enhanced time overcurrent coordination
TRANSCRIPT
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Electric Power Systems Research 76 (2006) 457–465
Enhanced time overcurrent coordination
Arturo Conde Enrıquez ∗, Ernesto Vazquez Martınez
Universidad Aut´ onoma de Nuevo Le´ on, Facultad de Ingenierıa Mec ´ anica y El´ ectrica, Apdo. Postal 114-F,
Ciudad Universitaria, CP 66450 San Nicol´ as de los Garza, Nuevo Le´ on, M´ exico
Received 1 August 2005; accepted 15 September 2005
Available online 16 November 2005
Abstract
In this paper, we recommend a new coordination system for time overcurrent relays. The purpose of the coordination process is to find a time
element function that allows it to operate using a constant back-up time delay, for any fault current. In this article, we describe the implementationand coordination results of time overcurrent relays, fuses and reclosers. Experiments were carried out in a laboratory test situation using signals of
a power electrical system physics simulator.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Time overcurrent relay; Coordination; Time function
1. Introduction
The application of time overcurrent relays in power systems
has serious limitations in terms of sensitivity and high back-uptimes for minimum fault currents. The high load current and
the different time curves of overcurrent protection devices,
such as fuses and reclosers, reduce reliability and security of
the relay. The overcurrent coordination is done using maximum
fault currents (3–5% of all faults) during maximum demand
conditions (only for a total of a few minutes per day) because
the convergence of overcurrent relay time curves for high fault
currents; for other fault types and other demand situations,
the time curves diverge for minimum fault currents, and the
back-up times are much higher.
A new time element function for overcurrent relays is pro-
posed to enhance the overcurrent coordination system. This
criterion can be applied to phase and ground time overcurrentrelays, and can be applied in both power and industrial systems.
The main goal of the coordination process is to find a time func-
tion that gives a constant back-up time delay forany fault current.
The proposed relay has a time curve that is similar to the primary
∗ Corresponding author. Tel.: +52 81 83294020x5773
E-mail addresses: con [email protected] (A.C. Enrıquez),
[email protected] (E.V. Martınez).
device. The coordination process is automatic between the pro-
posed relay and the overcurrent primary device (fuse, relay or
recloser). Results of fitting curves are presented for both fuses
and reclosers.The relay logic is evaluated using fault current signals. The
proposed algorithms have being tested in a personal computer
that has a signal acquisition card. The test was carried out in
a laboratory test setting using signals from a power electrical
system simulator.
The main benefits of the proposed time overcurrent relay are:
the back-up time is independent of the magnitude of the fault
current, resulting in less back-up time than in the conventional
overcurrent relay system; coordination is carried out by the pro-
posed criterion; the coordination is independent of any future
system changes (such as topology, generation and load); and the
proposed overcurrent relay is obtained with only a small change
in the firmware’s relay, without any additional cost.
2. Time overcurrent relay
The basic model and digital implementation of an overcur-
rent relay system is presented in [1]. In this section, we present
the functional structure as the basis of the proposed relay. The
input signals are the fundamental current phasor I rk and the pick-
up current I pickup. The relay generates the no lineal function
H ( I k ), where I k = I rk/I pickup is the operating current. The func-
0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2005.09.009
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tion H ( I k ) is integrated, and the output integrator signal is
Gk = t k=1
H (I k) (1)
where Gk is the accumulated value of the integrator in the sample
k and t is the sampled period.
The operating condition is obtained when:
Gk = t
kopk=1
H (I k) = K (2)
The relay operation is complete when k = k op and Eq. (2) is
satisfied. The functional relationship for overcurrent relays is
obtained from T = k opt and Eq. (2):
For constant fault current:
T =K
H (I ) (3)
Then, in each sample period:
T (I k) =K
H (I k) (4)
For variable fault currents, using Eqs. (4) and (2), we obtain
kopk=1
1
T (I k)
t = 1 (5)
In Eqs. (3)and(5), we observe that the functional relationship
between K and H ( I k ) defines the characteristics of overcurrent
relays. The shape of the time curve produced is dependent on the
H ( I k ) function. We can modify this function to obtain different
time curves for enhanced coordination.
3. Operative limits of overcurrent relay
Theovercurrent protection systemuses thecurrent as theonly
indicator of fault location. However, the fault current depends
on fault type and prefault steady-state operations. Moreover,
the maximum load current can be similar in magnitude to the
minimum fault current. This increases the difficulty in correctly
discriminating between a stable state and fault conditions.
As a consequence of these factors, the overcurrent relay
reaches changes dynamically, and protection can be lost dur-
ing minimum fault current conditions. This is particularly thecase for phase protection, in which the maximum load current
defines the pick-up current relay. Therefore, the sensitivity limi-
tation of overcurrent relays is the fault detection under minimum
demand conditions.
Another problem in overcurrent protection is the high back-
up time for minimum fault current conditions, as the coordina-
tion criteria are only established for maximum fault currents.
The different load current in each protection location produces
a higher divergence of time curves for minimum fault currents.
When both primary and back-up overcurrent protection systems
have different time curves, adequate time coordination is diffi-
cult. In these situations, the time limitation of overcurrent relays
is high back-up times for both minimum fault current and dif-
ferent time curves devices.
In this paper, time overcurrent relay coordination is obtained
using a new time function. The objective is to simulate the
primary dynamic device to obtain a minimal back-up time oper-
ation. In [2–4], the different coordination methods are proposed;
all methods are dependent on communication channels for
changing settings, and economic factors need to be considered.
The new relay proposed here does not require communication
channels for improving the time overcurrent coordination.
4. Time coordination
The basic idea for time coordination is to satisfy Eq. (6) f or
any current value (see Fig. 1):
T backup = T primary(I primaryk ) +T (6)
where T backup is the time curve of the back-up relay,
T primary(I primary
k ) the time curve of the primary overcurrentdevice, I
primaryk the operating current of primary device and T
is the coordination interval (0.2–0.4 s).
The main purpose is to find a time element function T backup
that ensures that the back-up relay operates with a constant time
delay T relative to the primary device, for any fault current.
For this to happen, it is necessary to change the shape of the time
curve of the relay.
Fig.1 shows the overcurrent relaycoordination system. Relay
A is the back-up relay, and Relay B is the primary relay. By load
current (pick-up setting), the back-up time is increased, although
both relays have the same time curve. To obtain the same back-
up time delay (T ) in all fault currents, there are two differentmechanisms: the first is to change the dial time for each fault
current (curves 2, 3 and 4 in Fig. 1); and the second – a better
solution – is to change curve 5, which is different from the Relay
B time curve (curve 1). Curve 5 is not obtained using a dial time
setting due to the load current. In order to change the overcurrent
relay time curve, curve 5 needs to change shape.
In Fig. 1, we observed that curve 5 is similar to curve 1. For
this to occur, it is necessary to use the pick-up setting of the
Fig. 1. Adaptive time curve of overcurrent relay.
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Fig. 2. Proposed time curve.
primary device to calculate the operating current. This results in
a minimum time curve for the back-up device, as the back-up
curve is asymptotic to the pick-up primary current (Fig. 2). The
analytical time curves were analysed using IEC Standard 255-4 [5]. On the basis of these results, we considered the pick-up
current of the back-up relay to be the fault detector.
Theequation of the proposed relay is obtained by substitution
of Eq. (6) in (5) f or each current sample. The operating current
was calculated using the pick-up current of the primary device
and the fault current I primaryk = I rk/I
primarypickup :
Gk = t k=1
H (I primaryk ), where H (I
primaryk )
=1
T primary(I
primary
k )+T
(7)
The computed time curve proposed is illustrated in Fig. 3. If
the time curve of the primary overcurrent device is analytical
(digital relays), the setting curve is computed to directly substi-
tute for the function T primary(I primaryk ). When the characteristic
is not available (for example, in fuses, electromechanical relays
andreclosers),it is possible to calculatethe analytical expression
using fitting curve algorithms [6–9].
The fault current in the primary device location can be cal-
culated. The goal is to compensate for the fault current in Relay
A by calculating the fault current in Relay B. The difference
between the nominal voltage (V nom) and the real voltage is small
and the effect in the proposed coordination is a small increase in
Fig. 3. Process of calculated time curve proposed.
Fig. 4. Time curve fitting diagram of overcurrent protection devices.
time coordination (T ). I r,backupk and I
r,primaryk are the measured
fault currents in Relay A and Relay B, respectively.
5. Fitting curve algorithm
Fig. 4 shows the diagram for fitting curves. The algorithm is
composed using two factors—no lineal regression and polyno-
mial regression. These factors comprise the main mathematical
models that are proposed in the technical literature [6–9]. The
program selects the best fitting equation using no lineal regres-
sion and polynomial regression. This step is crucial, as the best
fitting equation depends on the type of curve. It is recommended
that the best fitting of all possible fitting equations is selected.
For this fitting application, electromechanical relay, fuse and
recloser curves are available.
Appendix A includes the fitting results for fuse and recloser
curves. Statistical error in thefittingcurves for fuses wasreduced
to acceptable values. The fitting results are reported because
the new coordination approaches see Eq. (7) have been devel-
oped on the basis of the analytical equation of overcurrent
devices.
6. Test
6.1. Steady stable
The coordination example was carried out in the 13.8 kV dis-
tribution system shown in Fig. 5, which is a typical distribution
system. It is not necessary to consider a more complex power
system configuration, as the use of a complex power system
does not reach an unexpected place. Most scenarios have the
same effect on the operating current; therefore, the time over-
current relay coordination process is carried out using pairs of
relays.
The maximum short-circuit current coordination is shown in
Fig. 5. We observed that the back-up time of Relay B (sections
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Fig. 5. Time coordination example of overcurrent relays.
a–b) is greater than that of proposed Relay B. Therefore, the
coordination proposed allows a rapid time curve to be selected
for Relay A. The coordination between proposed Relay B and
Relay C is carried out in the same relay. Using the time curve
(see Eq. (7)), coordination is automatic; even when there is an
increase in the maximum fault current (topology changes or
additional generation of power), coordination is carried out and
setting changes are not necessary. Therefore, the coordination
between Relay C and Relay A can be achieved with 2T , asshown in Fig. 5. The time required for the proposed Relay B
for fault currents in sections b–c (Fig. 5) is slightly more than
Relay B (lack of time curves convergence). Nevertheless, this
time increment is minimal.
Another such case occurs when using a fuse. Coordination
between the fuse, proposed relay (B) and the conventional relay
(A) is shown in Fig. 6. The maximum fault current in each coor-
dination location is shown in thesame figure.The proposed relay
curve is thesame (plusT ) asthatof the maximum clearingtime
fuse curve. The coordination process between the conventional
relay and the fuse can be achieved with 2T as a coordination
interval or with the proposed time curve directly.
In Fig. 7, the coordination of a recloser and relay is shown.The 13.8 kV radial systems are used. The coordination proposed
is achieved with minimal back-up time.
In the shown coordination test, we observed that the minimal
back-up time is obtained. In addition, the coordination process
occurs with the relay; following this, coordination between the
proposed relay and the overcurrent protection device (such as
an electromechanical relay, fuse or recloser) is automatically
obtained. The data necessary for coordination of the proposed
relay is the data system: voltage system and impedance line.
For data protection, the time curve and pick-up of the primary
device are needed. With this available information, coordination
is achieved.
Fig. 6. Time coordination example of fuse and overcurrent relay.
6.2. Dynamic state
The integration process of Eq. (7) simulates the disk dis-
placementprocess in inductionof overcurrent electromechanical
relays. The time function of the primary device is added in Eq.
(7) and evaluated with the fault current in the same place. In this
way, the proposed relay has the same dynamic operation as the
primary device.
The structural diagram of the dynamic test is shown in Fig. 8;
it includes a connection module as the interface between thepower system and the relay. A real-time data acquisition card
Fig. 7. Time coordination example of recloser and overcurrent relay.
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Fig. 8. Structural diagram of overcurrent relay.
Fig. 9. Time coordination in laboratory test.
was used and the relay algorithm was implemented in a personal
computer.
In Fig. 9, the time coordination between Relay B, RelayA and proposed Relay A* are shown. The integration process
of overcurrent relays with variable fault currents was obtained
in a laboratory test situation and are shown in Fig. 10. The
dynamic fault current ( I sc)andtheintegratedvalueintheRelayB
(Gprimaryk ),RelayA(G
backupk ) and proposed Relay A* (G
backup∗k )
are shown. For all relays, the time curves are inverse [5].
For the shown example, the load current difference between
Fig. 10. Accumulated value of the relays integrators in laboratory test.
Relay B and Relays A–A* is 33%. In the laboratory test, we
observed that the time interval between Relay B and Relay A
is 0.61 s, although the operation time difference between Relay
A* and Relay B is 0.3 s (T ). This highlights the advantage of
the proposed time relay versus conventional relay in back-up
zones.
7. Conclusions
The coordination process hasbeen used to find a time element
function that ensures that the time overcurrent relay operates
with a constant time delay relative to the primary device, for all
current values. The main goal of this process is to reduce the
back-up time in the phase time overcurrent relays during poor
fault current conditions.
For the proposed coordination process, it is necessary to
obtain the time curve of the primary device. The analytical
expression is obtained and included in the dynamic equation of
the time overcurrent relay. The coordination process is obtained
using the minimal back-up time. The time operation of the other
relays (the back-up of the proposed relay) is reduced, and the
final effect in the network is a reduction of time operation for
relays.
The benefits of the coordination system proposed are: fast
back-up protection, an automatic coordination process and coor-
dination that is independent of future system changes (such as
topology, generation and load).
Appendix A
In distribution systems, the relay should be coordinated with
other overcurrent protectiondevices,such as fuses and reclosers.In this section, the fitting program was evaluated using fuse and
recloser time curves.
A.1. Fitting fuses
The time curves of fuses are not defined in analytical form.
The values for the fitting process were obtained from time
curves using the manufacturer’s information. The precise cri-
teria are the same ones used for relays and are composed
of 10 current–time data sets. For fuses, there is no critical
region for curve fitting; the whole current range is considered,
and the shape of the time curve has more variety than doesrelays.
Fig. A1 shows the graphical output results of the fitting pro-
gram during cycles of error ( E r). For the four fuses selected,
the fitting result was deficient. Table A1 shows the statisti-
cal fitting output errors of the fitting program. The statisti-
cal indicators (the bold numbers) indicate the best fit. The
statistical indicators [7] were: sum of error squares S ; mean
error E MED; maximum error E MAX; and standard deviation of
errors σ .
The two exponential equations used in this paper have, in
general,poorresults,asthefusetimecurvesaresodifferenttothe
relay time curves. On the other hand, the polynomial equations
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Fig. A2. Fitting results of commercial fuses using the H ( I k ) function.
Table A2 shows the statistical fitting output errors. The expo-
nential equations have, in general, good results in comparison
to the results obtained when the T ( I k ) function was used. How-
ever, the polynomial equation (4) [7] is the best model for
obtaining a good fit for fuses for the sample selected in this
paper.
A.2. Fitting reclosers
Fig. A3 shows the output results. For three reclosers, the
selected fitting result was good because the time curve is similar
to relaying.Table A3 shows the statistical indicatorsof the output
results of the fitting program.
Table A2
Data output fitting program using the H ( I k ) function
Fuse T = AI n−1 + B [10] T = C+
K
(I −h+wI −2I )q − b
I
50
n[8]
S E MED E MAX σ S E MED E MAX σ
Exponential
1 0.0 0.0 1.84 1.61 0.6 0.59 9.39 5.5
2 39.6 −0.004 31.14 28.1 971 −49.9 171.9 Inf
3 0.68 0.0 0.41 0.37 32.5 −1.25 3.22 4.03
4 0.01 0.0 0.075 0.05 0.015 0.0 0.068 0.087
Fuse logT = A0 + A1log I +
A2
(log I )2 + · · · [7] T = A0 + A1I −1 +
A2
(I −1)2 + · · · [7]
S E MED E MAX σ S E MED E MAX σ
Polynomial
1 8.8e13 −7.2e6 7.2e7 2.4e7 0.0 0.0 1.712 0.8
2 8.3e7 −8.8e3 7.0e4 2.6e4 1.48 0.0 6.33 3.5
3 6e6 −254 2e3 848 0.0 0.0 0.05 0.02
4 1e31 −3e14 3e15 1e15 0.0 0.0 0.0 0.001
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Fig. A3. Fitting results of commercial reclosers.
Table A3
Data output fitting program equations using the T ( I k ) function
Recloser T = AI n−1 +
B [10] T = C+ K
(I −h+wI −2I )q − b
I
50
n[8]
S E MED E MAX σ S E MED E MAX σ
Exponential
1 000 000 000 000 0.129 −0.131 0.149 0.254
2 000 000 0.005 0.003 000 000 0.002 0.002
3 90.11 000 7.83 4.245 0.031 000 0.091 0.124
Recloser logT = A0 + A1log I +
A2
(log I )2 + · · · [7] T = A0 + A1I −1 +
A2
(I −1)2 + · · · [7]
S E MED E MAX σ S E MED E MAX σ
Polynomial
1 337 −7.98 8.673 8.209 25.60 −2.236 1.791 1.91
2 000 000 0.001 0.001 000 000 0.001 0.001
3 0.01 000 0.05 0.051 0.008 000 0.06 0.044
References
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[10] IEEE Std C37.112-1996, IEEE Standard Inverse-Time Characteristic
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Arturo Conde Enrıquez received the B.Sc. degree in mechanic and electric
engineering in 1993 from Universidad Veracruzana, Veracruz, Mexico. He
received the M.Sc. and Ph.D. in electric engineering in 1996 and 2002 from
de Universidad Autonoma de Nuevo Leon, Mexico. Actually he is a professor
of the same university, and he is member of the National Research System
of Mexico.
Ernesto V´ azquez Martınez received his B.Sc. in Electronic and Communica-
tions Engineering in 1988, and his M.Sc. and Ph.D. in Electrical Engineering
from the Universidad Autonoma de Nuevo Leon (UANL), Mexico, in 1991
and 1994, respectively. Since 1996 has worked as Research Professor in Elec-
trical Engineering for the UANL. He is IEEE member and he is member of
the National Research System of Mexico.