The HIF generates unequal

and non-uniformly distributed series of spikes in the CODO

output over an extended period of time. These spikes are

distinctly larger in magnitude compared to the CODO output

during the healthy condition, which is almost zero.


sponding CODO output for a three phase capacitor switching

(ON) simulated at 6.8043 s at location C-2 (Fig. 1). The CODO

Fig. 8. Phase A voltage waveform and the CODO output for Capacitor Switching.

Fig. 9. Phase A voltage waveform and the CODO output for Load Switching.

output for the disturbance caused by capacitor switching shows

two continuous large spikes, when the disturbance occurs. It

was observed in other cases of capacitor switching reported in

Section V that capacitor switching gave either a single spike or

a series of consecutive spikes, which is distinctly different than

the non-uniformly distributed spikes generated due to an HIF.Since the effect of capacitor switching on voltage waveforms

is short-lived, the duration of such continuous spikes was never

observed to be more than one eighth of a cycle, as opposed to

the spikes corresponding to an HIF, which continued over time.


sponding CODO output for a two-phase (A-C) load switching

at 6.8043 s at location L-1 (Fig. 1). The switching is captured

by a single, relatively smaller spike in the CODO output, as the

effect of load switching on the voltage waveforms is minimal.

Figs. 7–9 show that the inception of disturbances are cap-

tured by one or more distinct high magnitude spikes in the

output of the CODO operation, which otherwise lies below

a low threshold during healthy condition. The observation of

the CODO output of the three disturbances also reveal that the

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pattern of a series of spikes generated by the HIF is clearly

different from the single or continuous spikes over a short time

span generated by capacitor switching, and load switching. This

distinction in signatures can be exploited to detect and classify

HIF and non-HIF disturbances. The detection and classification

method is described in the following section.

IV. FORMULATION OF METHOD TO DETECT AND

CLASSIFY A HIGH IMPEDANCE FAULT

This section describes a method to detect an HIF, and distin-

guish it from other disturbances discussed in Section III. The

first step in this process is the detection of disturbance. Based

on the analysis of the CODO output for the three different dis-

turbances in Section III, a disturbance is detected if a spike is

present in the output of the CODO operation. A threshold value

is set and the CODO output is tracked for each phase-voltage

to detect the disturbance. For the application proposed in this

paper, the threshold value was set at 115% of the maximum

value of the CODO output during the healthy condition. As

mentioned in Section III, the CODO output is close to zeroduring healthy condition; the 15% margin is simply a buffer.

This threshold value translates to approximately 0.0053 pu for

the examples shown in Figs. 7–9.

The next step is to distinguish an HIF from other distur-

bances. As mentioned in Section III, the comparison of the

CODO output for different disturbances in Figs. 7–9 shows that

an HIF generates a series of non-uniformly distributed spikes

over an extended time-period, whereas a capacitor switching

and a load switching generate either a single spike or multiple

consecutive spikes over a short time period never longer than

one eighth of a cycle. The difference in the signatures is so

clear, there is no need for any learning based pattern recogni-tion method. A rule-based method is therefore adopted. This

method, and an algorithm to implement it are described now.

In addition to the threshold value defined previously in this

section to detect a disturbance, the algorithm requires two other

parameters—wait-time and reset-time —for the clas-

sification of HIF. Wait-time is implemented to avoid the

initial multiple consecutive spikes that are sometimes generated

by capacitor switching. To make sure such spikes are no longer

present in the CODO output, a conservative choice of a quarter

cycle is made for the wait-time. For the chosen sampling rate of

64 sample per cycle, the wait-time translates to 16 samples, and

equals to 4.17 ms in a 60-Hz system.Once the wait time is over, the method prepares to detect an-

other spike in the CODO output. If such a spike is detected, it

is certainly due to an HIF. The detection time for this second

spike, or the detection delay, depends upon the amount of tran-

sients present in the voltage waveform. A slower change in the

effective impedance of HIF implies less transients in voltage

waveform and thus, a larger separation of spikes, and a larger

detection delay. Similarly, a faster change implies more tran-

sients and thus, a smaller separation of spikes, and a smaller

detection delay. Therefore, it is necessary to wait for some time

to allow even the most sparsely separated spike to be detected.

This time is defined as the reset time . If no spike is en-

countered during the reset time, the algorithm determines the

detected disturbance was not an HIF, and resets itself. However,

Fig. 10. Flowchart for the proposed detection and classification method.

if a spike is detected between the end of the wait time and end of

the reset time, the HIF flag is made high. At the end of the reset

time, if the HIF flag is high, a trip or alarm signal is generated,otherwise the algorithm resets and starts afresh. Based on the

simulation studies, a conservative choice of 1 s is made for the

value of the reset time . This means any HIF will be detected

and classified within 1 s.

The algorithm that captures this logic is shown in Fig. 10.

As can be seen from this flowchart, at the very beginning of

the process, a pickup signal from an overcurrent relay is in-

cluded. If the relay picks up, it means there is a conventional

fault, and the whole algorithm is simply suspended by resetting

all flags and timers. Thus, the proposed detection and classifi-

cation method is integrated with a digital overcurrent relay, and

simply suspends operation for all faults detected by the over-

current relay. The rest of the algorithm is self-explanatory, as it

basically implements the detection and classification logic de-

scribed in the previous paragraphs. The threshold value Th is

taken as described previously in this section. DF stands for Dis-

turbance Flag.

V. SIMULATION R ESULTS

A total of 15 HIF cases were simulated at different loca-

tions, on different phases and at different time-instants in the

IEEE 13-node test feeder. The HIF locations were chosen at

nodes as well as at intermediate points. Intermediate points were

chosen in the branches with distributed loads. The locations

were chosen to include 1-phase, 2-phase, and 3-phase branches;

and both unbroken (denoted as type-1) and broken (denoted

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TABLE ISIMULATION R ESULT FOR IEEE 13-NODE TEST FEEDER

as type-2) conductors were considered. Six cases of capacitor

switching and four cases of load switching were also simulated.The simulation consisted of switching ON and OFF of the ca-

pacitor banks at node 611 and node 675. Capacitor switching

also included switching the banks ON and OFF at different time-

instants (at different points on the voltage waveform). Similarly,

load switching consisted of switching ON and OFF of 2-ph and

3-ph loads at node 692 and node 671 at different time-instants.

The different disturbance inception times were considered since

the transients in the voltage waveforms are dependent on in-

ception times. All these cases are marked out in Fig. 1, with

legend explained in Section III-B. The algorithm described in

Section IV was implemented on the sampled voltage waveforms

from the VT secondary. Table I summarizes the results.The table shows the disturbances simulated along with their

location, type (nature), and inception time. For the HIF cases,

the time of occurrence of the second nonconsecutive spike, and

the corresponding detection delay are also shown. For other dis-

turbances, there is no second spike detected. As seen from the

table, the algorithm successfully detects all cases of HIF while

segregating all other disturbances. The detection delay varies

from 17 ms for the fastest detection to 588 ms for the slowest

one.

The study was then carried out for the 34-node feeder. The

process of selecting disturbances, their locations, and types was

the same as for the 13-node case. Fig. 2 shows all the distur-

bances simulated. Table II summarizes the results for 34-node

feeder, which also shows excellent detection and classification

TABLE IISIMULATION R ESULT FOR IEEE 34-NODE TEST FEEDER

of HIFs. The detection delay in this case varies from less than

10 ms for the fastest detection to 66 ms for the slowest one. As

mentioned in Section II-A, the 34-node feeder is lightly loaded.This means the method is not affected by loading conditions.

To test the reliability and robustness of the method even further,

a study was performed with both test systems operating at half

load. The performance of the method was similar to that ob-

served with full load. This underscores the rationale described

in Section II-C in choosing the voltage waveform for this study,

making the method robust against pre-fault (load) conditions.

These results show that the algorithm is robust, since it success-

fully works on two standard distribution systems with very dif-

ferent properties, simulated with varying load conditions. The

100% success rate of detection and classification for both sys-

tems indicates the proposed method exhibits excellent reliabilityand security.

VI. CONCLUSION

This paper summarizes the use of MM to detect high

impedance faults which are otherwise undetected by the over-

current protection scheme in a power distribution system. An

MM based tool is proposed, implemented and tested to develop

a method that can be integrated as a separate module with a

digital overcurrent relay. The detection method uses voltage

waveforms sampled at the substation. The proposed method is

designed to operate in parallel and assist the existing protection

scheme to detect an HIF. This method is fast, with a detection

delay of 1 s. The method is shown to exhibit reliability, as all

the HIF cases simulated were detected, even for fault currents

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less than 5% of the full load feeder current. It also exhibits

security, since there was no false operation for other distur-

bances in the system. The method benefits from the inherent

advantage of low computation burden of all MM based tools,

which is an advantage for real-time applications. The method

is successfully tested on different standardized test feeders,

with different types and locations of disturbances at different

inception times, and for different pre-fault loading.

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Suresh Gautam (S’08) received the Bachelor of Engineering degree and the Master of Sciencedegree in electrical engineering from the Institute of Engineering, Tribhuvan University, Nepal, in 2002and 2007, respectively, and the Master of Sciencedegree in electrical engineering from New MexicoState University, Las Cruces, in 2010, where he iscurrently pursuing the Ph.D. degree.

From 2002 to 2004, he was with Kathmandu En-gineering College, Kathmandu, Nepal, as a lecturer.From 2004 to 2007, he was with Nepal Electricity

Authority, a public utility of Nepal, as an electrical engineer. His research inter-ests are power system protection, digital relaying, power system transients, and power quality.

Sukumar M. Brahma (M’04–SM’07) receivedthe Bachelor of Engineering degree from L. D.College of Engineering, Ahmedabad, India, in 1989,the Master of Technology degree from the IndianInstitute of Technology, Bombay, India, in 1997,and the Ph.D. degree from Clemson University,Clemson, SC, in 2003, all in electrical engineering.

From 1990 to 1999, he was a lecturer in the

Electrical Engineering Department with B. V. M.Engineering College, Vallabh Vidyanagar, India.From August 2003 to June 2007, he was an Assistant

Professor at Widener University, Chester, PA. He is presently an AssociateProfessor and Associate Director of the Electric Utility Management Program(EUMP) at New Mexico State University, Las Cruces.

Dr. Brahma is the past Chair of the IEEE Power and Energy Society’s LifeLong Learning Subcommittee, Chair of the Distribution System Analysis Sub-committee, Secretary of the Power and Energy Education Committee, and is onseveral working groups of the Power System Relaying Committee.

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