2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
MODELLING OF NUMERICAL DISTANCE RELAYS USING MATLAB
Eng. Abdlmnam A. Abdlrahem
Electrical Engineering Dep.
Omer Al-Mokhtar University
El-Bida - Libya
Man_5166@Yahoo.com
Dr. Hamid H Sherwali
E&E Engineering Dep.
Faculty of Engineering Al-Fatah University
Tripoli - Libya
Hsherwa@ee.edu.Ly Or Hsherwa@hotmail.com
ABSTRACT
Numerical relays are the result of the application of
microprocessor technology in relay industry.
Numerical relays have the ability to communicate with
its peers, are economical and are easy to operate, adjust
and repair. Modeling of numerical relay is important to
adjust and settle protection equipment in electrical
facilities and to train protection personnel. Computer
models of numerical relays for the study of protection
systems are greatly enhanced when working along with
an Electromagnetic Transient Program (EMTP).
This paper describes distance relay model built
using MATLAB environment. The behavior of the
distance relay model has been verified using data about
different faults generated by the Electromagnetic
Transient Program (EMTP-ATP). Data generated by
EMTP-ATP describes the voltage and current signals at
the relay location both immediately before and during
the fault. The signals include the dc offset and the high
frequency traveling waves. The data is applied to the
relay simulator, which then evaluates whether the
impedance trajectory of the fault enters one or more of
the operating zones. The results are presented in
graphical form using an R-X diagram. The model is
then verified by checking the model impedance
measurement at different fault locations, and resistive
faults. The paper demonstrates the benefits achieved
when using a computer simulation of a relay in
conjunction with a transient power system simulation.
network. The evaluation of the operating performance
of a distance relay using a dynamic simulator, can help
determine the appropriate values for the zone one, zone
two, zone three impedance settings and help determine
whether an actual distance relay behaved correctly or
incorrectly during a fault on the real network.
The distance relays were modeled using MATLAB
and the algorithm is based on the calculation of the
voltage and current phasors using Fourier filters. At
present the simulator include mho distance relay. The
power system network has been simulated using
EMTP-ATP.
II- NUMERICAL DESTANCE RELAYS
Distance relays used to calculate line impedance
by measuring voltages and currents on one single end.
The relays compare the setting impedance with the
measured impedance to determine if the fault is inside
or outside the protected zone. They immediately
release a trip signal when the impedance value is inside
the zone 1 impedance circle of distance relay. For
security protection consideration, the confirmation of a
fault occurrence will not be made until successive trip
signals are released in one zone.
Different formulas should be adopted when calculating
the fault impedance due to different fault types. Table
(1) indicates calculation formula for all of the fault
types. Any three-phase faults can be detected from
every formula in table (1). In order to reduce
calculation burden, we design a fault detector and fault
type selector. The fault detector can judge which fault
type it is and then calculate fault impedance by
selecting a suitable formula from table (1). If fault type
judgment is not invoked first, then the impedance
calculation by using the all six formulas shown in table
(1) would be initiated simultaneously which causes
much calculation burden.
Keywords—Numerical distance relays; Impedance trajetory;
Simulation; Fourier transform; MATLAB; EMTP
I-
INTRODUCTION
When a short-circuit fault occurs on a
transmission line, the distance relays protecting the line
trip the circuit breaker at either end of the line and
disconnect the line from the network. To study the
behavior of a distance relay during a short-circuit fault
it is necessary to accurately simulate the distance relay
and then inject into the simulator, the voltage and
current signals seen by the relay during the fault. The
voltage and current signals can be obtained from power
system transient simulators such as EMTP-ATP. The
impedance seen by the distance relay during the fault
EE&E Department-Faculty of Engineering Al-Fatah
University depends on the type and location of the fault
and also the configuration and parameters of the
978-1-4244-4683-4/09/$25.00 ©2009 IEEE
III- SIMULATION PROCEDURE
When the distance relays receive discrete voltage and
current signal, it converts it to a phasor. The Discrete
Fourier Transform (DFT) is the most popular method
to estimate fundamental phasors for digital relaying.
389
2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
Table 1: Input signals of ground and phase distance
relays
Distance Element
Phase A
Voltage signal
Current signal
Va
Ia +3K0I0
Phase B
Vb
Ib +3K0I0
Phase C
Vc
Ic +3K0 I0
Phase A - Phase B
V a − Vb
Ia − Ib
Phase B - Phase C
Vb − Vc
Ib − Ic
Phase C - Phase A
Vc − Va
Ic − Ia
Read and store
V, I from
EMTP/ATP
Low
pass
Filter
Compute Z
using
DFT
algorithm for
a-g a-b, fault
When a fault occurs on transmission lines, the voltage
and current signals are severely distorted.
These signals may contain decaying dc components,
subsystem frequency transients, high frequency
oscillation quantities, and etc. The higher frequency
components can be eliminated using low pass antialiasing filters with appropriate cut-off frequency, but
the anti-aliasing filters cannot remove decaying dc
components and reject low frequency components.
This makes the phasors very difficult to be quickly
estimated and affects the performance of digital
relaying. Therefore, the Discrete Fourier transform is
usually used to remove the dc-offset components.
The voltage and current data are derived using an
EMTP-ATP model of the power system. These data are
then converted to a MATLAB. The sampling rate used
in the distance relay is 1.0 kHz. i.e (20 sample/cycle).
The samples are 1ms a part.
Sample
V, I
Dc-offset
correction
And
Compute V,
I phasor
using DFT
Figure 1, distance relay modeling procedure.
IV- DISCRETE FOURIER TRANSFORMER
ALGORITHMS (DFT)
When a power system is operating under steadystate conditions, both the voltage and the current
signals are periodic and the fundamental frequency
component of each is at the power frequency.
Therefore it is possible to calculate the impedance
corresponding to a given voltage and current by
determining the fundamental components of voltage
and current using a discrete Fourier transform (DFT)
technique.
Assuming the N samples are obtained for each period
and that discrete time signals are X (K ) then sampled
signals are given as in equation (1).
EMTP-ATP has been used to generate, the data at
a 100 kHz sampling rate this allows the effect of
traveling waves to be included in the signals. The
sampling rate of the EMTP-ATP output file is reduced
from 100 kHz to 1 kHz. After that the data input to
digital filter "low pass filter" using cut-off frequency
360Hz this to remove the effects on the voltage and
current signals of the traveling waves instigated by the
fault. The data then be input to Discrete Fourier
Transformer DFT window. The DFT is ideal method
of detecting the fundamental frequency component in a
fault signal. However, DFT, Least Error Square LES
and Walsh Function algorithms are among the most
popular phasor estimation techniques employed in
numerical relays. As result, the magnitude and the
phase angle of voltage and current obtained for the
input signal, where it is then transformed to rectangular
form.
The model is then proceeded to calculate the
value of resistance and reactance of the line as seen by
the relay by using the equations (3) and (4). Figure 1,
shows block diagram for distance relay modeling
procedure.
MATLAB program was used then to plot on graph
characteristic of mho distance relay the behavior of Z
during the sampling period.
X (n ) =
X1 =
N −1
∑
X ( k ). e
⎛ 2 Π nk ⎞
−i⎜
⎟
⎝ N ⎠
………….(1)
k =0
2
2 .N
N −1
∑
X k .e
⎛ 2 Π nk ⎞
−i ⎜
⎟
⎝ N ⎠
…………(2)
k =0
Where n is the order of the harmonics. The
fundamental frequency signals are the ones with n=1.k
is the number of samples contained in the data
window. In equation (2) all the N samples are used in
the calculation of the fundamental frequency signal,
resulting in a full cycle Discrete Fourier Transform
(DFT).
The extraction of fundamental frequency
components of voltage and current signals via discrete
Fourier transformer is used and then impedance
calculation, resistance and reactance is calculated from
voltages and currents samples (K) at relaying point as
in (3) and(4).
RK =
X
K
=
VK
I K + 3 . Re( K 0 ). I 0 K
VK
I K + 3 . Im( K 0 ). I 0 K
K 0 is Zero compensation factor =
390
…….. (3)
…….. (4)
2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
=
1
3
VI- SIMULATION RESULTS
⎛ Z0
⎞
⎜⎜
− 1 ⎟⎟
Z
⎝ 1
⎠
The developed mho distance relay model is evaluated
using data generated from EMTP. A single 220 kV
over head line with length of 120 Km and a source
with above sequence impedances is simulated. The
overhead line is modeled as a lumped π model.
Different fault locations on the transmission line with
different arc resistances were simulated by EMTP. The
behavior of the mho distance relay model is as
explained hereinafter.
Case one: - Single line to ground faults at different
distances from the relay location.
V- POWER SYSTEM PARAMETERS
A Single line diagram of the simulated power
network operating at 220kV 50 Hz is shown in figure
2a. The positive and zero sequence impedance of the
source are
Zs0= 3.681+j24.515 Zs1=0.819+j7.757
BUS B
BUS A
10km
BUS D
BUS C
30km
30km
50km
Single line to ground faults were set on EMTP model
of the shown power system at 10 Km, 15 Km and 25
Km from the location of bus-A. The lengths are
representing 10% to 80% of line A-B length,. Similarly
few more Single line to ground faults at 5 Km, and 10
Km from the location of bus-B and bus-C were set.
The voltage and current signal before and during fault
were fed to the relay model. Figures 2 to 5, Show the
impedance trajectory for these cases.
In all cases the output results which are the impedance
trajectory of the digital distance relay model had the
expected behavior where the impedance trajectory
calculations start the trajectory from the load area,
before fault, and end up at the proper zone.
R
Figure 2: Single line diagram of simulated power
network.
The current transformer ratio is 1000/1A and the
voltage transformer ratio is 220kV/110V.
Setting of the relay is
Zone-one = 6.5 ohm-secondary (80 percent of
protected line1).
Zone-two = 11.23 ohm-secondary (100 percent of
protected line1+ 50 percent of the line 2).
Zone-three = 16.34 ohm-secondary (100 percent of
protected lines 1 and line 2 + 20 percent of line 3).
Arc Resistance
The single line to ground fault is the most common
fault that occurs on transmission line due to the nature
of climates .When it occurs it is usually accompanied
by a fault resistance, i.e. resistive line faults. The value
of the arc resistance can be calculated by knowing the
length of the arc. The relation is:
R
=
ARC
2500
I
⋅ l ARC
[Ω ]
ARC
20
15
jX
10
5
0
Where:
lARC =Ar
-5
-15
c length in m
IARC =arc current in A.
For various voltage levels, the following average
values may be used:
-10
-5
0
5
10
15
20
25
30
R
Figure 3: Trajectory of phase-to-ground fault at 10 Km
from bus A, impedance Z f = .19 + 1.98j
25
20
Table 2: Typical arc resistance
Arc- resistance
Voltage level
At
Isc = 1000A
jX
15
10
At Isc = 10000A
5
0
380kv
27.5 Ω
2.75 Ω
220kv
17.5 Ω
1.75 Ω
-10
-5
0
5
10
R
15
20
25
30
35
Figure 4: Trajectory of phase-to-ground fault at 35 Km
from bus A, impedance Z f = 0.89 + 6.75j
391
2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
25
20
20
15
jX
jX
15
10
10
5
5
0
0
-5
-5
-10
-5
0
5
10
15
R
20
25
30
35
-15
-10
-5
0
5
40
10
R
15
20
25
30
Figure 7: Trajectory of phase-to-ground fault at 10Km
from bus-A with 2 Ω resistance, impedance Z f =0 .88
+ 1.99j
Figure 5: Trajectory of phase-to-ground fault at 10 Km
from bus B, impedance Z f = 1.14 + 9.55j
25
25
20
20
15
jX
jX
15
10
10
5
5
0
0
-5
-10
-5
0
5
10
R
15
20
25
30
35
-15
-10
-5
0
5
10
15
20
25
30
R
Figure 6: Trajectory of phase-to-ground fault at 5 Km
from bus C impedance Zf = 1.83 + 14.005j
Figure 8: Trajectory of phase-to-ground fault at 10Km
from bus-A with 5 Ω resistance, impedance Z f = 1.89
+ 2.01j
Case two: Faults accompanied by a resistance
Single line to ground faults with different fault
resistance were set on EMTP model of the shown
power system at different fault locations. Figures 7 to
9, Show the impedance trajectory for few of these
cases.
In all cases the output results which are the impedance
trajectory of the digital distance relay model had the
expected behavior where the effect of the arc resistance
reflected on the value of the impedance seen by the
relay. Impedance trajectory calculations start the
trajectory from the load area, before fault, but, in few
results, due to the resistance the relay misjudges the
exact location of the fault.
20
jX
15
10
5
0
-5
-10
-5
0
5
10
R
15
20
25
30
Figure 9: Trajectory of phase-to-ground fault at 10Km
from bus-A with 10 Ω resistance impedance Z f = 3.54
+ 2.09j
392
35
2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
VII- CONCLUSIONS
The impedance's trajectory after faults represents
numerical output of the impedance calculation. The
output results reflected the behavior of the developed
model under different fault locations and at different
arc resistances. The simulation study presented in this
paper assist in demonstrating the importance of and
requirement for accurate dynamic modeling of distance
protection relays. Different case studies have been
presented in order to illustrate the response of the
developed distance relay model at different operating
scenarios, i.e. non-resistive faults and resistive faults.
For the particular system studied it was found that the
three-zone protection would not see a fault at the reach
setting, resistive fault causes the relay to under-reach.
The exact and misjudgment of the fault location in the
cases demonstrated in this paper reflects the accuracy
of the developed model. It is noted that the
impedance's trajectory after faults were depends on
digital filter type and relay algorithm.
The distance relay model may be used as a training
tool to help users understand how the relay works. The
distance relay model offers an inexpensive alternative
to evaluating a relay on a test set and generally will
involve significantly less time and effort.
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