610
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
Current Differential Protection of Transmission Line
Using the Moving Window Averaging Technique
Sanjay Dambhare, S. A. Soman, Member, IEEE, and M. C. Chandorkar, Member, IEEE
Abstract—We propose a new approach to current differential
protection of transmission lines. In this approach, we transform
the instantaneous line current(s) by using a moving window averaging technique. If the time span of moving window is equal
to one-cycle time, then the steady-state value of the transformed
current is zero for a periodic signal which is composed of fundamental and harmonic frequencies. Signal distortions (e.g., a fault)
cause the transformed currents to deviate from the nominal zero
value. This permits the development of a sensitive, secure, fast, and
yet simple current differential protection scheme. The scheme can
be applied in toto to series-compensated transmission lines. Results on a four-machine ten-bus system and comparative evaluation
with state-of-the-art methods brings out promise of the proposed
method.
Index Terms—Current differential protection, global positioning
system (GPS), moving window averaging technique, series-compensated lines, transmission line.
= 50 = 0:06
Fig. 1. Effect of dc offset on phasor computation. (a) Input I
;
s. (b) Amplitude of phasor. (c) Phase angle of the phasor in radians.
I. INTRODUCTION
T
RADITIONALLY, transmission protection systems have
been developed by using the phasor model of the power
system. The distance relaying scheme as well as the current differential protection schemes are based upon the phasor model
[1], [2] of the transmission system. However, immediately after
the occurrence of a fault, system behavior cannot be accurately
modelled by phasors. Hence, programs which are used for simulation of fast transients (i.e., Electromagnetic Transient Program
(EMTP) [3]) are not based on phasor modeling. Fast transients
manifest themselves for the first few cycles after a fault or a
disturbance. Typically, faults arising at the voltage peak have
high-frequency components due to the discharging of energy
stored in the electric field while faults at a current peak of sinusoid lead to the decaying dc offset current component due to
the discharging of energy stored in the magnetic field [4]. These
transients die down due to losses in the transmission system and
over a period of time, the steady-state phasor model emerges.
For example, consider a current waveform [refer Fig. 1(a)]
given by
Manuscript received July 14, 2008; revised July 07, 2009. First published
November 13, 2009; current version published March 24, 2010. This work was
supported by PowerAnser Labs, Indian Institute of Technology Bombay. Paper
no. TPWRD-00555-2008.
The authors are with the Department of Electrical Engineering, Indian Institute of Technology–Bombay, Mumbai 400076, India (e-mail: dambhare@ee.
iitb.ac.in; soman@ee.iitb.ac.in; mukul@ee.iitb.ac.in).
Digital Object Identifier 10.1109/TPWRD.2009.2032324
where
is the amplitude,
is the frequency,
is the period, is the time constant, and
is the unit step
function. Then, the fundamental phasor estimate is given by
Argument
simplicity.
For
in
is dropped here onward for the sake of
For
is given by
is given by
Clearly, the computed phasor value differs from the desired
value
due to the contribution from decaying dc offset current as shown in Fig. 1(a) and (b). Even if mimic impedance is
used to cancel decaying dc offset current component, exact compensation is not possible. This is because the Thevenin equivalent circuit of a fault depends upon system topologies and,
hence, cannot be computed exactly.
Similarly, if the current waveform [refer to Fig. 2(a)] is given
by
0885-8977/$26.00 © 2010 IEEE
DAMBHARE et al.: CURRENT DIFFERENTIAL PROTECTION OF TRANSMISSION LINE
611
Fig. 3. Basic current differential protection scheme.
2) The transformed differential current used to detect a fault
is given by
(1)
Fig. 2. Effect of acharacteristics harmonics on phasor computation. (a) Input
I
;f
50 Hz, f 75 Hz,
0.2 rad. (b) Amplitude of phasor. (c)
Phase angle of phasor in radians.
= 50
=
=
8 =
where
is a transformed differential current1 (refer to
is a linear transformation used on current .
Fig. 3).
The transformation is designed to reject the fundamental
component at nominal frequency, i.e.,
then, the fundamental phasor estimate is as follows: For
In other words, the transformed differential current
zero under the steady-state condition. It is given by
is
(2)
and for
3) For an external fault, the transformed differential current
even in the presence of fast transients. This is a necessary
requirement of the differential protection scheme.
4) For an internal fault, transformed differential current
where
. It is shown in Fig. 2(a) and (b).
Clearly, by the nature of sinc function, harmonic frequencies
are rejected but this is not the case with acharacteristics harmonics. Oscillation in magnitude and angle is a consequence of
the second term. Further, the higher the frequency, the better the
attenuation.
We conclude that the presence of a decaying dc component
as well as characteristic frequencies distorts the phasor computation. Further, to speed up the phasor computation, relays use
algorithms such as half-cycle discrete Fourier transform (DFT),
phasorlet, etc. Their use improves the speed of phasor estimation at the cost of filtering accuracy.
Ideally, relays should operate before the onset of current-transformer (CT) saturation. Fast clearing of faults also
improves the stability of the system by reducing the intensity
of power swings.
In this paper, we propose a new differential protection scheme
for transmission lines. The salient features of the proposed approach are as follows.
1) Detection of the fault is not based upon the fundamental
frequency phasor model of the line. It improves the dependability of relaying without compromising security and
speed.
for at least one cycle after the fault inception. This gives
adequate time for the relay to respond to the internal fault.
As the proposed approach does not require fundamental
phasor computation, we show that:
1) sensitivity of the differential protection scheme is improved at least by a factor of 2 to 3 over existing methods
[5], [6] without compromising the security of the relays;
2) speed of relaying is improved (i.e., the relaying decision
can be arrived in 4–14 ms for a 50-Hz system; we also observed that the fault detection time increases as the magnitude of fault current is reduced;
3) the proposed scheme can be applied as it is to a seriescompensated transmission line.
This paper is organized as follows: A transformation approach to current differential protection scheme is introduced
in Section II. The desired characteristics of transformation are
developed in Section III. Section IV develops the proposed
relaying algorithm. In Section V, we present the simulations
1i-notation is used for instantaneous current and I for phasor current. Similar
convention is used for describing voltage.
612
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
in the Electromagnetic Transients Program–Alternate Transients Program (EMTP–ATP) package on a 4-generator, 10-bus
system. Section VI concludes this paper.
II. TRANSFORMATION APPROACH TO
CURRENT DIFFERENTIAL PROTECTION
Traditionally, current differential protection schemes compare the current at the terminals of a transmission line. If the
differential current is not zero, i.e.,
then it indicates a fault.
A more abstract view can be taken of current differential proand
for
tection by comparing transformed currents
differential protection, i.e.,
Fig. 4. Current differential protection scheme with an equivalent -model of
line.
approach is suggested in [6] which uses a distributed line
model.
4) The charge comparison scheme suggested by Ernst et al.
[9] defines
(9)
Different realizations of current differential protection correspond to different definitions of transformation . Illustrative
examples are as follows.
1) Traditional current differential protection methods [1] use
the following transformation:
and
and
(4)
and
are the phase angle of phasors and ,
where
respectively. In this case, the current differential protection
is given by the following logic:
then there is no fault and
(5)
else if
(10)
(3)
and
are the phasors at the fundawhere
mental frequency . The function described by (3) is
a noninvertible linear transformation, as it only filters the
fundamental frequency component.
2) The phase-angle comparison scheme [7] uses a transformation
If
where and correspond to the recent zero crossing of
the rising edge and falling edge of current .
5) The wavelet-based approach [10] uses the discrete wavelet
transformation of , i.e.,
then there is a fault
(6)
3) Enhancements of the current differential protection scheme
use transformations which also depend upon the local bus
voltage. Phadke and Thorp [8], have suggested that series
and
be used in current differential proteccurrent
tion (refer to Fig. 4) where
(7)
and
(8)
The transformation described by (7) and (8) is again
a noninvertible linear transformation. The variant of this
and
refer
where represents the wavelet function,
to the dilation and translation of the wavelet, and and
are the integer constant. The function described by (10)
is again a noninvertible linear transformation.
When viewed from this perspective, it appears that the research effort is aimed at correctly defining transformation to
improve the sensitivity of current differential protection without
compromising its security. The choice of transformation also
depends upon the technology constraints. With the advances
in communication technology, such as synchronous optical
network/synchronous digital hierarchies (SONET/SDH)2 [11],
[12] for reliable, fast fiber-optics communication and global positioning system (GPS) technology for synchronized sampling
(and time stamping) [13]; the challenge lies in synthesizing
under more idealized technological contransformation
ditions to improve dependability, security, and speed of the
protection system.
III. DESIRABLE ATTRIBUTES OF TRANSFORMATION
The simplest realization of function
tion i.e.,
is an identity func-
This realization can be used for the differential protection of the
generator stator windings [8]. Note that such a function is linear
and invertible; hence, it satisfies the following conditions:
2Modern high-speed communication networks, typically use the SONET or
SDH standard for communication with transmission rates of the order of 274.2
Mb/s or 155.5 Mb/s, respectively. They also provide network protection during
the failure of a communication link.
DAMBHARE et al.: CURRENT DIFFERENTIAL PROTECTION OF TRANSMISSION LINE
613
1)
(11)
2)
(12)
3)
(13)
where and are scalars (i.e., real numbers). However, as
pointed out by Phadke and Thorp [8], somewhat more secure
and
for
decision making is achieved if one uses phasor
decision making. The phasor computation technique uses the
following definition of function
~ t) for the sine input. (a) Input. (b) Response.
Fig. 5. Response 9(
and
Notice that function is linear but due to the filtering process,
it is no longer invertible.
We conclude that the function may be linear but is usually
not invertible in the current differential protection scheme of the
transmission line. Linearity is a desirable property of function
. It implies that if
, then
(refer to (12)). From (11), it implies that
.
The discussion so far suggests that there could be many choices
on transformation , other than the extraction of fundamental
phasor, which would affect dependability and security features
of the current differential protection scheme. Here, the linear
given by (2) is proposed as a suitable choice
transformation
of transformation .
The transformation , is an average taken on a moving
window of one cycle length at nominal frequency. Thus,
20 ms at 50-Hz and 16.67 ms at the 60-Hz system. The function
has the following desirable properties:
1) For a sinusoidal excitation
where
and are the harmonic number.
rejects fundamental and harmonic
In other words,
frequencies. Thus, differential protection schemes implemented with will not pick up on load currents as they
contain primarily fundamental and harmonic frequencies.
for the sinusoidal input is shown in
The response of
Fig. 5. It shows that it takes one cycle for
to latch on
to its steady-state value which is zero.
2) For an unit impulse excitation at time
~ t) for an impulse input. (a) Input. (b) Response.
Fig. 6. Response 9(
3) The response of
for the unit step function is shown in
Fig. 7. It shows that:
essentially acts like a dc filter;
a)
b) further, being an integrator, except for impulse function, its change is continuous.
4) For the decaying dc offset, the current component is given
by
(15)
The response is given by
(14)
(16)
This is visualized in Fig. 6. The impulse response of
transformation in (14), implies that function quickly
detects discontinuities, jumps, or major changes in the
can quickly detect a fault. It
signal. Therefore,
also remembers this change for one cycle—the width
of moving window—which is adequate for the relaying
decision.
This is visualized in Fig. 8 which shows that the transformation responds to the decaying dc offset current component. It increases until the width of the moving window
s) and then exponentially decreases to zero.
(i.e.,
The following discussion will demonstrate the suitability of
transformation for transmission-line protection. For this purpose, first its frequency response is evaluated.
elsewhere.
614
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
The dc filtering characteristic can be further improved by increasing the width of the window (refer to the dotted characteristics in Fig. 9). This would slow down the relaying decision.
This captures the well-known speed versus accuracy conflict of
relaying. Better filtering action is obtained at the cost of time. A
moving window width of 20 ms is found satisfactory for 50-Hz
nominal frequency.
The moving window averaging technique presented in this
paper can also be motivated by the conventional analysis using
the Fourier series for the periodic signal. This permits us to use
phasors3 as follows.
Lemma-1: Consider the equivalent model of a transmission
be
line at frequency (refer to Fig. 4). Let a current of
injected at the sending end of the line. Let the receiving-end
and
.
current and voltage phasors be given by
Then
~ t) for step input. (a) Input. (b) Response.
Fig. 7. Response 9(
(18)
Proof: Current injection equations at the sending and receiving end of the line are as follows:
(19)
(20)
~ t) for a decaying dc input a = 50. (a) Input. (b) Response.
Fig. 8. Response 9(
Substituting
from (19) in (20), the desired result can be
obtained.
Further, for a lossless transmission line having series inductance L H/m and a shunt capacitance of C F/m, it can be shown
that4
(21)
and
(22)
~ t) (the dotted line sketches the response for
Fig. 9. Frequency response of 9(
a window width of 40 ms).
A. Frequency Response of
The frequency response of
is as follows [14]:
(17)
Fig. 9 sketches the frequency response. From the response, it
is clear that:
is an excellent dc filter;
1) function
2) it rejects fundamental and harmonics completely;
3) it attenuates high-frequency components significantly.
where
is the velocity of wave propagation.
For positive sequence, it is close to the velocity of light. The
following two corollaries are the most important results of this
paper.
Corollary 1 implies that a secure protection scheme can be derived by using the moving window averaging technique. Corollary 2 establishes that such a scheme would be dependable.
3The assumption of a periodic waveform is implicit in conventional phasor
analysis which is the backbone of various protection schemes, such as distance
relaying and current differential protection. However, immediately after the fault
inception and in the interval where relaying decisions are made, current is not
periodic. Therefore, we categorize the results in Lemma-1, corollaries 1 and 2
as motivational results.
4The equations can be derived by substituting = 0 and = j! LC in
(6.25) and (6.26) of [15, pp. 207].
p
DAMBHARE et al.: CURRENT DIFFERENTIAL PROTECTION OF TRANSMISSION LINE
615
Also,
equivalence of
and
. The
follows from (1).
IV. ALGORITHM
Fig. 10. Internal fault on the line.
Corollary-1: For an unfaulted line, at
0
(23)
Proof: Following from Lemma 1, (21) and (22), use the
fact that:
The algorithm for current differential protection by using the
proposed moving window averaging technique is as follows.
0, current counter
1) Initialize the current sample number
0, and
0. Input the slope
value
of the percentage differential characteristics , threshold
, and sampling rate per cycle.
counter value
and
. With GPS syn2) Obtain the current sample
chronization, the current samples should correspond to the
same time stamp.
3) Compute transformation by using the recursive update
formula.5
a)
In fact, for a lossless line
b)
4) Assign
Thus
(24)
Remark 1: The significance of (24) is that the differential
0 is zero for the external fault even
current measured at
in the presence of the shunt capacitance of line.
This property is not valid at the fundamental frequency due
to the line-charging current contribution.
Corollary-2: For an internal fault at F on the transmission
line (refer Fig. 10)
or
Proof: By Corollary 1, for section SF of the line
5) Check if6
a) If Yes and
0, there is no internal fault. Further,
0, then
.
if
.
b) If No, increment counter
6) If
, issue trip decision.
The proposed algorithm is based upon percentage differential characteristics with slope . A counter scheme is implemented to avoid any nuisance tripping. If a fault is detected,
samples, then trip decision is invoked.
continuously for
The -latest samples can be stored in a circular buffer.
(25)
V. CASE STUDIES
Similarly, for the section FR
(26)
Applying Kirchoff’s current law at node F, from (25) and (26)
To evaluate performance of the proposed scheme, the following methodology has been used.
0N ) = i (N 0 1) = 1 1 1
0 1) = 1 1 1 = i (01) = 0.
5Set i (
i (N
0
= i ( 1) = 0
and
0N ) =
i (
6With the conventional approach, the choice of restraint quantity (i
) may
~
~
(0) + 9
(0) ]. But it is zero at steady state. Hence, we provide the
be [ 9
restraint by ( I
+ I
), where I
and I
are the rms values
of the sending and receiving end currents, respectively.
j
j j
j
j
j j
j
616
Fig. 11. Single-line diagram of a 2-area, 4-generator, 10-bus system.
1) Simulate the power system response to disturbances (e.g.,
faults using EMTP simulations). ATP [16] software has
been used for simulations.
2) Samples obtained from the EMTP simulation are fed to
a MATLAB program which implements the proposed
current differential protection scheme using the moving
window averaging technique.
3) The proposed scheme is compared and contrasted with 1)
the conventional GPS-based current differential scheme of
[5] and 2) a more recent method was reported in [6].
Case studies on a two-area, 230-kV, 4-generator, 10-bus
system (refer Fig. 11) are presented. The detailed generator,
load, and line data on a 100-MVA base are given in [17]. The
two areas are connected by three parallel ac tie lines of 220 km
each.
In ATP–EMTP simulation, transmission lines are represented
by Clarke’s model (distributed parameters) and the detailed
model is used for representing generators. Initial values of
generator voltage magnitude and angles are calculated from
the load-flow analysis. The proposed scheme is applied for the
between nodes 3
primary protection of one of the tie lines
and 13. The fault location is measured from bus 3. The ANSI
1200:5, class C400 CT model [14] and 250-kV:100-V CVT
model [18] have been used for obtaining the realistic CT and
CVT response during EMTP simulations.
Samples obtained from ATP-EMTP simulation correspond to
time-synchronized GPS samples. The time step used for ATPEMTP simulations is 20 s. However, the relaying system dataacquisition rate is set to 1000 Hz.
The performance of the proposed scheme can be gauged by
its ability to balance the following well-known contradictions
of power systems relaying:
• dependability versus security;
• speed versus accuracy.
The performance of the proposed protection scheme with series-compensated and mutually coupled lines is also evaluated.
A. Dependability versus Security
1) External Faults: To ascertain security, it must be ascertained that the differential relay does not operate for any external fault. This verification is usually carried out on the severe
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
Fig. 12. Performance of the proposed current differential protection scheme on
~ i )
the bolted external LLL fault at bus 13 (fault inception angle 270 ). (a) 9(
~ i ) for phase-a. (c) Differential and restraining currents of
for phase-a. (b) 9(
phase-a (K = 0.07). Note that ji j Ki .
external faults. All four types of external shunt faults (LG, LL,
LLG, and LLL) are simulated on busses 3 and 13 as well as on
adjacent lines 3–102 and lines 13–112 at 25%, 50%, and 75%
length. In each case, the fault resistance is varied from 0 to
100 in steps of 10 and the fault inception angle is varied
from 0 to 300 in steps of 15 .
Fig. 12 illustrates the performance of the proposed current
differential protection scheme on a bolted external LLL fault at
0.07 for
bus 13 with the fault inception angle 270 and
phase a. Notice that as
and
are nearly equal and
. Hence, the relay does not pick up
opposite and
on an external fault. Similar behavior is observed for other two
phases. We observe that the proposed scheme does not operate
for any of the external faults. However, the conventional scheme
of [5] operates on a low-resistance external fault on buses 3 and
13. We conclude that the proposed scheme does not pick up on
an external fault.
Remark 2: The external system can change due to various
factors, such as a sudden large change in load or generation,
outage of an adjacent line, single-pole tripping, nonsimultaneous opening of adjacent line circuit breaker, etc. Simulations
have been carried out to ascertain that the proposed current
differential scheme is very robust and does not maloperate on
any of the aforementioned system disturbances.
2) Internal Faults: EHV and UHV lines require a highly sensitive differential protection scheme to discriminate a high-resistance internal fault from heavy load current. The sensitivity
of the proposed scheme can be evaluated by its ability to detect a high-impedance internal fault. As the proposed scheme
(refer
is applied for the primary protection of the tie line
to Fig. 11), all four types of internal faults (LG, LL, LLG, and
LLL) are simulated on the line . For each type of fault, the
fault location is varied from 0% to 100% in steps of 10%; fault
resistance is varied from 0 to 600 in steps of 10 , and fault
inception angle is varied from 0 to 300 in steps of 15 .
Fig. 13 illustrates the performance of the proposed current
differential protection scheme on an internal LLL fault at midpoint of the line with a fault inception angle of 270 and a
for phase a. For a preset value of
fault resistance of 650
. Hence, there is a relay pickup on
DAMBHARE et al.: CURRENT DIFFERENTIAL PROTECTION OF TRANSMISSION LINE
Fig. 13. Performance of the proposed current differential protection scheme on
an internal LLL fault at the midpoint of line (fault inception angle 270 , fault re~ (i ) for phase-a. (b) 9~ (i ) for phase-a. (c) Differential
sistance of 650 ). (a) 9
and restraining currents of phase-a (K = 0.07). Note that ji j Ki .
617
Fig. 15. Performance of the proposed current differential protection scheme
on an internal LL fault on phase a-b, near bus 3 (fault inception angle 270 ,
fault resistance of 2400 ; K = 0.07). (a) Differential and restraining currents of phase-a ji j Ki . (b) Differential and restraining currents of
phase-b ji j Ki . (c) Differential and restraining currents of phase-c,
.
ji j Ki
TABLE I
SENSITIVITY FOR THE HIGH-RESISTANCE INTERNAL FAULT
Fig. 14. Performance of the proposed current differential protection scheme
on an internal LG fault on phase a, near bus 3 (fault inception angle 270 ,
fault resistance of 1600 ; K = 0.07). (a) Differential and restraining currents of phase-a ji j Ki . (b) Differential and restraining currents of
phase-b ji j Ki . (c) Differential and restraining currents of phase-c,
.
ji j Ki
the internal fault. Similar behavior is observed for the other two
phases.
Figs. 14 and 15 illustrate the performance of the proposed current differential protection scheme on internal LG and LL faults.
Simulation results show that the proposed scheme discriminates
the faulted phase correctly.
Table I shows the highest resistance internal fault that can be
detected by the differential protection schemes on line , irrespective of fault location and fault inception angle. The relays
were set to provide maximum sensitivity without compromising
security.
Table I shows that the proposed scheme enables a far more
sensitive relay setting than the schemes of [5] and [6]. We notice that the sensitivity of the protection improves by a factor
of about 2 to 3 with the proposed current differential protection
scheme. We emphasize that this improvement in the sensitivity
is not at the cost of the relay security.
under the
3) Line Charging: The energization of line
no-load and heavy-load condition is simulated. Simulation re-
sults show that the proposed scheme is immune to line-charging
current.
4) Effect of a Mutually Coupled Line: In principle, a current
differential relay should be immune to the effect of mutual coupling of double-circuit transmission lines. To ascertain this, line
and
(refer Fig. 11) are modelled as individual continuously transposed double-circuit lines with intercircuit zero-sequence coupling, using distributed parameters (Clarke-2 3)
model. The proposed scheme is applied to line
and is tested
and on line . The fault lofor all four types of faults on line
cation, fault resistance, and fault inception angle are also varied.
Simulation results confirm that the proposed current differential
scheme trips correctly on all internal faults and does not maloperate on any external fault.
B. Speed versus Accuracy
In the proposed current differential protection scheme, the
moving window average is updated after every sample. The
scheme is very fast (refer to Figs. 16 and 17) even if the trip decision is taken on the basis of error exceeding the threshold value
consistently for four samples. Simulation results show that the
proposed scheme takes less than half a cycle to detect low-resistance faults and less than one cycle to detect the high-resistance
faults (above 500 ).
1) Comparison with Phasor Estimation-Based Methods: In
the phasor-based approaches, the relay operating time is affected by the method of phasor estimation. The relaying speed
618
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
Fig. 16. Relaying speed of the proposed algorithm: comparison with the
phasor-based approach (for LLL fault at the midpoint of line, the sampling
frequency is 1 kHz).
Fig. 18.
faults.
i
versus i trajectories of the proposed algorithm for severe external
Fig. 19.
i
versus i trajectories of the proposed algorithm for internal faults.
Fig. 17. Effect of sampling frequency on the relaying speed of the proposed
protection scheme (for the LLL fault at midpoint for the line).
of the proposed method is compared with the recently reported
method in [6]. The required phasors are computed by using the
full-cycle recursive DFT (FCDFT), half-cycle recursive DFT
(HCDFT), and phasorlet [19]. Fig. 16 shows that the proposed
scheme is faster than the phasor-based approach, irrespective of
the method of phasor estimation.
2) Sampling Frequency: The sampling rate affects the operating time (i.e., speed of the relay). Fig. 17 shows the operating time of the proposed scheme for sampling frequencies
of 1, 2, and 2.5 kHz. The studies show that 2.5 kHz gives the
fastest relay operation followed by 2 kHz and 1 kHz, respectively. However, the marginal gain in speed reduces with the
higher sampling frequency, a result in concurrence with the law
of diminishing marginal utility. Similar observations have been
made in the context of digital distance relay in [20].
3) Effect of CT Selection: To study the robustness of the algorithm for different CT choices, the following combinations
were simulated:
1) C400, 1200:5 CTs at both ends of the transmission line;
2) C100, 1200:5 CTs at both ends of the transmission line;
3) C50, 600:5 CTs at both ends of the transmission line;
4) C100, 1200:5 CT at one end and C50, 600:5 CT at the other
end of the transmission line.
The results on C400, 1200:5 CT have already been described.
When simulations were repeated with identical lower voltage
class CTs [i.e., choices (2) and (3)] no significant reduction in
sensitivity was observed. With choice (2), the sensitivity was reduced by approximately 2% while with C50 CTs [i.e., choice
(3)], the sensitivity was reduced by approximately 4%. This
clearly brings out the merit of the proposed scheme.
To conduct the worst-case performance evaluation, simulations were then repeated with choice (4). In this case, both CTs
characteristics also do
have low-voltage ratings and their
not match. Further, the nominal current ratio of one end the CT
is 1200:5 while that of the other end CT is 600:5. With this extreme scenario, we observed that the performance of the proposed algorithm deteriorated. Maloperation on external faults
was observed. This is due to the CT saturation problem, with
the degree of saturation being different in two CTs.
Ziegler [21] has discussed a method to identify the CT saturation problem in differential relay protection and thereby prevent the relay maloperation on CT saturation. This method is
based upon the observation that on an internal fault, the differential current increases rapidly in comparison to the restraining
current. In contrast, on an external fault, the restraining current
pickup precedes differential current pickup. This is because the
CT core requires some time to saturate after the inception of
fault. With the onset of core saturation, the differential current
picks up. This knowledge is useful in detecting the CT saturation problem and, hence, helps in preventing maloperation of the
differential relay. Note that the logic is specifically designed for
differential relays.
Fig. 18 shows the versus trajectories with the proposed
algorithm for severe external faults when the differential relay
maloperates. Fig. 19 shows the corresponding trajectories for
internal faults. It is seen that the method described by Ziegler
provides a consistent signature of CT saturation, even with the
proposed algorithm.
When this method was used to detect CT saturation and,
therefore, prevent relay maloperation, it was found that the
sensitivity of the proposed algorithm was reduced by only 13%,
from the choice (1). This number is quite promising considering
the extremely adverse choice made in CT selection.
DAMBHARE et al.: CURRENT DIFFERENTIAL PROTECTION OF TRANSMISSION LINE
TABLE II
SENSITIVITY FOR THE HIGH-RESISTANCE INTERNAL
FAULT FOR THE SERIES-COMPENSATED LINE
We conclude that proposed method is quite robust as far as the
CT selection is concerned. However, its security can be further
improved by incorporating a restraint function based upon CT
core saturation detection logic.
C. Performance With Series-Compensated Line
The proposed current differential scheme can also be applied
in toto for the protection of a series-compensated transmission
line. All three tie lines between nodes 3 and 13 (refer to Fig. 11)
are compensated with 30% series capacitive compensation. The
metal–oxide varistor (MOV) data (connected across the series
capacitors) are given in [16]. The parallel combination of series
capacitor and MOVs is placed at the midpoint of lines. The initial value of the generator voltage magnitudes and angles is computed from the load-flow analysis of the compensated system.
The proposed scheme is then applied for the primary protection of the tie line . All four types of faults (LG, LL, LLG,
and LLL) are simulated on both sides of series capacitors on
to test the performance of the proposed scheme on inline
ternal faults. Similar faults are simulated on bus 3 and bus 13 as
well as on lines 3–102 and lines 13–112 to test the performance
of the proposed scheme on external faults. For every fault, the
fault location is varied from 0% to 100% in steps of 10%, fault
resistance is increased from 0 in steps of 10 , and the fault
inception angle is varied from 0 to 300 in steps of 15 . It is
validated that the relay discriminates between internal and external faults and trips on internal faults only.
Extensive simulation studies are carried out to compare the
sensitivity of the proposed scheme with schemes of [5] and [6].
Table II shows the highest resistance fault that can be detected
by the differential protection schemes on line , irrespective
of fault location and fault inception angle. Note that the proposed scheme is more sensitive for the high-resistance LG fault
than the scheme of [5] and [6]. Also, the sensitivity of the proposed scheme on other types of faults is better than conventional
schemes.
VI. CONCLUSION
Equation (18) shows that at the fundamental frequency, differential phasor current is not zero even under the steady-state
condition. This can adversely affect the sensitivity of the current differential protection scheme. One approach, suggested in
the literature, to improve sensitivity is to use a charging current
compensation.
0)
Instead, in this paper, we show that the dc component
of the differential current will be zero if there is no internal fault
619
on the transmission line. Hence, it can provide a sensitive and secure protection scheme. It can be computed by a simple moving
window averaging technique. This transformed current will be
nonzero for at least one cycle after the inception of a fault which
is adequate for the relaying decision.
The results show that the proposed method is two to three
times more sensitive than current differential protection using
charging current compensation and faster than even phasorletbased implementation.
The proposed method does not require charging current compensation for enhancing sensitivity. This makes the proposed
method simple and attractive from an application perspective.
The proposed scheme can also be applied in toto for the protection of series-compensated transmission lines. Results demonstrate the promise of the proposed approach.
REFERENCES
[1] S. C. Sun and R. E. Ray, “A current differential relay system using fiber
optics communications,” IEEE Trans. Power App. Syst., vol. PAS-102,
no. 2, pp. 410–419, Feb. 1983.
[2] W. A. Lewis and L. S. Tippett, “Fundamental basis for distance relay on
3-phase system,” AIEE Trans. Power App. Syst., vol. 66, pp. 694–708,
1947.
[3] H. W. Dommel, “Digital computer solution of electromagnetic transients in single- and multiphase networks,” IEEE Trans. Power App.
Syst., vol. PAS-88, no. 4, pp. 388–399, Apr. 1969.
[4] L. J. Vitins, “A correlation method for transmission line protection,”
IEEE Trans. Power App. Syst., vol. PAS-97, no. 5, pp. 1607–1617, Sep.
1978.
[5] H. Y. Li, E. P. Southern, P. A. Crossley, S. Potts, S. D. A. Pickering, B.
R. J. Caunce, G. C. Weller, and R. E. Wilson, “A new type of differential feeder protection relay using global positioning system for data synchronization,” IEEE Trans. Power Del., vol. 12, no. 3, pp. 1090–1099,
Jul. 1997.
[6] Z. Y. Xu, Z. Q. Du, L. Ran, Y. K. Wu, Q. X. Yang, and J. L. He, “A
current differential relay for a 1000-kv UHV transmission line,” IEEE
Trans. Power Del., vol. 22, no. 3, pp. 1392–1399, Jul. 2007.
[7] B. Kasztenny, I. Voloh, and E. Udren, “Rebirth of the phase comparison
line protection principle,” in Proc. 59th Annual Conf. Protective Relay
Engineers, Apr. 2006, pp. 193–252.
[8] A. G. Phadke and J. S. Thorp, Computer Relaying for Power Systems.
Taunton, Somerset, U.K.: Research Studies Press Ltd., 1988.
[9] L. J. Ernst, W. L. Hinman, D. H. Quam, and J. S. Thorp, “Charge
comparison protection of transmission lines-relaying concepts,” IEEE
Trans. Power Del., vol. 7, no. 4, pp. 1834–1852, Oct. 1992.
[10] C. K. Wong, C. W. Lam, K. C. Lei, C. S. Lei, and Y. D. Han, “Novel
wavelet approach to current differential pilot relay protection,” IEEE
Trans. Power Del., vol. 18, no. 1, pp. 20–25, Jan. 2003.
[11] Working Group H9 IEEE Power Syst. Relaying Committee: G. Michel,
G. Pleinka, M. Adamiak, K. Behrendt, D. Dawson, K. Fodero, W. Higinbotham, G. Hoffman, C. Huntley, B. Lowe, J. Johnson, K. Martin, T.
Phillippe, R. Ray, M. Simon, and J. Zipp, Digital Communications for
Relay Protection. [Online]. Available: http://www.pes-psrc.org/
[12] M. G. Adamiak, A. P. Apostolov, M. M. Begovic, C. F. Henville, K.
E. Martin, G. L. Michel, A. G. Phadke, and J. S. Thorp, “Wide area
protecion—Technology and infrastructures,” IEEE Trans. Power Del.,
vol. 21, no. 2, pp. 601–609, Apr. 2006.
[13] IEEE Standard for Synchrophasors for Power Systems, IEEE Std. C37.
118-2005, 2005.
[14] P. V. Chawande, “A high fidelity and robust closed loop active flux
compensation scheme for mitigating CT saturation,” Ph.D. dissertation,
Indian Inst. Technol.-Bombay, Mumbai, India, 2008.
[15] P. Kundur, Power System Stability and Control. New York: McGrawHill, 1993.
[16] H. W. Dommel, Electromagnetic Transients Program (EMTP) Theory
Book. Portland, OR: Bonneville Power Administration, 1986.
[17] K. R. Padiyar, Power System Dynamics, 2nd ed. Hyderabad, India:
BS Publications, 2002.
[18] D. Fernandes, W. L. A. Neves, and J. C. A. Vasconcelos, “Coupling
capacitor voltage transformer: A model for electromagnetic transient
studies,” Elect. Power Syst. Res., no. 77, pp. 125–134, Mar. 2006.
620
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010
[19] M. G. Adamiak, G. E. Alexander, and W. Premerlani, “A new approach
to current differential protection for transmission lines,” in Proc. Protective Relaying Committee Meeting, Electric Council of New England,
Portsmouth, NH, Oct. 1998, pp. 1–16.
[20] J. M. Kennedy, G. E. Alexander, and J. S. Thorp, Variable digital filter
response time in digital distance relay. [Online]. Available: http://www.
geindustrial.com/multilin/notes/ger3798.htm
[21] G. Ziegler, Numerical Differential Protection Principles and Applications. Erlangen, Germany: Publicis, 2005.
Sanjay Dambhare received the B.E. degree in electrical engineering from
the Visvesvaraya National Institute of Technology, Nagpur, India, in 1989, the
M.Tech. degree in electrical engineering from the Indian Institute of Technology, Bombay, India, in 1998, and the Ph.D. degree in electrical engineering
from the Indian Institute of Technology–Bombay, Mumbai, in 2009, in the field
of transmission system protection.
Currently, he is an Associate Professor of Electrical Engineering at the College of Engineering, Pune, India. His research interests include power system
protection, numerical relays, applications of power electronics to power system
and power system computation.
S. A. Soman (M’07) received the B.E. degree in electrical engineering from
the Maulana Azad College of Technology, Bhopal, India, in 1989 and the M.E.
and Ph.D. degrees in electrical engineering from the Indian Institute of Science,
Bangalore, India, in 1992 and 1996, respectively.
Currently, he is a Professor in Department of Electrical Engineering, Indian
Institute of Technology-Bombay, Mumbai, India. He has authored a book titled
Computational Methods for Large Power System Analysis: An Object Oriented
Approach (Kluwer, 2001). His research interests and activities include largescale power system analysis, deregulation, application of optimization techniques, and power system protection.
M. C. Chandorkar (M’84) received the B.Tech. degree in electrical engineering from the Indian Institute of Technology–Bombay, Mumbai, India, in
1984, the M.Tech. degree in electrical engineering from the Indian Institute of
Technology–Madras, Chennai, India, in 1987, and the Ph.D. degree from the
University of Wisconsin, Madison, in 1995.
He has several years of experience in the power electronics industry in India,
Europe, and the U.S. From 1996 to 1999, he was with ABB Corporate Research Ltd., Baden-Daettwil, Switzerland. Currently, he is a Professor in the
Department of Electrical Engineering, Indian Institute of Technology–Bombay,
Mumbai, India. His research areas include the application of power electronics
to power-quality improvement, power system protection, power-electronic converters, and the control of electrical drives.