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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
Adaptive Current Differential Protection Schemes
for Transmission-Line Protection
Sanjay Dambhare, S. A. Soman, Member, IEEE, and M. C. Chandorkar, Member, IEEE
Abstract—Throughout the history of power system protection,
researchers have strived to increase sensitivity and speed of apparatus protection systems without compromising security. With
the significant technological advances in wide-area measurement
systems, for transmission system protection, current differential
protection scheme outscores alternatives like overcurrent and distance protection schemes. Therefore, in this paper, we address this
challenge by proposing a methodology for adaptive control of the
restraining region in a current differential plane. First an error
analysis of conventional phasor approach for current differential
protection is provided using the concept of dynamic phasor. Subsequently, we extend the methodology for protection of series compensated transmission lines. Finally, we also evaluate the speed
versus accuracy conflict using phasorlets. Electromagnetic Transient Program simulations are used to substantiate the claims. The
results demonstrate the utility of the proposed approach.
Index Terms—Adaptive protection, current differential protection, dynamic phasor, global positioning system (GPS), mutually
coupled lines, phasorlets, series-compensated lines, tapped lines.
I. INTRODUCTION
I
T is a well recognized fact that differential protection
schemes provide sensitive protection with crisp demarcation of the protection zones. In principle, the differential
protection is also immune to tripping on power swings. Such
schemes when used for transmission systems using pilot wires
are called pilot relaying schemes [1]. In 1983, Sun and Ray
[2] published a seminal paper describing current differential
relay system using fiber optics communication. An effective
transmission rate of 55 samples per cycle at 60-Hz frequency
was achieved in [2]. Since, differential comparison of the
local and remote end currents must correspond to the same
time instant, a delay equalizer is used with the local sequence
current component signal to compensate the delay in receiving
the remote end currents.
The inaccuracies in such a current differential protection
scheme arise, primarily, due to the following reasons:
• effect of the distributed shunt capacitance current of the
line is neglected;
• modelling inaccuracies with series-compensated transmission line;
Manuscript received May 30, 2008; revised December 13, 2008. Current version published September 23, 2009. This work was supported by PowerAnser
Labs, IIT Bombay. Paper no. TPWRD-00395-2008.
The authors are with the Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India (e-mail: dambhare@ee.
iitb.ac.in; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRD.2009.2028801
• approximate delay equalization between local and remote
end current;1
• current transformer (CT) inaccuracies, in particular errors
due to saturation of the core in the presence of decaying dc
offset current [3].
Conventional current differential schemes employing GPSsynchronized current measurements are discussed in [4]–[6]. If
ultra high transmission system voltages are used (e.g., 765 kV
and above), then line charging current component is significant.
It causes a large variation in phase angle of the line current from
one end to another. In traditional pilot wire schemes, relaying
sensitivity will have to be compromised to prevent the mal-operation. Reference [7] proposes a current differential relay which
uses distributed line model to consider line charging current.
An adaptive GPS-synchronized protection scheme using Clarke
transformation is proposed in [8]. The multiagent-based wide
area current differential protection system is proposed in [9].
References [10], [11] propose the use of phasorlets for fast computation of phasors in distance and differential relaying. Analytical treatment of phasorlets is presented in [12].
If a transmission line has a series capacitor, then dependability of the conventional current differential relay may be compromised due to current inversion. Current inversion depends
on degree of compensation, fault parameters and metal oxide
varistor (MOV) conduction. MOVs have nonlinear V-I characteristics and they are connected in parallel with series capacitors
to protect them from overvoltage. The performance of transmission system protection scheme in presence of series capacitor is
discussed in [13]. In the case of distance relaying, effect of series
compensation is even more serious due to presence of current or
voltage inversion [14]–[16]. Even segregated phase comparison
scheme may fail to operate on current inversion [17].
The paper on digital communication for relay protection [18]
authored by working group H9 of IEEE Power System Relaying
committee is an excellent reference to understand the implications and consequences of digital communication technologies on relaying. Modern high speed communication networks,
typically use Synchronized Optical Network (SONET) or Synchronized Digital Hierarchies (SDH) standard for communication with transmission rates of the order of 274.2 Mbps or
155.5 Mb/s, respectively. They permit “network protection,”
that is, during failure of a communication link, communication services are restored by reconfiguring flow of information
in alternate paths. A typical example is self healing ring architecture used with SONET [19]. In such networks, synchronization by delay equalizers become difficult due to channel asymmetry. Due to channel asymmetry, communication delays for
1For example, at 50 Hz an uncompensated delay of 1 ms in communication will translate into an error of approximately 13 degrees in the phase
computation.
0885-8977/$26.00 © 2009 IEEE
DAMBHARE et al.: ADAPTIVE CURRENT DIFFERENTIAL PROTECTION SCHEMES
transmit and receive paths are not identical. This may lead to
differential currents arising out of inaccurate delay equalization,
especially if, identical time for transmit and receive paths are
considered. However, if current samples are time stamped by
a global positioning system (GPS), then for calculation of differential current, samples corresponding to the same time instant can be compared, thereby providing immunity to channel
delays, asymmetry, etc. [5], [20]. Differential current may be
calculated either using instantaneous sample values, or by extracting phasors. Further, dynamic estimate of the channel delay
can be easily maintained by subtracting the GPS time stamp at
the transmit end from the receiving end time stamp. This permits back up operation even during GPS failure modes.
The primary objective of this paper is to propose a methodology to improve sensitivity and speed of the current differential protection scheme for transmission-line protection without
compromising its security. To meet this objective, we first develop a dynamic phasor model of transmission line. The model
help us to analyze errors associated with steady-state phasor
and
are demodel of transmission line. Two parameters
fine to quantify errors arising out of neglecting dynamic phasors.
Subsequently, we propose an adaptive procedure to set the restrain region in the current differential plane. We show that the
proposed methodology significantly improves sensitivity and
speed of the current differential protection scheme without sacrificing the security.
This paper is organized as follows: a current differential
protection framework is introduced in Section II. In Section III,
a dynamic phasor model of transmission line is developed. It is
used for understanding modelling errors in current differential
protection scheme. Consequently, in Section IV, the idea of
adaptive restrain region is developed. Section V explains the
implementation in phase co-ordinates. Section VII extends it
to series-compensated and multiterminal lines. In Section VIII,
we present simulation case studies in EMTP-ATP package
on a 4-generator, 10-bus system with the capacitance coupled
voltage transformer (CCVT) model. Section IX concludes the
paper.
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Fig. 1. GPS-synchronized current differential protection scheme with equivalent -model of line.
Hence,
can be used as discriminant function to detect a
fault on transmission line. This approach has been suggested by
Phadke and Thorp [21, p. 257].
With a conventional relay-setting approach, operating current
and restraining current
for the current differential scheme
can be expressed as follows:
(3)
and
(4)
The percentage differential relay pick up and operate when
(5)
(6)
where
is a pick-up current and
is the restraint coefficient
. However, it has been shown in [22] that numerical differential relay can be set more accurately in a current
differential plane. Using the phase and magnitude information
of series branch current, we calculate
ratio
(7)
(8)
II. FUNDAMENTALS
Let us consider the positive sequence representation of an uncompensated transmission line. As shown in Fig. 1, the line can
be represented by an equivalent -model. Equivalent circuit
models the effect of distributed line parameters at the line terminals at the fundamental frequency.
Let the positive sequence component of line current for refer. Then, current
ence phase measured at bus be given by
, in the series branch of the -equivalent line model at node
can be computed as follows:
(1)
is the current in shunt path at bus and
where
is the positive sequence voltage of reference phase . Simican also be computed.
larly, current in series branch at bus
If there is no internal fault on the line, then
(2)
In absence of an internal fault, we have
and
As shown in Fig. 2, this can be visualized in the current differat (180 , 1). Ideally, every point other
ential plane by point
than indicates an internal fault. However, even in the absence
of an internal fault, in real life the operating point may deviate
from the point (180 , 1) due to following reasons:
1) synchronization error;
2) delay equalizer error;
3) modelling restrictions (i.e., assumptions, approximations,
or inaccuracies of the algorithm);
4) ratio and phase angle errors of CT. These errors may become significant when a CT core saturates because of large
currents during an external fault.
Since GPS provides time synchronization of the order of 1
sec, the synchronization error can be practically eliminated.
Also, if the same time stamped samples of two end are processed, delay equalizer error can be eliminated. Further, explicit
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
where Re denotes the real part,
,
and
represent a dynamic phasor at the th harmonic frequency. Then, dynamic phasor at fundamental frequency can be
evaluated as follows:
(14)
Equation (14) indicates that well known phasor computation
algorithms like full-cycle recursive DFT, half-cycle recursive
DFT etc., actually compute a dynamic phasor. However, information of rate of change of phasor is not utilized.
Rate of change of a dynamic phasor is given by the following
equation:
Fig. 2. Trip and the restrain region in current differential plane.
modelling of the shunt capacitance of the line reduces the modelling errors. Therefore, we can reduce the width of the restrain
for phase
region in the current differential plane. We use
error2 and
% for magnitude error in current differential
plane. Hence,
and
(refer Fig. 2). The corresponding value of
in conventional relay setting approach is nearly 0.43.
(15)
Prior to a fault or a disturbance,
. Subsequent
to a disturbance, voltage and current signals are not periodic.
Hence, a dynamic phasor should be preferred for modelling.
Using (15), an appropriate phasor representation of (9) and (10)
is given by
III. ERROR ANALYSIS USING DYNAMIC PHASORS
In principle, one can question the validity of phasor computation in relaying algorithms, irrespective of whether it is distance
protection or differential protection, because if the relaying decision has to be arrived within one cycle of the fault inception,
then, the actual voltage and current signals can differ appreciably from a sinusoid. This motivates us to develop a dynamic
phasor model of transmission line.
Fundamental equations used to describe propagation of a disturbance on a lossless single-phase transmission line are [21]
(16)
(17)
where
(9)
(10)
where and are the inductance and capacitance of the line
per unit length and is distance measured from relay location.
If
and
are assumed periodic, then, (9) and (10) can
be transformed to the well-known phasor model of line
(11)
(12)
where
and
denote fundamental voltage and current phasors respectively. The -equivalent circuit is an “exact” two-port
equivalent of (11) and (12). In that sense, methods based upon
-equivalent model are equivalent to method proposed in [7]
which uses an explicit long line model.
The extension of phasors for the dynamic situation is discussed in [23]. In this approach, signal
can be represented
as follows:
(13)
2Reference
[22] has suggested
640
margin for phase angle error.
By comparing (16) and (17) with (11) and (12), we can conclude
that inaccuracies in differential protection based upon phasor
model arises due to neglecting the dynamic phasor contribution terms
and
in (16) and (17). Parameters and
define gain associated with dynamic phasor
model. Further,
and
do not directly depend upon the parameters of the line. Under the steady-state condition,
and
are unity. Hence,
and
measures the inaccuracies associated with the steady-state modelling of the system. Prior to a fault, the terms
and
are
unity. After the fault, and
will deviate from unity. As the
transients die down,
and
returns back to unity.
Figs. 3 and 4 shows the behavior of
and
for a severe
three phase bus fault.3 We observe that the transmission-line
steady-state phasor model is erroneous immediately after a fault.
For a severe fault, model accuracy improves within two cycles.
Fig. 5 shows variation of
and
for a less severe fault. In
this case behavior of
and
shows that steady-state model
provides a reasonably good approximation of system behavior.
The behavior of error terms
and
suggest that threshold
parameter used to detect fault in differential protection should
have adaptive parameters. When model inaccuracy is high, then
restraint should be high and vice versa.
3The
system details are provided in Section VIII.
DAMBHARE et al.: ADAPTIVE CURRENT DIFFERENTIAL PROTECTION SCHEMES
Fig. 3. Variation in k and k at end i (refer Fig. 1) for phase a. The external
LLL bus fault is at bus i on 230-kV system (fault resistance is 0.1 and fault
occurs at 0.115 sec). Observe that both k and k are affected by a close in bus
fault.
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Fig. 5. Variation in k and k at end i (refer Fig. 1) for phase a. The external
LLL bus fault is at bus i on the 230-kV system (fault resistance is 100 and
fault occurs at 0.115 s).
1) high impedance fault may not involve appreciable transients (refer Fig. 5);
2) high impedance faults should not lead to gross errors due
to CT saturation and
3) large disturbances (e.g., load throw off and external faults)
will cause large differential currents because 1) the phasor
model is not truly valid under such situations (as shown
in Fig. 3) and 2) CT errors may increase due to partial
saturation; hence, large transients or disturbances demand
a larger restrain region.
The aforementioned observations suggest that the height of
the restrain region should be a function of the current magniand
. In particular, we propose the following
tudes of
restraining function:
Fig. 4. Variation in k and k at remote end j (refer Fig. 1) for phase a. The
external LLL bus fault is at bus i on the 230-kV system (fault resistance is 0.1 and fault occurs at 0.115 s). Observe that k remains close to unity for the
remote bus and the behavior of k is similar to k at bus i.
IV. ADAPTIVE CONTROL OF RESTRAIN REGION
A protection engineer strikes balance between dependability
and security of a relay by controlling the sensitivity. Dependability of a relay can be improved by increasing the sensitivity.
Sensitivity of the differential relay can be improved by reducing
the area of the restrain region in the Fig. 2. Since, we have already tightened the width of the restrain region, this implies that
we should reduce height of the rectangle representing the restrain region. However, it is equally important to keep it large
enough so that relay does not pick up on transients or external
disturbance which includes a fault. Too sensitive relay setting
increases the possibility of relay maloperation and hence compromises security.
We now propose an important enhancement to improve sensitivity of the current differential relay without compromising on
its security. Basically, sensitivity implies an ability to detect low
current or high impedance fault. The proposed enhancement is
based on the following observations:
(18)
where
and
are suitable constants. We assume that
is greater than 1. In case the ratio is less than
one, then the numerator and the denominator should be interchanged. The relay trips when either: 1) the restraining function
is greater than zero or 2) when the angular separation criterion
described in the earlier section is violated.
1) Selection of Constants and : Under no-fault and
is equal to one.
steady-state conditions, ratio
depends upon line current
Further, the term
and hence it can be very small (
and
). This
suggests that constant should be at least equal to 1. Further,
for sensitive protection, constant should be chosen close to
and
0.0015
unity. In particular, we have found
to be a satisfactory choice. Small magnitude of
is chosen
because fault current range is approximately in kiloAmperes.
At lower values of , possibility of relay maloperation on
extreme load throwoffs have been observed.
V. CURRENT DIFFERENTIAL PROTECTION IN
PHASE COORDINATES
Positive sequence network is excited by both ground and
phase faults. Hence, in principle, current differential protection
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
Indices
, and represent the respective phases. Similarly, the
line current equation at bus can be expressed as follows:
(24)
Thus, we conclude that there is no fault on the line if
(25)
(26)
(27)
Fig. 6. Equivalent- model of three phase transposed transmission line [24].
scheme using a positive sequence network representation can
alone detect all possible faults. However, sensitivity using positive sequence component alone will vary with the type of fault.
It will be maximum for a bolted three-phase (LLLG) fault. In
contrast, for a single line to ground fault, the sensitivity for
ground fault detection will be reduced by a factor of three approximately.4 This motivates that either all the sequence networks (positive, negative, zero) be used for decision making,
or computation in phase co-ordinates should be employed. We
prefer the phase domain approach because of its simplicity and
accuracy.
Let us consider the equivalent- model of a three phase transposed transmission line as shown in Fig. 6.
Let
and
be the self and mutual series impedance of the
line. For a transposed line, they can be easily computed from the
sequence data as follows:
(19)
(20)
where
and
are the positive, negative and zero sequence impedance of the transmission line. Similarly,
and
are self and mutual shunt susceptance of the transmission
line. They can be computed as follows:
In practice, each phase tripping logic can be set using the procedure described in Section IV.
and
can be comRemark 1: The currents phasors
puted from GPS-synchronized measurements using (23) and
(24). Total twelve GPS-synchronized measurements are required, three currents and three voltages at each end. Phasors
are computed from most recent samples by recursive discrete
Fourier transform (DFT) [21] or phasorlets [12]. An alternative
and
in the phase domain
to estimation of currents
would be computation in the time domain. However, phasor
approach has been preferred because it avoids numerical
differentiation.
Remark 2: There is no possibility of inadvertent tripping of
the transmission line due to line charging current. This is bewill be zero
cause the discriminant function value
even during line charging.
VI. RELAYING ALGORITHM
We now propose following algorithm for sensitive and secure
current differential protection scheme.
A. At Node “i”
1) Input line parameters, relay settings (
and
), sampling frequency
and trip value for
.
counter
0.
2) Set
3) Acquire latest GPS-synchronized time-tagged samples
and
where
(21)
(22)
It has to be noted that, usually,
will be negative as
.
Now from Fig. 6, the line current equation at bus in phase
coordinates can be expressed as follows:
4)
5)
6)
7)
(23)
4Note
that for LLLG fault, I
=I
and for LG fault I
3I
.
Time “t” indicates an instant corresponding to latest sample
and , , and designate the three phases.
Update phasors5
and
.
by using (23).
Compute
Acquire the latest phasors,
from the other end.
Note that due to communication latency
.
and
by using (18) and
For instant , compute
(8).
5Phasors can be updated using full-cycle recursive DFT, half-cycle recursive
DFT, or phasorlet.
DAMBHARE et al.: ADAPTIVE CURRENT DIFFERENTIAL PROTECTION SCHEMES
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From the bus voltage and line current measurements at bus
, we estimate current in the series capacitor-MOV combination
as follows:
(28)
(29)
(30)
Similarly, current
equations:
can be estimated by the following
(31)
Fig. 7. GPS-synchronized current differential protection scheme for seriescompensated line (series capacitor at end).
(32)
(33)
If there is no fault on the line, then we have
However, if there is a fault on the line, then discriminant funcwill not be zero.
tion
Remark 3: The extension of the aforementioned scheme in
phase coordinates is straightforward. For the simplicity of illustration, we have used sequence representation, but all calculations are carried out in phase coordinates. The method can be
easily adapted even if the series compensation is not at the center
of the line. Similarly, the scheme can be extended for the protection of a multiterminal line.
Fig. 8. GPS-synchronized current differential protection scheme for the seriescompensated line (series capacitor at mid point).
8) Check if:
OR
.
If TRUE, then
.
else, if
9) If
issue the trip decision.
Else, go back to step 3.
Similar algorithm is also applied at node the “ ”.
.
VII. CURRENT DIFFERENTIAL PROTECTION SCHEME FOR
SERIES-COMPENSATED TRANSMISSION LINES
Series capacitor on a transmission line can be installed at either end or at the midpoint. If a line is compensated at its terminals, then the scheme described in the previous section can
be applied in toto using line connected GPS-synchronized line
current and bus voltage measurements (see Fig. 7). However,
if midpoint compensation is used, then the basic scheme using
sequence network representation (proposed in the Section II)
should be modified as follows.
Fig. 8 shows a line with series compensation at midpoint. The
line sections of either side of series compensation are accurately
modelled by the equivalent model of transmission line.6
6Each equivalent model corresponds to half of the line length of uncompensated line. Notice that with equivalent ; B 6 B= , where h corresponds
to half the line length.
= 2
VIII. CASE STUDIES
To evaluate the performance of the proposed scheme, the following methodology has been used.
1) Simulate power system response to disturbances (e.g.,
faults using Electromagnetic Transient Program (EMTP)
simulations. ATP [24] software has been used for
simulations.
2) Samples obtained from the EMTP simulation are fed to a
MATLAB program which implements the proposed differential protection scheme. Full-cycle recursive DFT, halfcycle recursive DFT, and phasorlets algorithms are used to
estimate the phasors.
3) The proposed scheme is compared and contrasted with:
1) the conventional GPS-based current differential scheme
of [4] and 2) a more recent method reported in [7].
We report results on a two-area, 230–kV, 4–generator, 10–bus
system (refer to Fig. 9). Detailed generator, load and line data on
a 100-MVA base are given in [25]. 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 a detailed model
is used for representing generators. The initial values of generator voltage magnitude and angles are calculated from the
load-flow analysis. The proposed scheme is applied for primary
between node 3 and 13.
protection of one of the tie lines
The fault location is measured from bus 3. ANSI 1200:5, class
C400 CT model [26] and 250 kV:100-V CVT model [27], have
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
Fig. 9. Single-line diagram of a two-area, four-generator, ten-bus system.
Fig. 10. Equivalent circuit of CT used in ATP simulation R
:
: .
mH and R
0 0003
= 24
= 0:63 ; L =
Fig. 11. Performance of proposed current differential protection scheme on external faults. Note that relay does not pick up as all the final operating points are
inside the restrain region.
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.
We also evaluate the performance with series-compensated and
mutually coupled lines.
A. Dependability Versus Security
TABLE I
0 i CHARACTERISTICS OF 1200:5 ANSI CT
been used for obtaining realistic CT and CCVT response during
EMTP simulations.
In these simulations, type-98 nonlinear saturable inductor
model has been used to simulate nonlinear magnetizing reactance of CT. It is connected across the secondary of ideal CT
(refer Fig. 10). The Type-98 model requires nonlinear
characteristics of the CT core. To convert the excitation curve
pairs, the methodology described
specified by
in [28], [29] is used. The CT model data have been given in
Table I.
Since standard data do not provide hysteresis information (hysteresis loss is practically negligible), the type-98
model7 was considered most suitable to simulate magnetizing
impedance.
Anti-aliasing filter [21], being analog filter has to be simulated through ATP. It is a two stage R-C filter with a cutoff frequency of 360 Hz, which is well below the minimum sampling
frequency of 1 kHz used in relaying and sufficiently above the
50-Hz frequency requirement for phasor extraction.
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 data
acquisition rate is set to 1000 Hz.
7Alternative
to this was type-96 model, which requires hysteresis details.
First, we consider nonadaptive setting of the relay in current
differential plane which has already been outlined in Section II.
Then, we provide results with the adaptive scheme.
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
external faults. All the four types of external shunt faults (LG,
LL, LLG and LLL) are simulated on buses 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 fault inception angle is varied
from 0 to 300 in steps of 15 . For each case, we compute
, and plot the
final operating point (marked by “ ” in Fig. 11) on current differential plane. As the “ ” always appear in restrain region, it
validates that the proposed relay will not trip on load or external
fault. The figure also shows that the restrain region cannot be reduced, significantly, without compromising the relay security.
Fig. 12 shows the trajectory of phase-a operating point on
current differential plane for the bolted LLL fault on bus 3 (external fault) for the fault inception angle of 270 . As the relay
operating point lies inside the restrain region, the relay does not
pick up on external fault.
Similar investigations carried out with the adaptive relay setting show that the relay does not pick up on any external fault or
large disturbance like load throw off etc. However, conventional
scheme of [4] tends to operate on low resistance external fault
on bus 3 and 13. We conclude that proposed scheme does not
pick up on external faults.
2) Internal Faults: Sensitivity of the proposed scheme can
be evaluated by its ability to detect a high impedance internal
fault. Fig. 13 shows the trajectory of phase-a operating points
on current differential plane for one of the cases of LL fault on
DAMBHARE et al.: ADAPTIVE CURRENT DIFFERENTIAL PROTECTION SCHEMES
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Fig. 12. Trajectory of phase-a operating point for proposed current differential
protection scheme on external fault (LLL bolted fault on bus 3, fault inception
angle 270 ). Note that the relay does not pick up.
Fig. 14. Effect of phasor computation algorithms on relay operating time of
phase-a for LLL fault at midpoint for the proposed current differential protection
scheme (sampling frequency is 1 kHz).
Fig. 13. Trajectory of phase-a operating point of proposed current differential
protection scheme for internal fault (LL fault at the start of line, fault inception
angle 270 ; fault resistance = 600 ). Note that the relay picks up.
TABLE II
SENSITIVITY FOR HIGH RESISTANCE INTERNAL FAULT
phase a-b, at the start of line for the fault inception angle of
270 and a large fault resistance of 600 . 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. The relays were set to provide maximum
sensitivity without compromising security.
The table clearly shows that the proposed scheme enables far
more sensitive relay setting than the conventional scheme of [4].
With nonadaptive setting, the relay sensitivity is similar to that
of scheme suggested in [7]. This can be explained from the fact
that both the methods account for line charging contributions.
However, with the proposed adaptive setting strategy of the restrain region, we notice that sensitivity of the current differential
protection scheme improves by a factor of about 2.5. We emphasize that this improvement in the sensitivity using adaptive
setting strategy is not at the cost of the relay security.
Remark 4: The external system can change due to various
factors like, sudden large change in load or generation, outage of
adjacent line, single pole tripping, non simultaneous 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 above system
disturbances.
3) Line Charging: The energization of line
under no load
and heavy load condition is simulated and the performance of
proposed current differential scheme is compared with other
schemes. Simulation results show that the proposed scheme is
immune to line charging current. This is because the actuating
is independent of the line
quantity of proposed scheme,
charging current.
4) Effect of a Mutually Coupled Line: In principle, a current
differential relay should be immune to effect of mutual coupling
of double circuit transmission lines. To ascertain this, line
and
(refer Fig. 9) are modelled as individual continuously
transposed double circuit lines with inter-circuit zero sequence
coupling, using distributed parameters (Clarke-2 3) model.
Proposed scheme is applied to line
and is tested for all four
and also on line . The fault location,
types of faults on line
fault resistance and fault inception angle is also varied. Simulation results confirm that 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 GPS-synchronized current differential protection scheme, the phasors are updated after every sample. The
scheme is very fast (refer to Figs. 14 and 15) 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 is very fast and takes less than half a cycle to
operate for low resistance faults. However, it needs one to two
cycles to detect the faults above 500 resistance. This is acceptable with high impedance faults as the fault current level is
low and CTs will not saturate.
1) Phasor Estimation Algorithms: The relay operating time
depends upon the method of phasor estimation. Fig. 14 shows
the operating time with the proposed scheme when phasors are
estimated by using full-cycle recursive DFT (FCDFT), halfcycle recursive DFT (HCDFT), and phasorlet with adaptive and
nonadaptive settings. The studies show that with the relay setting, phasorlets provide the fastest relay operation followed by
half-cycle recursive DFT and full-cycle recursive DFT, respectively, for the same sampling frequency. Similar behavior is observed for the other two phases.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
TABLE III
SENSITIVITY FOR HIGH-RESISTANCE INTERNAL FAULT FOR
SERIES-COMPENSATED LINE
Fig. 15. Effect of sampling frequency on the relay operating time of phase-a
for the LLL fault at midpoint for the proposed current differential protection
scheme when phasors are estimated by using full-cycle recursive DFT.
The results also show that relay operation is faster with the
adaptive control of the restrain region irrespective of the phasor
estimation algorithm. The fastest relay operation is achieved
with adaptive control of restrain region and when the phasorlet
algorithm is used for phasor computation.
Remark 5: It is interesting to observe that time to trip has an
inverse relationship to the magnitude of fault current.
This behavior can be explained as follows. For the sake of
simplicity, consider that the phasor is computed by using fullcycle recursive DFT and nonadaptive methodology is used. It
takes one cycle for the phasor computation algorithm to latch to
a fault current value. Assuming a linear change in the estimate,
we see that for a fixed pick-up value, larger fault currents imply
faster pick up (and vice versa).
2) Sampling Frequency: The sampling rate influences the operating time of the relay. Fig. 15 show the operating time of proposed scheme with adaptive and nonadaptive settings, for the
sampling frequency of 1, 2, and 2.5 kHz using full-cycle recursive DFT algorithm for phasors estimation. The studies show
that, 2.5 kHz sampling rate gives fastest relay operation followed by 2 and 1 kHz, respectively. However, marginal gains
in speed reduce at higher sampling frequencies i.e., a result in
concurrence with the law of diminishing marginal utility. Similar observations have been made in the context of digital distance relay in [10] and [30].
C. Performance With Series-Compensated Line
Application of proposed scheme to series-compensated transmission line is discussed in Section VII. All the three tie lines
between nodes 3 and 13 (refer Fig. 9) are compensated with
30% series capacitive compensation. The MOV data (connected
across the series capacitors) is given in [24]. The parallel combination of series capacitor and MOVs are placed at the midpoint
of lines. The initial value of generator voltage magnitudes and
angles are computed from the load flow analysis of compensated
system. The proposed scheme is then applied for the primary
protection of tie line . All the four types of faults (LG, LL,
LLG, and LLL) are simulated on both side of series capacitor on
line
to test the performance of proposed scheme on internal
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
proposed scheme on external faults. For every fault, fault location is varied from 0% to 100% in steps of 10%, fault resistance
is increased from 0 in steps of 10 and fault inception angle
is varied from 0 to 300 in steps of 15 . It is validated that the
relay discriminates between internal and external fault and trips
on internal fault only.
Extensive case studies are carried out to compare the sensitivity of proposed scheme with schemes of [4] and [7]. Table III
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
detects very high resistance LG fault. Also, the sensitivity of
proposed scheme on other types of fault is better than conventional scheme. Further, it is seen that with nonadaptive version of the proposed methodology, sensitivity of the proposed
method is comparable with that of method reported in [7]. However, sensitivity improves significantly when proposed adaptive
protection methodology is used. This brings out the importance
of the suggested adaptive control of the relay restrain region.
The proposed scheme is also compared and contrasted with
segregated phase comparison scheme and distance protection
scheme in presence of current and voltage inversion. It is observed that distance protection scheme maloperates for seriescompensated transmission lines and segregated phase comparison scheme fails to trip in presence of current inversion [31].
However, the proposed scheme works satisfactorily.
IX. CONCLUSION
Significant advances have been made in the current differential protection schemes for transmission-line protection. State of
the art methods consider both: 1) modeling of shunt capacitance
of line to account for line charging effect and 2) time stamped
and synchronized phasors to correctly account for relative phase
angle information. No doubt, these measures have significantly
improved the dependability and security of the current differential protection schemes.
In this paper, we have proposed enhancements to further improve the dependability and security of the current differential
schemes. Salient contributions of the paper are as follows.
1) Development of dynamic phasor model of a transmissionline and error analysis of current differential protection
scheme using steady-state phasor.
2) An adaptive relay setting procedure to control the area of
the restrain region in the current differential plane. The area
of the restraining region is made a function of line current.
At lower currents, restraining area is kept small. This increases the sensitivity of the relay. At larger currents, area
DAMBHARE et al.: ADAPTIVE CURRENT DIFFERENTIAL PROTECTION SCHEMES
of the restraining region is increased in proportion to the
current. This increases the security of the relay without
compromising the sensitivity. Simulation studies show that
this can improve sensitivity of the relay by at least a factor
of 2.5.
3) Extension of the proposed methodology for protection of
series compensated and multiterminal transmission lines.
Simulation studies show that this can improve sensitivity
of the relay by at least a factor of 2.
4) Comparative evaluation with state of the art methods.
5) An in depth analysis of the following contradictions:
• dependability versus security;
• speed versus accuracy.
We conclude that the proposed adaptive control of restrain
region together with phasorlet algorithm for phasor estimation
provides the best solution for current differential protection of
(series compensated) transmission lines. It enhances sensitivity
and relaying speed without compromising the security of protection system.
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Sanjay Dambhare received the B.E. degree in electrical engineering from
the Visvesvaraya Regional College of Engineering, Nagpur, India, in 1989,
the M.Tech degree in electrical engineering from the Indian Institute of Technology, Bombay, India, in 1998, and is currently pursuing the Ph.D. degree in
electrical engineering at the Indian Institute of Technology-Bombay, Mumbai.
He is currently Associate Professor at the College of Engineering, Pune,
India. His research interests include power system protection, numerical relays,
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 the Department of Electrical Engineering,
Indian Institute of Technology-Bombay, Mumbai, India. He is author of the
book Computational Methods for Large Power System Analysis: An Object
Oriented Approach. His research interests and activities include large-scale
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 TechnologyMadras, 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. During 1996-1999, he was with ABB Corporate Research
Ltd., Baden-Daettwil, Switzerland. He is currently Professor in the Department
of Electrical Engineering, Indian Institute of Technology-Bombay, Mumbai,
India. His research interests include the application of power electronics
to power-quality improvement, power system protection, power-electronic
converters, and control of electrical drives.