Australian Journal of Basic and Applied Sciences, 5(12): 2458-2474, 2011
ISSN 1991-8178
Comparison of Low-Impedance Restricted Earth Fault Protection in PowerTransformer Numerical Relays
1
B. Nim Taj, 1,2A. Mahmoudi, 1S. Kahourzade
1
Department of Electrical Engineering, University of Malaysia, 50603, Kuala Lumpur, Malaysia.
2
Faculty of Engineering, Help International College of Technology (HICT), Klang,
41050 Selangor, Malaysia.
Abstract: Low-impedance restricted earth fault (REF) protection protects transformer winding via
earthed star-point. This paper compares the REF algorithms of five numerical relays: ABB’s, AREVA
T&D’s, SIEMENS’s, SCHNEIDER ELECTRIC’s and GENERAL ELECTRIC’s. Investigated were
their advantages and disadvantages in speed, sensitivity, and selectivity. Also, magnetizing inrush
current, over excitation, and CT saturation impression on REF operation, are presented. Postassessment, the results were confirmed via simulation on MATLAB SIMULINK. Further investigated
were relay operation characteristic curves and restraint currents of each algorithm.
Key words: Transformer Protection, Numerical Relay, REF, Low-Impedance Restricted Earth Fault.
INTRODUCTION
Restricted earth fault (REF) protection detects earth faults in power transformers, shunt reactors, neutral
earthing transformers, reactors and rotating machines with earthed star-point (Siemens). Transformer is one of
the most important and expensive equipment in electrical power network, needing very sensitive and secure
protection. Most-common faults in a power transformer are winding and terminal faults (T and D, 2005). Most
restricted earth fault relays are based on percentage differential protection (Cordray, 1931). Importance of REF
relays surfaces when fault occurs near star point. An internal fault at star-point earthed via resistance in power
transformer has relatively low-amplitude fault current flowing from CT; it may not trigger differential
protection. For increased sensitivity in protection of power-transformer windings, another protection function
other than differential protection is thus necessary (ABB). Fig. 1 shows a protected winding’s percentage versus
its primary operating current. The graph compares the amount of protected winding in REF and differential
protection functions in terms of percentage (T and D, 2005; Iran electric distribution co., 1995; Robertson, 1982;
Horowitz and Phadke, 2008). If percentage of the rated primary operating current is 20%, the differential relay
protects nearly 45% of the winding but REF relay protects more than 78% of the winding (see Fig. 1).
Mal-operation in REF algorithms is caused by even harmonic components of magnetizing inrush current,
odd harmonic components of over-excitation, and CT saturation of severe external fault; see Section II. Five
REF relay algorithms were chosen and compared in terms of speed, selectivity, and sensitivity (Mason, 1956).
Section III presents their advantages and disadvantages. The algorithms were simulated on MATLAB
SIMULINK, Section IV showing how they differ. Section V briefs results, and concludes.
Fig. 1: Comparison of protected winding percentage between REF and differential relay (T and D, 2005).
Corresponding Author: B. Nim Taj, Department of Electrical Engineering, University of Malaysia, 50603, Koula Lumpur,
Malaysia.
E-mail: babak.nimtaj@gmail.com
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Mal-Operation:
Magnetizing inrush current, over-excitation, and CT saturation are possible causes for mal-operation in
REF relays (ABB; Horowitz and Phadke, 2008; IEEE, 2008; Guzman et al., 2004). REF relay could actually
operate in those conditions despite no fault. Their distinction and fault conditions are important to REF
algorithm.
Inrush Current:
If a transformer’s primary winding is connected to source, and its secondary winding connected to load,
magnetizing inrush current flows from supply to primary winding while there is no current or while much less
load current flows out from the secondary winding (IEEE, 2008). Magnetizing inrush current occurs when
residual flux polarity is opposite to polarity of ideal instantaneous value of steady-state flux (IEEE, 2008;
Guzman et al., 2004; Sonnemann et al., 1958). Fig. 2 shows a typical inrush current waveform obtained from
simulation in MATLAB.
Main characteristics of inrush current (Guzman et al., 2004):
1) It generally contains DC offset, odd, and even harmonics.
2) It typically comprises unipolar or bipolar pulses, separated by intervals of very low current values.
3) Peak value of unipolar inrush current decreases very slowly, the time constant much greater than DC offset
of fault-decay time.
4) Second harmonic constant starts at low values and increases as inrush current decreases.
5) If relay CTs are linked by delta connection.
6) DC component is subtracted.
7) Fundamental component is added at 60°.
8) Second harmonic is added at 120°.
9) 3rd harmonic is added at 180°, i.e., canceled.
Considerable-magnitude even harmonic components (especially second harmonic) thus result from inrush
current. Factors influencing magnitude and duration of inrush current (Kasztenny and Khulidjian, 2000):
 Transformer size.
 System impedance from transformer’s source side.
 Core material.
 Core’s remnant flux.
 Order of energizing of primary and secondary windings.
 Transformer’s switched-in wave-point.
Fig. 2: Typical magnetizing inrush current waveform.
Various methods distinguish between fault current and magnetizing inrush current; wavelet transform (Mao
and Aggarwal, 2000; Youssef, 2002; Mao and Aggarwal, 2001; Faiz and Lotif-Fard, 2006; Eissa, 2005),
improved Fourier series (Jiandong et al., 2009), artificial neural network (Perez et al., 1994; Pihler et al., 1997;
Zaman and Rahman, 1998; Orille-Fernandez et al., 2001; Şengül et al., 2009), fuzzy logic (Wiszniewski and
Kasztenny, 1995; Ferrero et al., 1995; Kasztenny et al., 1997), technique based on equivalent instantaneous
inductance (Inagaki et al., 1988; Sachdev et al., 1989; Baoming et al., 2005 Da-qiang et al., 2005), S-transform
(Samantaray et al., 2007), waveform analysis (IEEE, 2008; Guzman et al., 2004; Kasztenny and Khuldijian,
2000; Mekic et al., 2006; Phadke and Thorp, 1983; Verma, 1990; Murty and Smolinsiki, 1990; Rahman and
Jeyasurya, 1988; Atabekov, 1960; Rockefeller, 1969; Wilkinson, 1997), harmonic restraint and blocking (IEEE,
2008; Guzman et al., 2004; Kasztenny and Khuldijian, 2000; Sharp and Glassburn, 1958; Einvall and Linders,
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1980). Waveform analysis, and harmonic restraint and blocking, are the most common methods used (IEEE,
2008; Guzman et al., 2004) they are the methods used in protection devices for prevention of mal-operation.
The conventional way to distinguish fault current from inrush current is based on the principles of second
harmonic and dead angle (both influencing factors such as CT saturation) (IEEE, 2008; Guzman et al., 2004;
Kasztenny and Khuldijian, 2000; Jiandong et al., 2009; Babak.NimTaj, 2010).
Over-Excitation:
A transformer core’s magnetic flux is directly proportional to the supply voltage and inversely proportional
to system frequency. Over-voltage or under-frequency can produce flux in a transformer core, saturating
transformer, causing thermal damage. Under-frequency happens when system generators are cut out or overload occurs, and generators cannot recover and feed all loads. Over-voltage happens when loads cut the system
out or when a part of the system is separated by disturbance (IEEE, 2008; Guzman et al., 2004; Einvall and
Linders, 1975; Nutt).
Damnjanovic and Parsley and Huang et al., (2002) state that as excitation current is an odd function,
Fourier series thus contains odd components in period T/2. Over-excitation current hence contains odd harmonic
components. The 3rd harmonic is eliminated through CT with delta connection, so, Odd harmonics start from the
5th harmonic component, with the highest magnitude.
CT Saturation:
Severe external fault may cause CT saturation, whose main characteristics are:
 Momentary reproduction of spurious current upon inception of fault (Time-To-Saturation, 2006).
 (For severe CT saturation) secondary current’s content of DC offset, even and odd harmonic components
(Hayward, 1941; Wentz and Sonnemann, 1940).
Restraining components at CT saturation should be calculated in initial states, before saturation. While fault
current decays, restraint signal should be increased even if CT saturation produces lower restraint current
(Ziegler, 2005).
Restricted Earth Fault (REF):
Investigation results for restricted earth fault algorithms of five relays (Siemens’s, GE’s, ABB’s, AREVA
T&D’s, and Schneider Electric’s) are presented here.
Siemens:
Siemens’s 7UT613 relay manual was chosen for investigation of Siemens’s REF algorithm (Siemens). Starpoint current (IN) is the current flowing at star-point CT. Residual current is defined as summation of threephase currents (3I0). In normal condition, IN is zero, residual current (3I0) almost zero. Fault location (inside or
outside the protection zone) matters; current flowing into protected zone is designated positive-direction, and
current flowing outside the zone is designated negative-direction. If fault occurs in protected zone, residual
current will be more or less in-phase with star-point current. Whether fault occurs inside or outside protected
zone, star-point current remains. Conversely, if fault occurs outside protected zone, residual current polarity is
opposite-direction to star-point current. Figs. 3a and 3b show the current directions (Siemens; Siemens, 2008).
a-Earth fault inside the protected zone
b-Earth fault outside the protected zone
Fig. 3: Earth-fault current directions (Siemens; Siemens, 2008).
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Siemens’s REF algorithm compares the fundamental component of star-point current (3I'N) with
fundamental component of three-phase current summation (residual current) designated 3I''0. Tripping
command, called trip-effect current, is issued by 3I'N.
I REF  3I' N
(1)
If trip-effect current had exceeded restraining current or stabilization current, the relay sends operation
command. The restraining current is obtained from:
I REST  k.( 3I ' N 3I"0  3I ' N 3I"0 )
(2)
Where k is stabilization factor, its value depending on limit angle. Fig. 4 shows how k and limit angle relate
in polar plane. The limit angle is between zero degree for internal fault and 180 degrees for external fault.
The Siemens algorithm is based on vector summation; phase displacement between star-point current and
residual current is thus extremely important for correct relay operation. CT saturation can change phase
displacement between residual current and star-point current. The phase-shifting can reduce restraint current,
and consequently, the relay’s mal-operation. If phase displacement (  ) is 90 degrees, restraint current is then
zero. Phase shifting also can cause relay to operate at external earth fault. Fig. 5 is vector summation of residual
current and star-point current, from which restraint current can be calculated. It shows the phase displacement
(due to CT saturation) between residual current and star-point current; the restraint current is less than the
tripping effect current, so the relay operates during external fault.
Fig. 4: Stabilization factor variation against limit angle in polar plane (Ziegler, 2005).
 3I"0
 3I"0
I REST
3I'N
3I'N 3I"0
3I'N3I"0
Fig. 5: Phasor diagram for Siemens algorithm during external fault (Siemens).
Siemens relay uses separate filters for magnetizing inrush current and over-excitation (even, and odd,
harmonic-component filters). It is network-flexible, highly secure and selective (as shown by its various slopes
and characteristic graph), and is based on vector summation of currents (so operation is extremely highly
secure). Its disadvantage is the time-delay used for tripping. The time delay is for fault analysis, and does not
inherit the time delay of each process, but still, affects relay speed.
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ABB:
ABB REF algorithm is also based on vector direction of star-point and residual current. ABB’s RET 670
relay manual was investigated (ABB). Firstly, the zero sequence fundamental frequency of the input currents
was extracted. Other, zero-sequence components (such as 3rd harmonics) were thus suppressed. Residual-current
phasor was then added by vector, to star-point current. Fig. 6 shows vector summation of the residual current
and the star-point current when a fault happens outside the protected zone. Fig. 7 shows the internal earth fault,
a vector summation of star-point current and residual current. At external earth fault, the star-point current and
residual current have almost equal magnitudes but are 180 degrees out of phase. At internal earth fault, direction
of the star-point current and of the residual current almost equal. The differential current, as a phasor of the
fundamental frequency, is obtained from:
Idiff = IN + 3I0
(3)
Bias current is obtained from:
I  3I 0
I bias  N
2
(4)
From bias-current definition, if differential current exceeds bias current, relay operates, else, it does not.
REF algorithm for ABB RET670 relay’s technical reference manual states If star-point current (IN) is less than
50% of minimum base-sensitivity current (Idmin), service values only are calculated; exit REF protection (see
Table I); if star-point current exceeds 50% of Idmin, bias current is determined. The operating current or the
differential current is determined, and is calculated magnitude of the differential current. If Ibias and Idiff points
are at relay-operation characteristic curve inside operating area, set to 1, the trip counter, else, reset it to 0; if
trip-request counter is 0, search for heavy external earth fault.
If star-point current is at least 50% of bias current, external earth fault happens; flag sets until external earth
fault had been cleared (external earth fault flag resets if star-point current decreases less than 50% of base
sensitivity current (Idmin), any search for external fault is canceled if trip counter changes to 1). Upon an external
fault, REF desensitizes, so additional temporary trip is needed. If Idiff and Ibias are inside operating area, trip
request exceeds 0; make directional check if residual current exceeds 3% of bias current; if directional cannot be
executed, direction is no condition for tripping.
Ratio of 2nd harmonic to fundamental is calculated; if value exceeds 60%, trip-request counter is zero; if
trip-request counter equals 2 or exceeds 2, and bias current is at least 50% of highest bias current or Ibiasmax
(measured during disturbance), REF function block sets to 1 the output TRIP, else, TRIP signal is 0.
I N  3I zs1
3I 0  3I zs1
Fig. 6: Currents at an external earth fault.
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Aust. J. Basic & Appl. Sci., 5(12): 2458-2474, 2011
I N  3 I zs1
IN
3I 0  3I zs1
Fig. 7: Currents at an internal earth fault.
Like the Siemens relay, ABB relay operates on vector comparison. In Figs. 6 and 7, both CTs are assumed
to be the same (in CT class and ratio). In both internal and external earth faults, two ways exist for circulating
current: current flows toward star point and system (see Figs. 6 and 7). In external fault, IN and 3I0 have equal
magnitudes and 180 degrees phase displacement. In internal fault, IN and 3I0 are in almost the same direction.
The method distinguishing internal fault from external fault is called directional check. The relay operates on
fundamental zero sequence. The currents thus are the fundamental frequency of the zero sequence. Relay
Operating Angle (ROA), usually selected between 60 and 90 degrees, is an interval between two determined
angles. If it had been selected smaller, the REF can be stabilized under severe external faults (ABB).
Fig. 8 shows the ABB relay’s operation characteristic, with various sensitivities that users can configure. It
also reveals that the relay is dual slope. Slope 1 is in Zone 2, Slope 2 after Zone 2. Bias current from 0 till
1.25p.u determines Zone 1. Currents 1.25p.u to 2.5p.u determine Zone 2. Fig. 8 shows the operating area and the
restraining area. Changes to them are based on the sensitivity selected.
ABB relay filters all harmonic components; only fundamental frequency component for mathematical
equation is used. REF is insensitive to inrush current and over-excitation current but sensitive to CT saturation
(ABB). As mentioned, though, inrush current and over-excitation current are the most important reasons behind
REF relay’s mal-operation.
Fig. 8: ABB operation characteristic curve (ABB).
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Table 1: ABB REF’s Bias Characteristics.
Default sensitivity Idmin (zone1)
Maximum base sensitivity Idmax (zone1)
Minimum base sensitivity Idmin (zone1)
End of zone 1
First slope
Second slope
%Inom
%Inom
%Inom
%Inom
%slope
%slope
30
4
100
125
70
100
Table I extracted from Fig. 8 shows the various selectable sensitivities. The maximum and the minimum are
4% and 100% respectively, of nominal phase current. Fig. 10 shows Table I illustrating the boundary of each
zone, and the first and the second slopes of the relay operation characteristic. Like Siemens’ this relay needs
filters; one filter operating wrongly causes mal-operation, yet it is fast enough as parts of the relay operate
independently. It operates according to the fundamental frequency of the zero sequence; a condition such as CT
saturation in severe external earth fault, producing spurious zero sequence, causes mal-operation. Also, at
external earth fault, the relay is desensitized (see relay-operation diagram). An internal earth fault resulting from
severe external earth fault thus causes the relay to not operate though it should.
General Electric (GE):
GE’s 345 transformer protection system was chosen (Multilin, 2010). To avoid mal-operation of the
restricted earth-fault protection, GE algorithm defines restraining current with high sensitivity in internal faults.
The differential current or operating current is obtained from (Kasztenny and Khulidjian, 2000; Kasztenny,
2006; Kasztenny et al., 2004):
I diff  I N  3I 0  I N  I A  I B  I C
(5)
Stability and selectivity of the REF algorithm depends on the method for producing restraint current. In GE
algorithm, symmetrical component is used to produce restraint current for various fault types. During external
fault and to avoid mal-operation, maximum restraint current is needed. Intermediate restraint current is
calculated from:
I R _ aux  max( I R 0 , I R1 , I R 2 )
(6)
Zero sequence restraint (IR0) is vectorial difference between ground and residual current. It is calculated
from:
I R 0  I N  3I 0  I N  (I A  I B  I C )
(7)
Negative sequence restraint current is created as:
IR2 = 3. |I2| or IR2 = |I2|
(8)
Positive sequence restraint is created as follows:

 I1  1.5p.u (CT phase current )

I1  I 0
 I R1  3.( I1  I 0 )
(9)

I1  I 0
 I R1  0

 I R1  1 I1
else

8
At equation 8, multiplier of 3 is usually used, but in phenomena such as inrush current, multiplier of 1 is
used. Equation 8’s undesirable effect can be avoided by use of a filter (see Fig. 9).
Fig. 9: Logic controlling negative restraint.
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Either multipliers 1/8 at positive sequence, or 1 at negative sequence of restraint current, is used, as
spurious components may appear at transient conditions (Kasztenny et al.,). Exponentially decaying effective
restraint current (IR(k)) is obtained from maximum magnitude between IR_aux at tL and IR_aux at t(L-1) multiplied by
decaying factor (A):
IR(k) = max(|IR_aux,t(L)| , A. |IR,t(L-1)|)
(10)
In this algorithm, 0.5 is chosen for A, which decays 50 percent in about 15 power cycles. Equation 10
shows that in CT saturation, restraint current’s calculation is based on initial condition (before CT saturation).
While fault current decays, restraint current increases even as CT saturation produces lower restraint current
(owing to exponential decaying) (Kasztenny and Khulidjian, 2000; Kasztenny, 2006; Kasztenny et al., 2004).
GE algorithm is rather secure for magnetizing of inrush current, over-excitation, and CT saturation. Its
uniqueness as REF protection algorithm is its use of symmetrical components to produce restraint current. It
does not need complicated filters to define conditions such as magnetizing inrush current. In some conditions,
though, spurious zero and negative components are produced, causing mal-operation. The algorithm thus
operates on symmetrical components. For better sensitivity and better selectivity, extra algorithm is needed, for
filtering the spurious components and distinguishing between fault and false conditions.
Areva T&D:
Tan and Wai, 2007 and Alestom, 2003 investigated characteristics of two slopes and single slope operation.
The most common REF algorithm is dual-slope operation characteristic; see Fig. 10. (Tan and Wai, 2007)
mentions that the previous differential current is vector summation of all measured residual and star-point
current.
Idiff = |max (IA , IB , IC) + IN|
(11)
Bias current is half the scalar summation of maximum phase currents and star-point current.
1
I bias  max(I A , I B , I C )  I N
2
(12)
Fig. 10: Dual-slope relay-operation characteristic.
The restraint current is obtained from:
I REST  m1I bias  I REF  if I bias  I bias,m 2

I REST  m 2 I bias  (m 2  m1 ).I bias,m 2  I REF 

if I bias  I bias,m 2

(13)
At some conditions, the algorithm operates falsely; it is also affected by CT saturation and inrush current
[56]. To improve it, Areva T&D suggests a new one:
Idiff = │Kamp,Y . (IA+IB+IC) + Kamp,NIN│
(14)
Ibias = Kamp,Y|IA+IB+IC|
(15)
IREST = 1.005 . Ibias + IREF>
(16)
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where amplitudes matching Kamp,N and Kamp,Y are:
K amp,N 
I nom,CT ,N
I base, N

I nom,CT ,N
S base
(17)
3Vnom
K amp,Y 
I nom,CT,Y
I base,Y

I nom,CT,Y
S base
(18)
3Vnom
and 0.5  K amp, N & K amp, Y  16
To ensure stability in unbalanced three-phase current, the coefficient of 1.005 will be multiplied. Fig. 11
shows the relevant algorithm operation characteristic curve. The slope is 1.005 and for operation, the current
flowing in star point should exceed the settable pickup value plus 0.5% in three-phase unbalancing, else, the
relay stays in the restraining area and does not operate. For operation:
I diff  I REST
(19)
In this algorithm, Equation 11 for Idiff is wrong (Tan andWai, 2007). According to IEEE standard (IEEE,
2008), definition of Idiff maximum of three-phase currents is not used to make residual current. Equation 14
should be used instead, as mentioned in previous literatures (IEEE, 2008).
Fig. 11: Improved AREVA REF operation characteristic curve.
Conventional algorithm for restricted earth fault protection is subjected by CT saturation with high DC
external earth fault (Tan and Wai, 2007). AREVA algorithm, like Siemens’ and ABB’s, also needs separate
filters, for CT saturation condition. Also, when one slope characteristic had been chosen, differential current
exceeds pickup current, and restraint current is low, the relay does not operate (see (*) in Fig. 10). The algorithm
thus has selectivity issues. Also, from beginning until end of Zone One in the relay’s characteristic curve, the
slope is chosen to be extremely lower than one. The condition is used for the relay’s increased selectivity and
sensitivity in an internal fault. Contrarily, in the algorithm, the slope exceeds one, i.e., 1.05, thus severely
decaying selectivity and sensitivity.
Schneider Electric:
The Schneider protection relay is called SEPAM. The 87T relay manual was chosen to investigate
Schneider Electric REF algorithm (Electric, 2009). Differential current is defined as (Bertrand et al., 2011):
Idiff = Ia+Ib+Ic+IN
(20)
The restraint current is obtained from:
IREST = Ia+Ib+Ic
(21)
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With the assumptions, phase currents are positive when flowing to the transformer and star-point current is
positive when flowing to ground. The relay operates when:
Idiff exceeds IREF > (5% to 50% of transformer’s rated current)
Idiff/IREST exceeds 1.05
Fig. 12 shows SEPAM Schneider relay’s operating and restraining area. If REF protection is on
transformer’s primary side, stability during energizing of transformer must be ensured. The DC component of
the inrush current saturates phase CT, creating false differential current. As current does not flow through the
star point, IREST=Idiff and the SEPAM REF protection remains stable (no tripping). If REF protection is on
transformer’s secondary winding, when a three-phase fault occurs outside the protected zone, the phase CTs
may saturate (as seen in IREST=Idiff) and the protection’s stability is ensured (Bertrand et al., 2011).
Fig. 12: SEPAM REF operation characteristic curve.
In an external fault, the restraint current is increased (see below) to ensure stability of the REF relay.
IREST(external fault) = Ia+Ib+Ic+IN/3
(22)
With this definition of restraint current, though, the relay operates wrongly at magnetizing inrush current,
over-excitation, and CT saturation, as it does not use any calculating diagram to avoid odd or even harmonics. It
also has no scheme for phase shifting at CT saturation. Also, the algorithm has two limitations (Bertrand et al.,
2011). Without earthed star point and in internal earth fault, REF does not operate. REF theory is applicable
only when star point is connected to earth; without earthed star point, the protection function is insensitive. A
second limitation is when the star point is earthed with neutral coil. The star point current is lower than the exact
value of the fault current, but correct choice of star point CT solves the problem.
Equations 21 and 22 show different restraint currents for internal and external earth faults. Internal and
external earth faults should be clarified by restricted earth fault algorithm. The algorithm has two restraint
currents, thus the relay is very low selectivity. The relay characteristic curve shows the algorithm has fixed slope
(1.05) for correct operation under saturated CT, but the fixed slope decreases relay sensitivity and selectivity.
Table II shows brief comparison of five presented REF algorithms which were investigated based on speed,
sensitivity and selectivity.
Table 2: Advantage and Disadvantage of Presented Algorithms.
Relay Manufacturer
Advantage
Siemens
Good in selectivity and sensitivity
ABB
Good in selectivity and sensitivity
General Electric
Good in selectivity and sensitivity
Areva T&D
Schneider Electric
Good in speed and selectivity
--
Disadvantage
Speed problem
Need more filter for spurious zero sequence
Calculating time
Sensitivity problem (according to relay operation
characteristic curve)
Sensitivity and selectivity problem
Case Study:
Matlab Simulink was used to show operation characteristic curves and restraint currents of the five relays
compared. To simplify the problem enough for simulation, these assumptions were made:
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1)
2)
3)
4)
5)
In the first step, the transformer is not energized
To show the inrush current, C.B, is closed after 2 cycles
Two-phase short circuit occurs after 9 cycles
Fault is cleared after 12 cycles, by relay trip command
In all simulations, the main relay is joined with the lock-out relay.
Fig. 13: System sample (E.S. Co).
All the algorithms presented were simulated on Matlab Simulink. Fig. 13 is single-line diagram of the
power transformer installed at MSDS3 substation of Esfahan Steel Co. and chosen for simulation.
Siemens Algorithm Simulation:
Fig. 14 shows the restraining current calculated from Equation 2. It shows that before switching, restraint
current was zero. While C.B. was connecting, and before fault had occurred, the restraint current had been
positive, proving that the relay stays stable at inrush current, no mal-operation. After short-circuit had occurred,
the restraint current suddenly changed to negative, and the relay operated. The restraint current then changes
abruptly.
Fig. 15 shows Siemens’ relay operation characteristic curve. The curve indicates star-point current (IN)
variation against summation of phases, and star-point current amplitudes(∑│I│ = │3I'N│+│IA│+│IB│+│IC│).
Comparing the graph with linear reference line, the curve clearly goes out of the operating area after relay had
detected the short-circuit current and sent the command trip. Before the C.B. is opened, the curve returns to the
operating area and then to (0, 0). Twice tripping during fault clearing is this relay’s disadvantage.
General Electric Algorithm Simulation:
Fig. 16 shows the restraining current of GE algorithm, calculated from Equations 6-10. Fig. 17 shows the
GE relay operation characteristic curve, the vertical axis representing differential current (Idiff) and the horizontal
axis, restraint current (IREST). When the fault occurs, the restraint current and the differential current increase,
and the curve goes to the operating area. When the fault clears, both currents decrease, the switch-off trajectory
neither causing the relay to return to the operating area nor mal-operation.
ABB Algorithm Simulation:
Figs. 18 and 19 respectively show the bias current and the relay operation characteristic curve. The bias
current is like Siemens’ restraint current, but in Siemens, during a fault, the restraint current becomes negative
(in ABB it is still positive). Fig. 19 shows the ABB relay operation characteristic curve to be the same as that of
Siemens, but worse than Siemens’ in that switching-off the curve more than once sends the relay to the
operating area and the restraining area.
Areva T&D Algorithm Simulation:
Fig. 20 shows the bias, the differential, and the restraint currents. Equation 16 shows restraint current and
bias current to be similar; with 0.5% difference in slope and peak-up current is added. When the C.B. is closed,
and magnetizing inrush current happens, the restraint current exceeds the differential current, and the relay
remains stable. When fault occurs, the differential current exceeds restraint current, and the relay operates. Fig.
21 shows Areva relay’s operation characteristic curve. The relay operation curve is shown to be located at scope
boarder. During switching-off, the curve thus probably goes to the operating area.
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Schneider Electric Algorithm Simulation:
Fig. 22 shows the differential current and the restraint current of a Schneider relay, without fault. Schneider
algorithm is shown to also operate at magnetizing inrush current; at normal condition (no fault), the differential
current is larger than the restraint current. Figs. 23 and 24 respectively show the restraint current and the relay
operation characteristic curve, during a fault. Fig. 24 shows the relay always being in the operating area. At
switching-off condition, the relay remains in the operating area. Figs. 22 and 24 show the algorithm having
selectivity issues with inrush current, and the relay remaining in the operating area when command to open the
C.B. had been sent.
Fig. 14: Siemens restraining current.
Fig. 15: Siemens relay operation characteristic curve.
Fig. 16: GE restraining current
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Fig. 17: GE relay operation characteristic curve.
Fig. 18: ABB bias current.
Fig. 19: ABB relay operation characteristic curve.
Fig. 20: Areva bias, differential, and restraining current.
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Fig. 21: Areva relay operation characteristic curve.
Fig. 22: Schneider differential and restraining current, no fault.
Fig. 23: Schneider restraining current, in fault.
Fig. 24: Schneider relay operation characteristic curve.
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Conclusion:
The restricted earth fault (REF) algorithms of five numerical relays have been compared. All five operate
correctly at internal zone fault. Schneider Electric’s and Areva T&D’s have issues on increased mal-operation
percentage. In GE’s, in switching or after fault had been cleared, restraint current is first high, then decreases
exponentially to avoid mal-operation, and detect fault from CT saturation, magnetizing inrush current, and over
excitation; the algorithm is based on sequential components, and stabilizes the relay when severe fault occurs
outside zone-conditions. Siemens’s operates on vector direction of star point and residual current. It changes
restraint current abruptly in CT saturation; mal-operation is possible. Also, phase displacement between restraint
current and star-point current is important to determining the relay’s operating angle. ABB’s also operates on
vector direction of star point and residual current.
Comparing GE’s and Siemens’s, GE’s is reasonably secure at second and fifth harmonic currents but needs
detailed mathematical calculations to advise operation command, i.e., for increased relay calculation speed, a
more-powerful processor is needed. Siemens’s mathematical calculation is simple, so calculation time and
creation of operating command is considerably less than that of GE’s. Its weakness is the extra filters it needs
for the second and the fifth harmonic currents during magnetizing inrush current and over-excitation.
Simulation result show that upon a fault, GE relay’s operation characteristic curve enters operating area
once, and returns to restraining area after fault clears. Siemens’s does this, too, but, after going to the restraining
area, it returns to the operating area. The problem is solved via a lock-out mechanism.
Nomenclature:
IN
3I0
IREF
IREST
K
IREF>

Idiff
Ibias
Id
ROA
IR_aux
IR0
IR1
IR2
I0
I1
I2
tL
t(L-1)
A
m1
m2
Ibias, m2
3I'N
3I''0
T
Kamp,N
Kamp,Y
Inom,CT,N
Inom,CT,Y
Sbase
Vnom
Inom
Star point current
Residual current (summation of three phase)
Trip effect current
Restraining current
Stabilization factor
Pickup current
Limit angle
Differential current
Bias current
Base sensitivity current
Relay operating angle
Intermediate restraint current
Auxiliary zero sequence restraint current
Auxiliary positive sequence restraint current
Auxiliary negative sequence restraint current
Zero sequence current
Positive sequence current
Negative sequence current
L thtime constant
(L-1)th time constant
Decaying factor which A<1
First slope of relay operation characteristic curve
Second slope of relay operation characteristic curve
Knee point of relay operation curve
Fundamental component of star point current
Fundamental component of residual current
Duration cycle
Star point current amplitude matching constant
Residual current amplitude matching constant
Nominal current of star point CT
Nominal current of residual CTs
Apparent power
Nominal voltage
Phase nominal current
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