Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1967

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

A Probabilistic Approach for the Evaluation of Fault
Detection Schemes in Microgrids

R. Eslami
Department of Electrical

Engineering
Amirkabir University of

Technology
Tehran, Iran

reza.eslami@aut.ac.ir

S. H. H. Sadeghi
Department of Electrical

Engineering
Amirkabir University of

Technology
Tehran, Iran

sadeghi@aut.ac.ir

H. Askarian Abyaneh
Department of Electrical

Engineering
Amirkabir University of

Technology
Tehran, Iran

askarian@aut.ac.ir

Abstract—An important challenge in protection of a microgrid is
the process of fault detection, considering the uncertainties in its
topologies. Equally important is the evaluation of proposed
methods as their incorrect performances could result in
unreasonable power outages. In this paper, a new fault detection
and characterization method is introduced and evaluated subject
to the uncertainties of network topologies. The features of three-
phase components together with the positive, negative and zero
sequences of current and voltage waveforms are derived to detect
the occurrence of a fault, its location, type and the engaged
phases. The proposed method is independent of the microgrid
topology. To evaluate the performance of the proposed method in
various network topologies, a Monte Carlo scheme is developed.
This is done by computing the expected energy not-supplied
reliability index and the percentage of successful performance of
the fault detection. Simulation results show that the proposed
method can detect faults in various microgrid topologies with a
very high degree of accuracy.

Keywords-fault detection; reliability; network sequences; S-
transform; signal energy

I. INTRODUCTION
Despite the benefits counted for the microgrids, their

designs remained at the laboratory level because of various
technical reasons. One of the most important technical issues is
the challenge of protecting these networks [1]. The dynamic
behavior of microgrids in which a distributed generation (DG)
is connected or disconnected from the network at any time and
also the performance of the microgrids in both normal and
isolated modes create the most important problems in
protecting these networks [2]. The dynamic behavior of
microgrids leads to diversity in magnitudes and the current
directions which encounters the fault detection procedure with
major problems. This issue signifies the necessity of studies in
the field of determining the appropriate protection method for
the microgrids [3]. The authors in [4-6] have introduced the
protection challenges of microgrids. In [3, 4, 7, 8], authors
categorized the various methods for solving this problem.
These methods included voltage analysis, harmonic analysis,

wavelet analysis, and S analysis. In this respect, authors in [9]
suggested monitoring output voltage of distributed generations
and transferring them from abc axis to dq axis and then
determining threshold value in dq axis for detecting fault in the
microgrids. In [10], authors detected faults using created
spectrums from the harmonic impedance and their comparison
by the central server. Using wavelet transform analysis and S
analysis was suggested in [11, 12] and deriving signal energy
was investigated in [13]. All these studies considered only a
certain topology for the microgrid so the effectiveness of these
methods may face challenge in other topologies. In [14], the
fault is detected by monitoring the THD of the output voltage
of distributed generations and its comparison with a threshold
value. In [15], authors used harmonic analysis for fault
detection and the proportion of zero sequence current to
positive sequence current in the fifth harmonic is used and only
single phase to ground faults could be detected by it. Lack of
attention to the dynamic topology of microgrids, difficulty in
detecting various faults (regular faults and high impedance) and
inability to identify the transient states from the persistent faults
were examples of problems seen in the previous studies. Thus,
in this paper a new method is suggested for fault detection in
microgrids and is evaluated by means of Monte Carlo
Simulation. S-Transform, positive, negative and zero sequences
of current and voltage waveforms are used to detect faults. The
presented method can respond to all dynamic topologies of
microgrids. As it was mentioned, the new method is evaluated
using Monte Carlo Simulation. To do this, the performance
accuracy of this method in detecting various faults is evaluated
by means of Expected Energy Not-Supplied reliability index
(EENS) and percentage of successful performances. Validation
results of the suggested method for the persistent and transient
faults properly show that this method has acted very well with
very high reliability in detecting various faults in different
topologies. In addition, this method can distinguish the
difference between the persistent faults and transient states of
microgrids.

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1968

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

II. PROBLEM STATEMENT
Due to the short lines in microgrids, the fault occurrence in

a point of network can lead to disturbance in other points of the
network. To show this, Figure 1 is presented. Based on
occurred fault in point F of Figure 1, Figure 2 shows the
current signals seen in the various line modules in the network.
As seen in Figure 2, by a fault occurring at F, the current
waveform of the faulted line is in overlap with the current
waveforms of the sidelines. This issue bears difficulty in
detecting the exact location of fault using traditional methods.
Meanwhile, this issue which the previous studies only
emphasized the detection of fault occurrence is not true
because inaccuracy in determining the fault location and fault
type can lead to unnecessary switching in the safe lines and as a
result reduction in protection system reliability.

Fig. 1. A sample microgrid

Another issue that challenged the previous microgrid
protection methods is their inability to detect different fault
types in the network. As mentioned before, short circuit current
has high diversity in microgrids. The low amount of this
current even encounters challenges of detecting regular faults.
However, high impedance faults are of the important possible
faults in the electricity networks in which the fault current
produced is very low [16]. Therefore, this type of faults
requires very accurate methods for detection. This issue caused
the authors in [16] to present a new relay design for detecting
these types of faults. The new presented relay in [16] can only
detect the high impedance faults and neglects the low
impedance faults. Therefore, it is obvious that to increase
reliability, protection systems have to be designed in such a
way that they could effectively protect the network in the all
operational structures. Meanwhile, protection has to be able to
detect various possible faults (not one special fault) plus their
exact locations by using various specifications of turbulent
signals.

III. INTRODUCTION AND EVALUATION OF THE PROPOSED
FAULT DETECTION METHOD

A. Required Substructure for the Implementation of the
Proposed Method

Figure 3 shows the required context for implementing the
proposed method in this paper for fault detection in microgrids.
As shown in Figure 3, fault detection modules ( 1 :m M ) are
installed at the beginning of network lines which have
connection with a central server through communication links.
The modules continuously take samples from voltage and
current signals and deal with the proposed fault detection
method to determine the occurrence of a fault, its type, and the

line within it occurs. It is worth noting that in order to increase
the accuracy of fault detection, the proposed strategy, for
detection of fault occurrence, fault location, fault type and the
engaged phases, is to use standard deviation (STD) and signal
energy obtained from the analysis of positive, negative and
zero sequences and meanwhile three-phase components of
voltage and current signal. This paper suggests using S-
transform to calculate the STD and energy of voltage and
current signals.

Fig. 2. Fault current signals in different modules of Figure 1 for fault F

Fig. 3. The required platform for the implementation of the proposed
method

B. Fault Detection Process and its Validation Using Monte
Carlo

Since the parameters and uncertainties vary through time,
sequential Monte Carlo simulation is used to implement the
proposed method. Details have been presented in [17]. During
simulation, the intended reliability indices are evaluated due to
the possibility of fault occurrence in various network lines and
dynamic behavior of microgrid topology. In this respect,
implementation flowchart has been shown in Figure 4. As
shown, seven subroutines have been considered for
implementing the suggested. It is worth noting that the
performance accuracy of the proposed method has been
evaluated in these subroutines based on the occurrence of
permanent faults and transient distortions (including lines
switching on and DGs switching on or off).

Subroutine 1: Fixing faulty elements

Step 1: Check whether the line is fixed due to repair rate.

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1969

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

Step 2: If a line had been fixed, it should be switched on.

Step 3: Implement changes of microgrid topology in the
network.

Step 4: If the network topology is changed go to subroutine 2;
otherwise go to subroutine 3.

Subroutine 2: Simulation of transient state.

Step 5: Simulate the transient state as a result of topology
change (repaired lines switching on or DGs switching on or
off) and then go to subroutine 4.

Subroutine 3: Random numbers for determining the faulty
lines.

Step 6: Compare generated random numbers with the failure
rate of lines, if there is a fault in a line, go to Step 7; otherwise
go to the step 1 in the next simulation.

Subroutine 4: Fault detection

Step 7: Sample three-phase current and voltage in different
points of the network. Signals are sampled by interval time of T
and total sampling number being N.

Step 8: Calculate positive, negative and zero sequences based
on three-phase components for sampled signals.

Step 9: Apply discrete S-transform to different signals as
follows,

,
1

2
[ , ] ( ). (( ) , ).exp( )

N
m m
u q q

n n j kn
S lT u kT k l T

NT NT N







  (1)

in which  is a running Gaussian function window,
1 :m M , 0 1 2, , , , ,q Seq Seq Seq a b c and ,u i v ; i and v indicate

the current and voltage signals respectively.

Step 10: S-matrix, S ,
m
u q , is the S-transform output as (2),

, , ,

,
, , ,

, , ,

1 2 1
[ , ] [ , ] [ , ]

1 2 1
[2 , ] [2 , ] [2 , ]

[ , ] 1 2 1
[3 , ] [3 , ] [3 , ]

1 2 1
[ , ] [ , ] [ , ]

m m m
u q u q u q

m
m m mu q
u q u q u q

m m m
u q u q u q

S T S T S T
NT NT T

n
S lT

S T S T S TNT
NT NT T

S NT S NT S NT
NT NT T

 
 
 
 
 
 

  
 
 
 
 
 
 



   



(2)

Step 11: Calculate the energy Matrix, E ,
m
u q , whose elements are

the square of the amplitude of the respective elements in the S-
matrix.

Step 12: Calculate the signal energy, ,
m
u qE , as follows,

2
, ,

1 1
| [ , ] |

N N
m m
u q u q

e g

g
E S eT

NT 
   (3)

Step 13: Calculate the standard deviation of signal, ,
m
u qSTD , as

follows,

2
,

1 12 2
2 , 2

1 1
, 2

| [ , ] |

(| [ , ] | ( ))

N N
m
u qN N

e gm
u q

g
S eT

NTg
S eT

NT N
STD

 

 




 
 

(4)

Step 14: Compare STD and signal energy values of voltage and
current signals for positive, negative and zero sequences with
threshold values.

Step 15: If all four values of each sequence at Step 14 are
above threshold values, it means a fault happened. Otherwise;
no fault occurred. If the last simulation was a result of topology
change, go Step 6.

Subroutine 5: Detection of fault location

Step 16: Calculate 1K index for modules which detected fault
as follows,

0 1 2

1 1 1
, , ,

2 2 2
, , ,

3 3 31
, , ,

, , ,

i Seq i Seq i Seq

L L L
i Seq i Seq i Seq

E E E

K
E E E

E E E

    
 
   

 
    
 
 
 
    



(5)

Step 17: Determine two modules with the largest K1.

Step 18: Determine current sign for these two modules (if the
crossing current from a module is entering the line of that
module, the sign of sensing current is positive. Otherwise; the
sign of sensing current is negative).

Step 19: If current sign of these two modules have the same
mark, go Step 20. Otherwise; fault location is between these
two modules.

Step 20: If there is another line at current flow path, go Step 21.
Otherwise, the fault is at the last line of this path.

Step 21: Determine the next module at current flow path and
analyze whether this module detects fault occurrence or not. If
it is detected, go Step 22. Otherwise; the fault is at the previous
passed line of this path.

Step 22: If current sign of this module changed, fault location is
at the line where this module locates. Otherwise, go Step 21.

Subroutine 6: Detection process of fault type

Step 23: Calculate m2K
 and m3K

 indices for module ( m m )
having the highest 1K index value as follows,

0 02 , ,
m m m

i Seq v SeqK E E
    (6)

1 2 2
1

3 , , ,
,

1( )m m m mi Seq i Seq v Seqm
v Seq

K E E E
E

   
    (7)

Step 24: Determine fault type as follows,

(8)double phase fault 2 2
m THK K  , 3 31

m THK K 

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1970

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

three phase fault  2 2
m THK K  , 3 31

m THK K 

single phase fault  2 2
m THK K  , 3 32

m THK K 
double phase to ground

fault  2 2
m THK K  , 3 32

m THK K 
Step 25: determine the engaged phases in the fault using the
energy values of the a , b , and c phase current waveforms,
knowing that the faulty phases have larger energy values.

Subroutine 7: Calculating reliability indices

Step 26: Execute load flow and calculate and save not-supplied
energy.

Step 27: If simulation state relates to a transient state, go Step
6. Otherwise, go step 28.

Step 28: If simulation time is lower than 8760 hours (one year),
go Step 1; otherwise calculate the EENS.

Step 29: Compare simulation time with 1000 years. If lower
than this value, go subroutine1; otherwise calculate ENS and
percentage of successful performances as the final result.

Based on the mentioned steps, implementing of the
proposed method is shown in Figure 4.

IV. SIMULATION RESULTS
To evaluate the proposed method, it was implemented on a

sample microgrid which is presented in Figure 5 having the
substructure pointed earlier, the same to the one used in [18].
This microgrid is connected to upstream network through Bus
1. Four DGs are connected in buses 4, 5, 6, and 9.
Specifications for network load are presented in Table I. Based
on the Table I, loads are categorized into three types of
residential, commercial and industrial. Blackout cost for each
load is extracted from [19]. In addition, daily load curve for
loads is based on the patterns in [20]. Considering the dynamic
state of microgrid topology, like study [20] it was supposed
that DGs in each feeder connect to the network when the feeder
load reaches 97% load peak.

TABLE I. CHARACTERISTICS OF THE NETWORK LOADS

Load type
Reactive power

(MVAr)
Active power

(MW)
Bus

number
Commercial 1.5 4.8 2

Industrial 2.5 4.5 3
Municipal 0.8 2.7 4
Municipal 0.5 2.5 5
Industrial 0.7 2.2 6

Commercial 4 3.4 7
Municipal 1 2 8
Municipal 1 3 9

For simplicity of calculations, it was assumed that all lines
have the same repair and failure rates, and their values were 3
hours per fail and 0.8 fails per year respectively. It is worth
noting that DGs’ reliability assumed 100%. The system studied
is analyzed in two different scenarios. In the first scenario, it is
assumed that fault is detected using traditional methods (high
current value of a threshold value) by the central server. In the

second scenario, according to the algorithm, the new method is
used for fault detection. The results of these scenarios are then
compared. It is worth noting that ENS reliability index and
percentage of successful performance of protection system
calculated and analyzed for both scenarios. In both scenarios,
transient states resulted from entering and exiting DGs and
entering lines are assumed as the transient states. It is necessary
that the proposed method does not react for these transient
states because some of loads will not be power supplied due to
the wrong reaction of the protection system.

As the results in Table II represent, the proposed method
has more appropriate indices for fault detection than those of
the traditional methods. The reason is that the new methods
have extraordinary accuracy in detecting faults with limited
current. See Table III for more explanation. According to this
table, while microgrid is working on isolated mode and only
DG1 exists in the network, a fault in line 7 occurs. As it is
clear, since one protected setup can be saved, therefore in the
traditional methods, covering all faults is not possible. This
issue is clear in Table III; while module 6 has been set up on
4kA performance current, and only DG1 exists in the network,
the provided fault current by this DG will be 1.96kA.
Therefore, the fault is not detected by the main protection
system and this issue will increase power outages. That’s why
in Table II both ENS index and percentage of successful
performance of the proposed method are higher than that those
of the traditional methods of fault detection. To do so, the
behavior of proposed method versus double phase to ground
fault, F1, on phases a and b with 100 Ω fault resistance on
line 2 of sample microgrid of Figure 5 will be analyzed.

To determine the values of the energy and the STD
thresholds of voltage and current signals for zero, positive and
negative sequences, the worst situations that could challenge
the proposed method which may interrupt the performance of
detection algorithm are considered. These worst case scenarios
are determined in such a way that fault detection algorithm can
detect all the occurred faults and become indifferent for the
transient stable states occurred in the network. The values for
the normalized energy thresholds and also the normalized STD
thresholds for the voltage and current signals for zero, positive
and negative sequences are presented in Table IV and also
based on the network topology, all possible fault types in
various locations of the microgrid are simulated and the values
of 2

THK , 31
THK , and 32

THK are found to be 0.458, 0.465, and
1.221, respectively.

Table V includes the values for the normalized energy and
the standard deviation for zero and negative sequences of
voltage and current signals obtained from S-transform for all
modules after fault F1 is occurred. Based on Table V, fault
occurrence is detected by 1, 2, 3, 5, and 6 modules. To find out
the location of fault, Table VI includes energy values of zero,
positive and negative sequences of current waveforms for the
modules which detected the fault. Based on Table VI, it is
observed that the values of 1K at sensing modules 2 3m and
are greater than the other ones and based on algorithm of fault
location in Figure 4, the detection algorithm has correctly
detected the fault location on Line 2.

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1971

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

Fig. 4. Evaluation algorithm of the proposed method using Mont Carlo simulation

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1972

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

TABLE II. RELIABILITY INDICES USING THE PROPOSED METHOD

The new proposed
method

Traditional
scenario

113400 213000 ENS (MWh/yr)

8010 7459
The number of occurred

faults

15301 14746
The number of stable

transient states

99.438 51.963
Percentage of successful

Operation

TABLE III. FAULT EVALUATION USING TRADITIONAL METHODS

Fault detection Threshold magnitude Fault current Fault location
Unsuccessful 4kA 1.96kA Line 7

TABLE IV. NORMALIZED THRESHOLD VALUES

Magnitude Parameter Magnitude Parameter

0.028683
0,

TH
i SeqSTD 0.045428 0,

TH
i SeqE

0.044978
1,

TH
i SeqSTD 0.128013 1,

TH
i SeqE

0.029851
2,

TH
i SeqSTD 0.061538 2,

TH
i SeqE

0.047726
0,

TH
v SeqSTD 0.032678 0,

TH
v SeqE

0.077512
1,

TH
v SeqSTD 0.07199

1
TH
v SeqE

0.060298
2,

TH
v SeqSTD 0.040853 2,

TH
v SeqE

TABLE V. OBTAINED NORMALIZED MAGNITUDES BY DIFFERENT MODULES AFTER OCCURRED FAULT F1

Current signal Voltage signal
Module
number

STD Energy STD Energy

Zero sequence
Negative
sequence

0.379362 0.039851 0.123389 0.09009 0.159037 0.063072 0.093733 0.165176 1
0.781557 0.113859 0.353886 0.195613 0.216125 0.142548 0.247754 0.595129 2
0.147892 0.072361 0.220038 0.13365 0.238648 0.084298 0.1834 0.383602 3
0.032486 0.020524 0.042004 0.058979 0.213662 0.105177 0.118865 0.102636 4
0.145174 0.03576 0.093558 0.097953 0.183455 0.070036 0.036288 0.156191 5
0.048626 0.032323 0.075094 0.08735 0.048201 0.045436 0.063322 0.050916 6
0.020046 0.013267 0.016833 0.040954 0.041121 0.028792 0.025332 0.026994 7
0.012456 0.00498 0.007304 0.022525 0.035604 0.020386 0.009474 0.016614 8

TABLE VI. CALCULATED MAGNITUDES OF DIFFERENT PARAMETERS BY

MODULES WHICH DETECT THE OCCURRED FAULT F1

Current
sign

K1
Energy of positive sequence of

current waveform
Module
number

+ 0.470175 0.133308 1
+ 1.148062 0.244677 2
- 0.739419 0.165693 3
+ 0.378299 0.09323 5
+ 0.319105 0.081567 6

Fig. 5. The microgrid studied

By comparing the above values with the values of

2 0.476
THK  , 32 1.232

THK  and using 2, 0.674645i aE  ,

2
, 0.783688i bE  , and

2
, 0.341458i cE  , based on (8), it is concluded

that the occurred fault type is double phase to ground on phases
a and b . To determine the fault type, using the values of

2
, 0.353886i SeqE  , 1

2
, 0.244677i SeqE  , 2

2
, 0.195613i SeqE  ,

2
, 0.247754v SeqE  ,

2
,

1 0.468523
v SeqE

 , and
2

2
, 0.595129v SeqE  , the

values of fault detection indices of 22 0.60164K  and
2
3 1.503942K  are calculated. It is worth noting that Figure 6

shows the way of convergence in ENS reliability index for both
methods. As it is clear, Monte Carlo algorithm reaches
convergence after 1000 years in both methods and the proposed
method created better ENS value than traditional methods. This
issue shows that the reliability of the proposed method is
strongly higher than traditional methods. It is necessary to note
that, in addition to the particular accuracy of the presented
method in detecting various permanent network faults, the
results show that this method has had the appropriate reaction
toward the transient states. The percentage of successful
Operations in Table II represents the appropriate performance
of the methods for both scenarios of permanent and transient
faults occurred.

Fig. 6. Monte Carlo simulation convergence in both proposed scenarios

Engineering, Technology & Applied Science Research Vol. 7, No. 5, 2017, 1967-1973 1973

www.etasr.com Eslami et al.: A Probabilistic Approach for the Evaluation of Fault Detection Schemes in Microgrids

V. CONCLUSIONS
Since the most important challenge of developing

microgrids is the matter of fault detection, the scope of this
paper is to present a new method for fault detection. The new
proposed method uses the signal’s energy and STD which has
been derived form S-transform. To evaluate the method and
determine its performance accuracy versus traditional methods,
Monte Carlo simulation was used. Using this simulation, ENS
reliability index and performance percentage of proposed
method was compared with those of the traditional methods.
The evaluations show that the proposed method has strongly
higher reliability in contrast to reliability obtained by the
transitional fault detection methods. Correct performance of the
proposed method was 99.44% in contrast to the 51.96% correct
performance for traditional methods which represents a
significant increase. It is worth noting that the performance
accuracy of the intended methods is measured based on their
proper reaction against permanent faults and the transient
states. Being independent from the topology is one of the
advantages of the proposed method for fault detection, since
the most important challenge in past designs was their severe
dependence on the network topology. Therefore, by using the
new proposed method, microgrids can be protected in different
topologies with very high reliability.

REFERENCES
[1] T. Liang, C. Schwaegerl, S. Narayanan, Z. Jian Hui, “From laboratory

Microgrid to real markets - Challenges and opportunities”, IEEE 8th
International Conference on Power Electronics and ECCE Asia (ICPE &
ECCE), pp. 264-271, 2011

[2] T. S. Ustun, C. Ozansoy, A. Zayegh, “Modeling of a Centralized
Microgrid Protection System and Distributed Energy Resources
According to IEC 61850-7-420”, IEEE Transactions on Power Systems,
Vol. 27, pp. 1560-1567, 2012

[3] W. Jiang, Z.-y. He, Z. Bo, “The Overview of Research on Microgrid
Protection Development”, International Conference in Intelligent System
Design and Engineering Application, pp. 692-697, 2010

[4] A. A. Memon and K. Kauhaniemi, “A critical review of AC Microgrid
protection issues and available solutions”, Electric Power Systems
Research, Vol. 129, pp. 23-31, 2015

[5] Z. Kai-Hui, X. Ming-Chao, “Impacts of microgrid on protection of
distribution networks and protection strategy of microgrid”, International
Conference on in Advanced Power System Automation and Protection
(APAP), pp. 356-359, 2011

[6] M. A. Redfern and H. Al-Nasseri, “Protection of micro-grids dominated
by distributed generation using solid state converters”, 9th International
Conference on Developments in Power System Protection, pp. 670-674,
2008

[7] S. A. Hosseini, H. A. Abyaneh, S. H. H. Sadeghi, F. Razavi, A. Nasiri,
“An overview of microgrid protection methods and the factors

involved”, Renewable and Sustainable Energy Reviews, Vol. 64, pp.
174-186, 2016

[8] P. Basak, S. Chowdhury, S. Halder nee Dey, S. P. Chowdhury, “A
literature review on integration of distributed energy resources in the
perspective of control, protection and stability of microgrid”, Renewable
and Sustainable Energy Reviews, Vol. 16, pp. 5545-5556, 2012

[9] H. Al-Nasseri, M. A. Redfern, F. Li, “A voltage based protection for
micro-grids containing power electronic converters”, IEEE Power
Engineering Society General Meeting, 2006

[10] S. A. Hosseini, H. Askarian Abyaneh, S. H. H. Sadeghi, F. Razavi, M.
Karami, “Presenting a new method for identifing fault location in
microgrids, using harmonic impedance”, Iranian Journal of Science and
Technology, Vol. 39, pp. 167-182, 2015

[11] A. M. El-Zonkoly, “Fault diagnosis in distribution networks with
distributed generation”, Electric Power Systems Research, Vol. 81, pp.
1482-1490, 2011

[12] S. A. Saleh, R. Ahshan, M. A. Rahman, M. S. A. Khaizaran, B. Alsayed,
“Implementing and testing d-q WPT-based digital protection for micro-
grid systems”, IEEE Industry Applications Society Annual Meeting
(IAS), pp. 1-8, 2011

[13] S. R. Samantaray, G. Joos, I. Kamwa, “Differential energy based
microgrid protection against fault conditions”, IEEE PES in Innovative
Smart Grid Technologies (ISGT), pp. 1-7, 2012

[14] H. Al-Nasseri and M. A. Redfern, “Harmonics content based protection
scheme for Micro-grids dominated by solid state converters”, 12th
International Middle-East in Power System Conference, pp. 50-56, 2008

[15] M. Petit, X. Le Pivert, L. Garcia-Santander, “Directional relays without
voltage sensors for distribution networks with distributed generation:
Use of symmetrical components”, Electric Power Systems Research,
Vol. 80, pp. 1222-1228, 2010

[16] M. A. Zamani, T. S. Sidhu, A. Yazdani, “A protection strategy and
microprocessor-based relay for low-voltage microgrids”, IEEE
Transactions on Ppower Delivery, Vol. 26, pp. 1873-1883, 2011

[17] R. Billinton, A. Sankarakrishnan, “A comparison of Monte Carlo
simulation techniques for composite power system reliability
assessment”, IEEE Conference Proceedings on Communications, Power,
and Computing in Wescanex 95, Vol. 1, pp. 145-150, 1995

[18] W. K. A. Najy, H. H. Zeineldin, W. L. Woon, “Optimal protection
coordination for microgrids with grid-connected and islanded
capability”, IEEE Transactions on Industrial Electronics, Vol. 60, pp.
1668-1677, 2013

[19] G. Wacker, R. Billinton, “Customer cost of electric service
interruptions”, IEEE Proceedings, Vol. 77, pp. 919-930, 1989

[20] M. Gilvanejad, H. A. Abyaneh, K. Mazlumi, “Estimation of the
overload-related outages in distribution networks considering the
random nature of the electrical loads”, IET Generation, Transmission &
Distribution, Vol. 7, pp. 855-865, 2013