Enhanced Time Overcurrent Coordination

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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



458 A.C. Enrıquez, E.V. Martınez / Electric Power Systems Research 76 (2006) 457–465

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.



A.C. Enrıquez, E.V. Martınez / Electric Power Systems Research 76 (2006) 457–465 459

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




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.




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






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]


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




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]


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]


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

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[10] IEEE Std C37.112-1996, IEEE Standard Inverse-Time Characteristic

Equations for Overcurrent Relays, September 1996.

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.

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Enhanced Time Overcurrent Coordination