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www.etasr.com Bangar Raju & Subba Rao: Evaluation of Passive Islanding Detection Methods for Line to Ground … 

 

Evaluation of Passive Islanding Detection Methods 
for Line to Ground Unsymmetrical Fault in Three 

Phase Microgrid Systems 
Microgrid Islanding Detection Method 

L. Bangar Raju 
Electrical and Electronics Engineering Department 
Koneru Lakshmaiah Educational Foundation 

Guntur, India 
lsmlbr@yahoo.in 

K. Subba Rao 
Electrical and Electronics Engineering Department 
Koneru Lakshmaiah Educational Foundation 

Guntur, India 
principal.coe@kluniversity.in 

 

 

Abstract-Distributed Generators (DGs) are incorporated in the 

power distribution systems to develop green energies in 

microgrids. Islanding is a challenging task in a microgrid. 

Different types of islanding methods, e.g. local and remote 
methods, have been developed for handling this task, with local 

methods being easier to implement, while remote methods are 

communication-based and costly. The local methods are classified 

as passive, active, and hybrid, out of which the passive methods 

are more simple and economical. In this paper, a passive 

islanding detection method is proposed to detect single line to 

ground fault. This fault is considered to represent the 60 to 70% 

of the total un-intentional faults of this category. The available 

passive methods cannot detect islanding at lower power 

mismatches as the variations in voltage and frequency fall within 

thresholding values. In this method, the voltage signals are first 

retrieved at the targeted DG output and then the phase angle is 

estimated. Finally, the phase angle is differentiated to get Rate Of 
Change Of Voltage Phase Angle (ROCOVPA) to detect islanding, 

and then it is compared with the Rate Of Change Of Frequency 

(ROCOF) at zero percent power mismatch. Simulation results 

depict that the ROCOVPA is more effective than ROCOF. The 

proposed method not only reduces detection time and Non-

Detection Zone (NDZ) but is also stable during non-islanding 

cases like load connection and disconnection to avoid nuisance 
tripping. 

Keywords-distributed generation; non detection zone; point of 

common coupling; ROCOVPA; ROCOF; line to ground fault 

I. INTRODUCTION  

During the normal mode, a microgrid is in synchronism 
with the main grid feeding the connected loads and importing 
the mismatch power of the load from the grid. Based on load 
demand, the mismatched power is supplied by the grid. But 
during unintentional unsymmetrical faults on the system, the 
microgrid has to detect the fault condition and isolate itself 
from the main grid within 2s as per IEEE-1547-2018 
regulations. There are symmetrical and unsymmetrical faults, 
but in this paper only unsymmetrical single line to ground fault 
was tested as the majority of faults are of this nature. The 
different islanding detection methods have their own 

advantages and disadvantages. The active methods affect the 
power quality due to perturbations during testing. The passive 
methods fail to detect islanding at lower power mismatches due 
to the smaller variation in voltage and frequency above 
threshold. The hybrid methods are good to detect islanding but 
power quality problems arise due to injections of perturbations. 
Communication methods are good with a smaller Non 
Detection Zone (NDZ) but are costly. The implementation of 
such methods depends on the size of the microgrid and the 
criticality of loads. 

To mitigate these problems, in this paper the Rate Of 
Change Of Voltage Phase Angle (ROCOVPA) method is 
proposed which detects islanding at zero percent mismatch 
power and also avoids nuisance tripping during non-islanding 
operations like load connection and disconnection. A simple 
methodology is used. At first, the voltage phase angle is 
calculated at the output of DG and then differentiated to get the 
ROCOVPA to detect islanding. In normal conditions, when 
there is no fault, the variations are within the threshold values 
but during fault conditions the variations exceed the threshold 
values to island the microgrid safely from the main grid within 
2s. The DG feeds the connected load in droop control in 
islanded mode, without any power interruption to load. 

The proposed ROCOVPA methodology can be extended to 
detect symmetrical and unsymmetrical faults. In this paper, the 
ROCOVPA is tested and compared with the Rate Of Change 
Of Frequency (ROCOF) method in Matlab/Simulink, in which 
ROCOVPA is proved to perform better. As per the result 
analysis, the proposed ROCOVPA method detects islanding at 
even zero percent mismatch power (0% NDZ). The testing is 
extended for non-islanding cases during load connection and 
disconnection for stability. The ROCOVPA method is proved 
to be stable during non-islanding cases and also avoids 
nuisance tripping. 

The comparison of the proposed ROCOVPA method with 
ROCOF proves that it is better in discriminating islanding and 
non-islanding operations with less NDZ and detection time.  

Corresponding author: L. Bangar Raju



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II. NETWORK AND MATHEMATICAL MODEL 

The network model is shown in Figure.1. The ROCOVPA 
islanding detection method is tested on a DG with 2.5KW with 
an interfaced inverter. A parallel RLC load is connected to the 
DG with a quality factor of 1.8 at the Point of Common 
Coupling (PCC). The DG inverter is connected to the main grid 
to the PCC through a 3-phase circuit breaker. The inverter is 
connected to the PCC with filter values: ��=2��	,��=2�	, 
and 
�=10�.	

 

 
Fig. 1.  Network model of the islanding detection ROCOVPA method. 

The mathematical model of the islanded microgrid in the 
abc frame is given by the following equations: 


�,��� �  �� � ��,���  �� �  
� ��,��� � 
���      (1) 
��,��� �  �  
��� /R � �!,��� � � ���  
���    (2) 


���  ��  �  � �"# �  �$,��� � 
$ �$,���    (3) 
where 
�,��� , Vabc, it,abc, and iL,abc are the terminal's phase 
voltages and currents respectively of the inverter at the PCC . 

These three-phase instantaneous voltages and currents are 
to be transformed to the synchronous rotating frame dq0 in 
order to have control of active power (d-axis) and reactive 
power (q-axis), to keep mutual inductance constant, to achieve 
the desired output, to have infinite gain control on PI, PID, by 
adjusting integrators, and to make steady state error to zero to 
make computations easy. 

)()()( tButAXtX +=
    
(4) 

)()( tCXty =
    
(5) 

tdVtu =)(     (6) 

A, B, C, and D are constants given by: 

1
0

0

02
00 0

1 20
0 0

1 1 1
0

Rt

L Lt t

RlCRt
L LA

RRl
C

L L

C C RC

ω

ω
ωω ω

ω ω

 
 
 
 
 
 
 
 
 
 
 
  

− −

−
−

= −
−

−

−
−

    (7) 









= 000

1

t

T

L
B     (8) 

[ ]0000=C     (9) 

[ ]0=D     (10) 
%& � '��� ��( �$� 
�)    (11) 

These equations give the transfer functions of
td

d
V

V
, 

where dV  and tdV are the input and output components of the d 
axis. 

III. NON DETECTION ZONE 

The efficacy of islanding detection depends on minimizing 
the NDZ [4, 5]. The method depends on the percentage of 
active power mismatch, which as per IEEE-1547 has to be 
smaller than 15% and the detection time has to be less than 2s. 
The network for the study of NDZ is shown in Figure 2. The 
DG is connected to the grid through an interfacing inverter, the 
PCC, and a utility switch [6]. The 3-phase parallel RLC load is 
connected at the PCC [7]. 

 

XDG Grid
P+JQ P+JQ

Circuit
Breaker Local

Load

Utility
Switch

R

P J Q∆ + ∆

L

L L
P jQ+

C

 
Fig. 2.  DG network connected with the grid system. 

Equations (12) and (13) give the voltage and frequency at 
the PCC: 

R

v
PP

2

=∆+     (12) 

fL

V
QQ

π2

2

=∆+     (13) 

( )PPRV ∆+=    (14) 

( )QQL
V

f
∆+

=
π2

2

    (15) 

In islanding conditions, Δ+	and Δ, become zero, as there is 
no main grid. The under/over voltage protection (UVP/OVP) 
and under/over frequency protection (UFP/OFP) methods are 
very simple and incorporated in all grid connected inverters 
and relays connected with DG system protection. In these 



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methods, the voltage and frequency are both constantly 
monitored at the PCC [1, 8], where: 

∆P = +$-./ − +/0    (16) 
∆Q = ,$-./ − ,/0   (17) 

If ∆P 1 0, then the voltage at PCC will fluctuate from the 
normal level, which is an indication of islanding condition. If 
∆Q 1 0, then the frequency at PCC will fluctuate from the 
normal level, which is an indication of islanding condition. 
Both these islanding detection methods leave behind a large 
NDZ. The islanding detection may fail, when ∆P and ∆Q are 
close to zero [8]. 

Voltage 
3  and frequency �3 under islanding mode are 
given by: 


3 �  4
5+6    (18) 
� 3 �  7389:$5;6  �  

<=
9:$5;6    (19) 

With these, the voltage and frequency deviations due to 
power mismatches are given by: 

>
 �  V’ – V �  4
5+6  - C
5+ � >+6    (20) 
>� � �3 D  � � 738$5;6 -

738
$5; EF;6�

<G=
$G;  - 

<G5=EFH6
$G5;EF; 6    (21) 

Equations (20) and (21) show the variations in voltage and 
frequency due to power mismatch [2]. If the power mismatch is 
substantial, the variations in voltage and frequency can be 
identifiable. If the mismatch is too small (less than 15%) the 
islanding cannot be detected and hence the formation of the 
NDZ. Figure 4 shows the NDZ for different power mismatch 
percentages [8, 9]. When the reference value is 88% and 110% 
(as per Table I), under / over voltage and grid RMS Voltage 
I 
= 415V, then Vmax = 456V and Vmin = 365V. The schematic 
diagram of the grid-connected microgrid is shown in Figure 3. 
The inverter gate pulses take the feedback grid voltage and the 
set reference. The trigger pulses are given to the inverter 
accordingly and the output voltage is controlled. The PV is 
connected to the buck/boost converter to have control on DC 
reference voltage. The DC/DC converter is connected to the 
interfacing inverter. The inverter is connected to the PCC via a 
low pass filter LCL. The microgrid is connected to the grid via 
a circuit breaker, so that the microgrid can be islanded during 
faults. A local parallel RLC load is connected to the microgrid 
at the PCC and the microgrid feeds this local load from the DG, 
even in the absence of grid. 

 

 
Fig. 3.  Schematic diagram of the grid-connected micorgrid. 

NDZ is the operating region in which islanding detection 
methods cannot detect islanding as specified by IEEE-1547. It 
is expressed in terms of % power mismatch or in terms of 
parameters of the load like R, L, and C. The NDZ of OVP/UVP 
and OFP/UVP islanding schemes are shown in Figure 4 [10, 
11]. These techniques fail to detect islanding in mismatched 
power less than 15%. In a distribution network, voltage values, 
as per standards are between 0.88p.u. and 1.1p.u. for voltage 
relays. These voltage levels are equivalent to DV = 0.12p.u. 
and DV = 0.1p.u. respectively. The calculated power mismatch 
for our test network (the inverter rated output power is 2.5KW) 
are 0.3KW and 0.25KW respectively. 

 

 
Fig. 4.  Mapping of the NDZ in ∆P versus ∆Q for OVP-UFP relays. 

In grid mode, the load consumes the reactive power [12]. 
But in islanding mode, DGs cannot inject reactive power to the 
load, as DGs operate at unity power factor, because the load 
behaves like a resistance [13], since the load resonance 
frequency is equal to the system frequency at the PCC. Hence, 
to find more deviations in frequency, the load selected is 
parallel RLC with a high quality factor of 1.8 in islanding mode 
[14, 15]. The quality factor is given by: 

,J � KL
� � MNO$ � 
C
P
$    (22) 

where KL  � 2R�L � S√$P. 
Equation (20) gives the energy stored in the RLC circuit. 

High quality factor loads have high capacitance and small 
inductance with or without a high parallel resistance [16, 17]. 
The islanding detection is complex with resonant frequency 
loads of higher quality factor [18, 19]. The percentage 
mismatch is not the criterion for load parameters [20, 21]. The 
load reactive power is given by: 

,$U�� � 
V�W9 X SN$ D K� Y  �  Δ,    (23) 
Equation (21) depicts the variation in reactive power for 

different values of L and C. The % mismatch power for 
OVP/UVP and OFP/UFP relays is shown in Figure 3 and is 
given by the equations for active power imbalance: 

∆P = 3VGI–35
 � ∆
6G [ � D3 G∆VG[    (24) 
∆Q = 3

]8
N^		$ 51 D K9��6=3

]8
N^	$ `1 D

N8̂
Na8b    (25) 

where		Kc		and		Kd		 are system and resonance frequencies [22, 
23]. The system frequency varies until it reaches the resonant 
frequency of the load in islanding mode and is given by: 



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Kde		 S√$P    (26) 
and the reactive power imbalance is given by: 

∆Q = 3
]8
N^		$ f1 D

Ĵ8
gJ^h∆i8jk    (27)	

where �c is the nominal frequency. 
The different islanding standards are shown in Table I. The 

frequency range as per IEEE-1547-2018 is between 49 and 
51Hz, the voltage is between 365 and 456V and the range of 
the parameter ∆V= V’ – V is not considered as the case of zero 
power mismatch is considered [24]. In this case, the voltage 
fluctuations will not cross the limits. But in other cases, when 
load active power PL > generated active power PG,(-15%) or  
PL < PG (+15%) the voltage suddenly goes down or up 
respectively. 

TABLE I.  ISLANDING STANDARDS 

Standard 
Detection 

time (s) 

Quality 

factor 

Trip frequency range, 

nominal frequency lm 
(Hz) 

Trip voltage 

range (V) 

IEC 62116 t < 2 1 �L D15n � n �L+1.5 0.88 n 
 n1.15 
Korean t < 0.5 1 59.3 n �L n 60.5 0.88 n 
 n 1.10 

IEEE-1547-
2018 

t < 2 1 58.8 n �L n	61.2 0.88 n 
 n 1.10 
IEEE-929-
2000 

t < 2 2.5 59.3 n �L n	60.5 0.88 n 
 n 1.10 
 

IV. THE PROPOSED METHOD OF ISLANDING DETECTION 

The proposed method can detect islanding at zero % power 
mismatch and the detection time is less than in ROCOF. In this 
method, at first the voltage phase angle is measured at the 
targeted DG and then the rate of change of voltage phase angle 
is calculated to detect the islanding phenomenon. In non-
islanding condition, the rate of change of the phase angle is 
negligible after certain time but in islanding this becomes 
substantial and the islanding is detected. ROCOVPA also 
avoids nuisance tripping, thus protecting the stability of the 
microgrid.  

 

 
Fig. 5.  Current controller block diagram. 

The ROCOVPA method is tested with the 2.5KW DG with 
a current control mode inverter connected to an RLC load with 
1.8 quality factor. Figure 5 shows the current control mode to 
control the active and the reactive power of the load. In the 
proposed method, the variation of voltage phase angle is 
monitored at the specified DG. If there is a change in the 
voltage phase angle, the rate with respect to time is calculated. 
During the islanding, the deviations of the rate of change of the 
phase angle exceed the threshold in order to detect the 
islanding condition. If the relay threshold is fixed, then the trip 
command to circuit breaker can be initiated. 

The algorithm of the proposed ROCOVPA method of 
islanding detection is shown in Figure 6. The voltage phase 
angle at the DG is measured first. After the measurement of the 
phase angle of the voltage, the rate of change of voltage phase 
angle is calculated. In a normal situation this value is smaller 
than 1deg/sec (fixed threshold value) but during islanding, the 
value suddenly crosses the threshold, depending upon the fault 
severity, by means of which the islanding is detected. During 
the non-islanding mode this value is in limit, hence nuisance 
tripping is avoided. 

 

 
Fig. 6.  Flow chart of the proposed ROCOVPA. 

V. DESIGN PARAMETERS OF THE INVERTER 

The proposed ROCOVPA method was tested on the 
network shown in Figure 1 with the parameters given in Table 
II. The DG capacity with interfaced inverter is 2.5KW. The 
interfaced inverter is connected to the main grid through a 
breaker via the PCC. A 3-phase parallel RLC load is connected 
at the PCC. The input DC Voltage to the inverter is 500V. The 
output line to line voltage of the inverter is 380V. The line 
resistance and inductance are 1.5mΩ and 2mH respectively. 
The nominal grid frequency is 50Hz. The inverter carrier 
frequency is taken as 1KHz. The load parameters with a quality 
factor of 1.8 are: 	
$ = 1.76mΩ, LL =3.2mH,	�$ = 3.2µF. The 
load resonant frequency is 50Hz. Current controller gains are 
op = 0.4 and o� = 500. 
    



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TABLE II.  SIMULATION INVERTER PARAMETERS  

Component Value and units 

DG power 2.5KW 
Switching frequency 10KHz 
DC input voltage 500 
Line voltage 440V 
Filter capacitance �J 2µF 
Filter inductance �J 5mH 
Damping resistance 
J 10hms 
Nominal frequency 50Hz 
Load resistance RL 1.76mΩ 
Load inductance LL 3.2 mH 
Load capacitance CL 3.2µF 
Load quality factor Q 1.8 
Load resonant frequency fr 50Hz 
Current controller proportional gain, qp 0.4 
Current controller integral gain,	q� 500 

 
VI. RESULTS, ANALYSIS, AND DISCUSSION 

The designed network was tested in Matlab/Simulink for 
the islanding case of unintentional unsymmetrical L-G fault 
and non-islanding cases of connection and disconnection of 
non-linear load. The Matlab Simulation results of ROCOVPA 
and ROCOF were compared. It was proved that ROCOVPA is 
better than ROCOF. The proposed method was tested and 
compared with ROCOF for the islanding case of unintentional 
unsymmetrical L-G fault at 0% power mismatch. In this section 
the simulations are discussed for both ROCOVPA and 
ROCOF. 

A. Islanding Case for Unsymmetrical Fault 

An L-G unsymmetrical fault was initiated on the system at 
the PCC at 0.4s at 0% power mismatch. +$  = +0  is the 
condition for 0% power mismatch and at that load, a single line 
to ground fault was initiated on the grid side at 0.4s. The 
simulation graph is shown in Figure 7. 

 

 
Fig. 7.  Islanding detection of ROCOVPA for a L-G fault on the system. 

The proposed ROCOVPA detected islanding in 10ms 
within a fixed threshold of 1deg/s and the relay exactly 
detected and sent command to trip the circuit breaker to bring 
the microgrid to islanding mode from the grid mode. The total 
time is the sum of relay time and breaker time. Any type of 
fault is to be cleared within 4 cycles (2 cycles, i.e.0.5s of relay 
operation plus 2 cycles, 0.5s). Hence the ROCOVPA can detect 
the fault condition within less than a cycle and island the 
microgrid in around 1s by tripping the circuit breaker, which is 

less than the 2s of the IEEE-1547 and UL-1741 standards. The 
same fault conditions were applied and tested with ROCOF in 
Matlab as shown in Figure 8 and the islanding was detected in 
30ms. If the threshold value is fixed at 0.02Hz/sec, the tripping 
of the circuit breaker can be actuated in around 1s which is 
below the 2s of the standards. The detection time of ROCOF is 
more than that of ROCOVPA. As the ROCOF is dependent on 
frequency, at lower % power mismatches, the threshold value 
cannot be fixed exactly. Hence, the detection time varies 
inversely with % power mismatch. To mitigate these issues, 
ROCOVPA was proposed and proved to be a better islanding 
detection method for unsymmetrical faults.  

 

 
Fig. 8.  Islanding detection of ROCOF for a L-G fault on the system. 

B. Non-Islanding Case for Non-Linear Load Connection and 

Disconnection at the PCC on the System 

System stability has been studied for different transient 
conditions during load connection and disconnection at the  
PCC with non-linear load for both ROCOVPA and ROCOF in 
Matlab/Simulink. Both methods proved their stability by 
avoiding nuisance tripping within the threshold values. The 
ROCOVPA threshold value is 1deg/s and that of ROCOF is 
0.02Hz/sec. 

 

 
Fig. 9.  Non-islanding case of ROCOVPA for non-linear load connection 
and disconnection. 

A non-linear load was connected at the PCC at 0.4s and 
was disconnected at 0.8s. The results of non-islanding 
scenerios of ROCOVPA and ROCOF are shown in Figures 9 
and 10. The readings of ROCOVPA and ROCOF show that the 
thresholds are much higher. Hence, the system is stable without 
any nuisance tripping of the circuit breaker. 



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Fig. 10.  Non-islanding case of ROCOF for non-linear load connection and 
disconnection. 

VII. CONCLUSIONS 

Islanding detection is a major challenge when considering 
microgrids. The most common unintentional faults on the 
system are supposed to the be unsymmetrical L-G faults, in 
which one phase snapping and making phase to ground is 
involved. The proposed ROCOVPA passive islanding detection 
method was tested for islanding detection at 0% power 
mismatch (0% NDZ) along with the widely used ROCOF and 
proved to be a better alternative having less detection time. The 
ROCOVPA method was also tested for its stability to avoid 
nuisance tripping during load connection and disconnection 
and found to be quite effective. It is also simple and faster in 
discriminating between islanding and non-islanding operations 
of the microgrid. The detection is more accurate as the phase 
angle does not depend on mismatched power like voltage and 
frequency relays. In the future, the proposed ROCOVPA 
method can be extended for the detection of symmetrical faults 
with hybrid DGs. 

ACKNOWLEDGMENT 

The authors wish to thank the faculty of Electrical and 
Electronics Department of Koneru Lakshmaiah Educational 
Foundation (Deemed to be University). 

FINANCIAL DISCLOSURE 

The authors declare that this research work received no 
financial support from anywhere. 

AUTHORS CONFLICT/COMPETING INTEREST 

The authors declare that there is no conflict/competing 
interest. 

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AUTHOR PROFILES 

 
L. Bangar Raju is currently working as an 
Associate Professor in Swarna Bharati Institute 
of Technology, Khammam, Telangana State, 
India. He received his B.E. from the Jawaharlal 
Nehru Technological University, Kakinada, A.P. 
India and M.Sc. (Engineering) in Power 
Systems from the Calicut University. He has got 
30 years of industrial experience in power, oil 
and gas, petrochemical, transmission, 
distribution, and utilization plants. He has 
published 10 international Scopus indexed 

papers. He is a Life Member of ISTE (India) and IE (India). He is currently 
pursuing his Ph.D. from the Koneru Lakshmaiah Educational Foundation 
(Deemed to be University), Guntur, A.P., India. His areas of interest are 
power system protection, distributed generation, and microgrids. 

 

K. Subba Rao is presently the Principal at the 
College of Engineering and a Professor of 
Electrical and Electronics Engineering, 
Department of  Koneru Lakshmaiah 
Educational Foundation (Deemed to be 
University), Guntur, A.P., India. He received 
his Ph.D. from Koneru Lakshmaiah 
Educational Foundation, M.Tech. from CIT, 
Coimbatore and B.Tech. from Dayalbagh 
University, Agra. He has earned the best 
teacher award10 times. He is a life member of 

ISTE and of the Indian Society for Quality. He has published national and 
international papers and a book. His areas of interest are power electronics, 
power systems, microgrids, and Security Systems