The Effects of Harmonics on Differential Relay for a Transformer
J.M.HO & C.C.Liu
Electrical Engineering Dept. Chung-Yuan U.
Chung-Li, Taiwan
Summary
The applications of nonlinear devices
such as rectifiers, converters, power supplies,
and other devices in utilizing solid state
switching have been increased in industries
during recent years. These induce a lot of
harmonics in the voltage and the current, and
therefore deteriorate the power quality. This
quality deterioration causes the power loss
increasing, resonance problem, insulation
deterioration and even safety problem for
system apparatus. The protective equipments
may work at normal situation. But they may
not protect accordantly when the pollutions of
harmonics exist in the system. It is necessary
to analyze the effects of harmonics to the
protective equipments.
This paper aims at analyzing and
probing into the influences of harmonics to
differential relays. It analyzes and compares
the mathematic models, which are constructed
by using EMTP and the test results.
There are many factors to be considered
in transformer differential protection designing
and practicing. This paper only analyzes the
influential phenomenon of harmonics to
differential relay, ignoring the magnetizing
inrush current of the transformer and the
saturation phenomenon of the CT; we
study the tripping time of the differential relay
under different working frequencies and
harmonics.
Because of the pollution of harmonics,
there are many differential relays designed in
order to solve these problems, but they are all
designed on the condition that the 2nd
harmonic component of inrush current does
not less than 15% of fundamental component
at normal situation. And the fault current,
which involve dc component, should have its
highest value of 2nd harmonic fewer than 7%
of fundamental component. We can distinguish
inrush current and fault current in according to
these two different characteristics. The
differential relays are always designed
according to these theorems, but they
don’t focus on the situation that the pollutions
of harmonics enter the differential protective
equipments. We aim at this problem and
analyze it.
According to the simulation results, we
know that most CT doesn’t perform well at
frequency domain. The magnetizing inrush
current of the transformer and the saturation
phenomenon of the CT may cause some
mistakes to the relay operations. These make
the real test very difficult. So we ignore the
magnetizing inrush current of the transformer
and the saturation phenomenon of the CT. The
tests are conducted with two conditions,
internal faults and external faults. Each test is
with different harmonic components, including
the 3rd harmonic components, the 5th harmonic
components etc, and the summations of
different order of harmonic components. From
the real test results, we learn that the trip time
of differential relay doesn’t always increase
with frequencies or harmonics. There is a
nonlinear region. Beside the nonlinear region,
the trip time is proportion to frequencies and
harmonics, or the relay doesn’t trip anymore.
When internal faults happen, the harmonic
components will delay the trip time of
differential relay. This will affect power
system very much. The relay will not trip
when 3rd harmonic are more than 66.66% of
fundamental component. The most important
point is that the trip time will delay when
harmonics enter the equipments. In addition,
the differential relay will become not so
sensitive if working frequencies are not
fundamental frequency. So the harmonics
affect the differential relay a lot. The results of
this research can provide the valuable
references and assistance in applying and
designing of protective system..
The Effects of Harmonics on Differential Relay for a Transformer
J.M.HO & C.C.Liu
Electrical Engineering Dept. , Chung-Yuan U, Chung-Li, Taiwan
I. Abstract
The use of nonlinear devices such as rectifiers,
converters, power supplies, and other devices utilizing
solid state switching have been increased in industry
during recent years. These equipments have deteriorated
the power quality. This deterioration causes the
increasing of power loss, resonance problem, insulation
deterioration, and even safety problem for system
apparatus.
This paper aims at analyzing and probing into the
influences of harmonics on a differential relay. First it
probes the operation of a CT in frequency domain. Then,
it analyzes and compares the mathematic model, which is
constructed by using EMTP, and the test results.
There are many factors to be considered in
differential protection design and application for a
transformer. This paper only analyzes the influential
phenomenon of harmonics to differential relay.
The results of this research can be valuable
references for applying and designing differential relay
protection.
I in
I out
Protection
equipment
I op
Figure 1(a) Normal or outer fault situation
I F1
IF2
Protection
equipment
I op = I F 1 + I F 2
Figure 1(b) Inner fault situation
II. Purpose
Because of the pollution of harmonics, there are
many differential relays designed in order to solve these
problems, but they are all designed on the condition that
the 2nd harmonic component of inrush current does not
less than 15% of fundamental component at normal
situation. And the fault current, which involve dc
component, should have its highest value of 2nd harmonic
fewer than 7% of fundamental component. Then we can
distinguish inrush current and fault current according to
these two different characteristics. The differential relays
are always designed according to these assumptions, but
they don’t focus on the situation that the pollutions of
harmonics enter the differential protective equipments
[1].
III. The testing methods and results
1.Principles of the differential protection
The differential protection is a primary protection
for power equipments, which depends on the difference
value between the input and output currents. The
protection method will not only fit a lot of power
equipments but also be the first aid to important power
equipments. The protection theorems of the differential
relay are shown in Figure 1(a) and Figure 1(b).
According to the capacity and the importance of
the transformer, the protection scheme may have
different types. But the differential protection is
mainly used to protect large power transformers or
some of the important power distribution transformers
with capacities less than 10MVA[2]. This paper
focuses on the differential relay for a transformer.
2.The equivalent circuit of CT
If the current ratio between the primary and
secondary side is 1:N2, the equivalent circuits of the CT
can be shown as Figure 2. It is often that RP and XP are
far smaller than Rs and Xs, even at system fault. So they
can be neglected. The equivalent circuits are shown as in
Figure 2 and 3.
Figure 2 The equivalent circuits with primary resistance
must be included, especially the transient state analysis.
For example, the inrush current, resonant, and saturation
should be concerned.
The 9th order mathematical model constructed by
M.Poljak is shown as below (4):
Figure 3 The equivalent circuits without primary
resistance
ZM and Zb mean the excitation and burden
impedance of the CT, respectively. Figure 4 shows the
voltage and current vectors of the CT. The accuracy of
the CT mainly depends on the quantity and the angle
between primary current and secondary current [3]. At
steady state, the Ratio Error and the Phase-Angle Error
of the CT can be shown as in Equation 1 and Figure 4,
respectively.
Ratio Error =
N 2 ⋅ IS
Ip
(1)
cδ
 (l − δ )

i1 =  c1 + 0 B − c3 B 3 + c5 B 5 − c7 B 7 + c9 B 9  ×
l
N2
δ
−


Where:
c0-c9:core material volume factors
:the air gap length of the core(m)
l : the average length of magnetic (m)
N2: the winding turns of the secondary
B: the magnetic flux density (T)
As shown in Figure 5, EMTP has built a singlephase saturation core transformer model. It consists of an
equivalent circuit on an ideal transformer. The - I data
can’t be get directly, so a program offered by EMTP is
needed to transfer the V-I characteristic of CT to - I
data. Besides, it can use the Type-96 from EMTP to
construct equivalent circuit [5].
Figure 4 The voltage and current vectors of CT
Where:
VS: the voltage on secondary
IM: the magnetic current
Ie: the excitation current
Ip: primary current
Is: the secondary current
3.The distribution model of CT by EMTP
The simulation problem of the transformer is the
nonlinear characteristic of magnetic core, which means
the B/H curve. The model of CT is often regarded as a
single-valued nonlinear inductance and neglecting the
hysteresis phenomenon. In order to increase the
accuracy, the hysteresis phenomenon of the transformer
Figure 5 The equivalent circuit of CT by EMTP
The current of CT
The characteristic of CT(
Frequency
(a) The burden at secondary side is zero
The current of CT
The characteristic of CT(
Frequency
(b)The burden at secondary side is 0.5Ÿ
Figure 6 The excitation curve of 10/5 CT
Figure 7 The characteristic of CT (primary side voltage
is 120V)
Because EMTP can’t directly use the characteristic
curve of V-I, the V-I curve must be transfered to - I data
by the program called SATURA. The characteristic of VI curve of 10/5 CAPV-type CT is shown as in Figure
6[6]. To build Type-96 symbol, the -I data are
constructed by SATURA and the hysteresis curve is
created by HYSDAT[7]. The simulation results are
shown as in Table 1 and Figure 7.
4.The experiment of the differential relay
a. The experiment layout:
Table 1 The characteristic of the CT
Working frequency
of CT (Hz)
50
60
120
300
540
660
Current on the
5.12 5.01 5.00 4.85 4.61 4.38
secondary side (A)
Working frequency
1000 2K
of CT (Hz)
3K
4K
5K
Current on the
4.06 3.62
secondary side (A)
3.2
2.9
2.8
Figure 8 The system block diagram
From these, one can see secondary current decreasing as
frequency increasing for a fixed primary current in 10
amperes. And the burden also affect the characteristic,
with larger burden, the accuracy of ratio becomes worse.
The experiment layout is shown as in Figure 8.
And the results are shown in table 2 to Table 5.
The working voltage F3 means
3rd harmonics (33.33%)
The working voltage F5 means
3rd harmonics (33.33%) and 5th harmonics (20%)
The working voltage F7 means
3rd harmonics (33.33%) , 5th harmonics (20%) and
7th harmonics (14.28%)
The working voltage F9 means
3rd harmonics (33.33%) , 5th harmonics (20%) , 7th
harmonics (14.28%) and 9th harmonics (11.1%)
The phase differences in above are all zero degree.
b. The simulation
protection
and
testing
of
differential
(1) The simulation results for inner faults:
With the setting as in Table 2
Table 2 The design example of differential relay
for inner fault
Primary 2.89A
The rate current of the
simulation transformer
Secondary 5A
I1/I2=2.9/1.45
CT current ratio
I3/I4=5.01/5
The current from the high
1.45A
voltage side
The current from the low
5A
voltage side
CT tap
CT current ratio
Table 4 The tripping time of the differential relay at the
inner faults
Tripping
Tripping
F.
Tripping
F.
Tripping
current
current
(HZ) time (ms)
(HZ) time (ms)
(A)
(A)
60
970
6.14
F3
928
6.18
120
1150
6.17
F5
920
6.21
180
5.88
F7
940
6.14
’
240
5.77
F9
956
6.12
’
300
5.69
’
360
5.59
’
420
5.59
’
*The tripping time is counted by oscilloscope
5-5
(2) The simulation results for outer faults:
Use same circuit but reserving the output CT. And
using settings as in Table 3
.
Table 3 The design example of differential relay
for outer fault
The rate current of the
simulation transformer
at fault situations, the differential current in the tripping
coil increases, the differential ratio increases, and the
relay will trip. Table 4 shows results of the tripping time
of the differential relay at the inner faults. Table 5 shows
the results of the tripping time of the differential relay at
the outer faults.
Primary 2.89A
Secondary 5A
I1/I2=2.9/2.24
I3/I4=5.01/5
The current from the high
voltage side
2.24A
The current from the low
voltage side
5A
CT tap
5-5
C.The experiment results:
When the system is at normal situation, the ratio
between the load current and differential current doesn’t
change. Therefore, the tripping coil will not operate. But
Table 5 The tripping time of the differential relay at the
outer faults
Frequency Tripping time
(HZ)
(ms)
Tripping current
(A)
60
2980
2.58
120
2.54
’
180
2.51
’
300
2.49
’
240
2.49
’
300
2.47
’
420
2.47
’
F3
2900
2.54
F5
3380
2.54
F7
3620
2.48
F9
4360
2.42
*The tripping time is counted by oscilloscope
IV. Conclusions
According to the simulation results, we know that
most CT doesn’t perform well at all frequency ranges.
The magnetizing inrush current of the transformer and
the saturation phenomenon of the CT may cause some
mistakes to the relay operations. These make the real test
very difficult. So we ignore the magnetizing inrush
current of the transformer and the saturation
phenomenon of the CT. The tests are conducted with two
situations, internal faults and external faults. Each test is
with different harmonic components, including the 3rd
harmonic components, the 5th harmonic components, and
etc, and summations of different harmonic components.
From real test results, we learn that the tripping time of
differential relay doesn’t always increase with frequency
increasing or harmonic contents increasing. There is a
nonlinear region, beside the nonlinear region, the
tripping time is proportion to frequencies and harmonic
contents, or the relay doesn’t trip anymore. When
internal faults happen, the harmonic components will
delay the tripping time of differential relay, this will
affect power system very much. The relay will doesn’t
trip when 3rd harmonic are more than 66.66% of
fundamental component. The most important point is
that the tripping time will be delayed when harmonics
enter the equipments. In addition, the differential relay
will become not so sensitive if working frequencies are
not at fundamental frequency. The results of this research
can provide valuable references and assistance in
applying and designing of differential protective system.
V. References
1.H.Z.LEE The experience of differential protection for
transformer The Electricity
magazine No.11th P109~P116, 1996.
2.American National Standard, "Guide for Protective
Relay Application to power Transformer, "ANSI/IEEE
C37.91-1985.
3.R.D.,Power
System
Protection
Manual,pp.66-102(1982)
Reference
4.Poljak, M. and N. Kolibas, " Computation of Current
Transformer Transient Performance," IEEE Trans. on
Power Delivery, Vol.3,No.4, pp.635-645(1988)
5.Kezunovic, M.,C. Wfromem and F. Phillips,"
Experimental Evaluation of EMTP-Based Current
Transformer Models For Protective Relay Transient
Study,"
IEEE
Trans.
on
Power
Delivery,Vol.9,No.l,pp405-413(1994)
6.The technical support from Shyh Lin Electricity.
7.Leuven,K.U.,EMTP Center, Alternative Transients
Program-Rule Book, Leuven EMTP Center,
Belgium,(1987)