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Engineering, Technology & Applied Science Research Vol. 9, No. 4, 2019, 4342-4348 4342

www.etasr.com Le & Vu: Performance Evaluation of a Generator Differential Protection Function for a Numerical Relay

Performance Evaluation of a Generator Differential

Protection Function for a Numerical Relay

Kim Hung Le

The University of Danang - University of Science and
Technology

Da Nang, Vietnam

lekimhung@dut.udn.vn

Phan Huan Vu

Central Power Corporation - Central Electrical Testing
Company Limited
Da Nang, Vietnam

vuphanhuan@gmail.com

Abstract-This paper describes the advantages and disadvantages

of a generator differential protection relay system which uses

double slope characteristics of Areva P343, ABB REG670,

SEL300G and GE G60. A Buon Tua Srah Hydropower Plant in

Vietnam was selected as an example for the relay setting

calculations of these characteristics. The performance of the

introduced relay model was tested at various fault conditions in

Matlab/Simulink. The results apply to the problems of solving the

performance of the relay accurately and with reliable differential
protection against internal faults, and keeping the generator

stable on all external faults and in normal conditions. The

simulation simplifies the process of selecting the relay and

protection system. This can improve the quality of the protection

system design early, thereby reducing the number of errors
found later in the operation.

Keywords-generator; differential protection function; slope 1;

slope 2; Matlab/Simulink

I. INTRODUCTION

The synchronous generator is the most important element
of a power system. Generator faults are considered serious
since they may cause severe and costly damages to insulation,
windings, and stator core. The large short circuit currents cause
large current forces, which can damage other components in
the power plant, such as the turbine and the generator-turbine
shaft, or even initiate explosion and fire. In addition, if the
generator is tripped in connection to an external short circuit, it
can give an increased risk of power system collapse. To limit
the damages in connection to a stator winding short circuits and
abnormal operating conditions, generators need to be protected
as much as possible by a proper protection system [1].
Nowadays, there are a variety of numerical different protective
relays on the market which include many functions in one unit,
and provide metering, communication, and generator
protection. These protective relays help us to simplify the
protection implementation in circuit design and setting
calculations. Although there is quite an agreement among
protection engineers as to what constitutes the necessary
protection and how to provide it, there are still many
differences of opinion in certain areas. As protection system
complexity increases with IEDs connected to the hydropower
plant, the evaluation of effective protection relay becomes a

need for well-designed algorithms that can allow or deny
arranged trip of generator, field circuit, and neutral breakers (if
used) through a lockout relay based on decisions, to enable
fault isolation. Among them, generator differential protection
function (F87G) is one of the most critical protection
applications. It is mainly employed for the protection of stator
windings of generator against earth faults and phase-to-phase
faults. It is also of great importance that the F87G does not trip
for external faults when the large fault current is fed from the
generator. The need to evaluate F87G with individual different
characteristics has been well known to generator protection
engineers. The techniques, methods and practices to provide
this coordination are well established but scattered in various
textbooks, papers, and in manufacturer’s user manuals [2].

Author in [1] evaluated the performance of the F87G of the
SEL 300G generator protection relay which was employed to
protect the particular low resistance grounded 555MVA
generator represented in the real-time simulation model of the
RSCAD generic software. Authors in [3] considered the F87G
and simulated this function using Simulink. Authors in [4]
described the effects of damages in secondary circuits and the
influence on disoperation of differential protection Micom
P633 of the unit generator–transformer in Simulink. Authors in
[5] conducted performance evaluation of the F87G by using a
dynamic model of ATP/EMTP software for a large steam
turbine synchronous generator. Authors in [6] used ATP-
EMTP package to simulate and generate fault data which were
processed in Matlab to implement relay logic for detecting
internal faults in the stator windings of F87G. Authors in [7]
used an ANFIS algorithm in Simulink to design a F87G. The
technical manuals of Schneider P343, ABB REG670,
SEL300G and GE G60 relay protections are in [9, 11, 14, 15]
respectively. The works on detailed settings guidance [10, 12,
13, 16] allow protective relaying engineers to have a clear
understanding of which methods are available on every relay
protection, what input parameters are required for each method
and the expected results of each. In practice, the worst
condition of unbalanced secondary currents is realized when
the current transformer (CT) in the faulted circuit is completely
saturated and none of the other CTs suffers a reduction in ratio.
It is a universal differential protection problem for an unwanted
trip of the generator [8]. Besides, there is a possibility that

Corresponding author: Phan Huan Vu

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www.etasr.com Le & Vu: Performance Evaluation of a Generator Differential Protection Function for a Numerical Relay

someone with unauthorized access might infiltrate the relay and
reconfigure incorrect settings instructing it to release a false trip
signal without the existence of a fault. When these types of
misoperation risks go undetected, it is very easy for operators
to mistakenly believe that their relay protection is secure.
Hence, the question that operators need to ask is: “How
confident am I that my relay protection is reliable and secure?”.
Therefore, the purpose of this paper is to provide a single
document that can be used to calculate relay setting parameters
with multi-vendors, to answer the most frequently asked
questions about F87G considering the Buon Tua Srah
Hydropower Plant in Vietnam. In addition, a Matlab/Simulink
model to check four generator differential characteristics to the
plant will be checked while simulating fault cases. It will equip
the reader with the knowledge to choose the most suitable
vendor for his or her project.

II. GENERATOR DIFFERENTIAL PROTECTION FUNCTION

This section shows how an F87G characteristic is
constructed and how it works. Selection rules for setting
parameters are discussed. As an example, Figure 1 illustrates
the schematic diagram for the implementation of the main
generator protection of a Buon Tua Srah Hydropower Plant.
Line side CTs and neutral side CTs are both ends of the stator
winding which are wye-connected. The F87G relies on
measurements of the currents of the protected generator in
order to calculate differential and biased currents which are
then utilized to make tripping decisions. On low-impedance
grounded machines, this scheme can detect phase-to-phase,
phase-to-ground, and three-phase faults. Equations (1) and (2)
show the mathematical definition of the differential and biased
currents, respectively, which are employed by various vendors
such as Schneider, ABB, SEL, and GE.

Fig. 1. Differential protection relay connection with a generator.

The differential current: ||
_

1 III DIFF += (1)

The biased current:
2

||||
_

II
I

BIAS

+
= (2)

Based on these values of IBIAS and of IDIFF, the trip/restrain
characteristics are applied in the vendors of protection relay
which has a three-step shape (two slopes and one pickup level)
as in Figure 2. The differential current pickup setting (IS1, Idmin,
87OP, Pickup) should avoid the maximum unbalance current
under normal load condition which is mainly caused by CT
error, the normal current error (KCT_ERR) must be less than 5%
the operating current for the 5P20 type CT, and we should

multiply by a reliable coefficient KREL that is normally equal to
1.5. This setting can be set as low as 5% of the rated generator
current, to provide protection for as much of the winding as
possible [10].

Fig. 2. Differential protection characteristics

Slope1 setting (K1, SlopeSection2, SLP1, and Slope1) is set
to ensure sensitivity to internal faults at normal operating
current levels. The criterion for setting this slope is to allow
maximum expected CT mismatch error when operating at
maximum permitted current. In this case, it combines the
KCT_ERR. The relay pickup accuracy (KRELAY_ERR) can be
obtained from the instruction manual of the relay, and an
operating margin (KMARGIN) of 5% is typically provided in order
to increase the security of the differential protection scheme
[13]. The purpose of the Slope2 setting (K2, SlopeSection3,
SLP2, Slope2) is to increase the security of the differential
protection scheme during heavy through-fault conditions. It can
result in severe saturation of a CT. When a CT saturates, it can no
longer trustworthy reproduce the primary current with a scale
factor on the secondary side of the CT. As a result, a very high
differential current may be obtained under this fault condition.
The Slope2 setting is typically set higher than the Slope1 setting.
Relay setting calculation is an important task for a power plant
before operating. The parameter in this calculation is used for
the setting of the relay protection equipment of the power plant.
Choosing the slope of a differential relay has been more art
than science. Manufacturer’s guidelines tend to be qualitative
or empirical in nature. They are based on the manufacturer’s
experience and knowledge of his/her design [9], as shown in
the above F87G using trip/restrain characteristics. We can
calculate detailed adjustable settings by using the generator
parameters as in Table I [10].

A. Schneider P343 [11, 12]

Is1 is calculated to avoid maximum unbalance under
normal load and the K1 should be 0% to assure the sensitive
under normal operating current.

. .
1

1.5 (2 0.05) 2116.5
0.127,

2500

REL ERR CT G N
S

K K I
I

× × × × ×
= = =

so, 0.2A is proper.

IBIAS

Slope2
IDIFF

Pickup

Slope1

Break1 Break2

(d). GE G60

IRT
Slope1

Slope2

IOP

O87P

IRS1

U87P

(c). SEL 300G

Zone3

Slope

Section2

Slope

Section3

IDIFF

IBIAS

Idmin

EndSection1 EndSection2

Zone1

Zone2

(b). ABB REG670

IBIAS

IDIFF

IS1
K1

IS2

(a). Areva P343

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The Is2 should be the same with CT rating current or
generator’s 120% nominal current. CT rating current is 2500A,
so Is2=2500A, the secondary value is Is2=1A. The K2 is
normally to avoid external max unbalance current under max
throughout fault near protection zone. This max unbalance
current can be calculated according to:

IUnb.Max=KREL×KAP×KCC× KERR.CT×I
(3)

Max (3)

where the external three phase short circuit current is:

(3) .

2116.5
4.045

0.2093 2500

G N
Max

I
I

X CT
= = =

××
. The CT type factor KCC

should be 0.5 when same type CT for each side, or be 1 when
different type CT for each side. In this paper, we select 0.5.

The non-periodic factor is KAP=1.5~2.0. In this paper, we
select 2.0. So: IUnb.Max=1.5×2×0.5×0.1×4.045=0.6068.

According to the equation:

. 1

(3)
2

0.6068 0.2
2 0.1336

4.045 1

Unb Max S

Max S

I I
K

I I

− −
= = =

−−
, we suggest

selecting K2=0.2. The F87G operates when IDIFF exceeds Is1
and the percentage of IBIAS, defined by a slope setting (K1, K2).
It can be calculated using the following:

IDIFF>K1×IBIAS+IS1 where IBIAS ≤IS2

IDIFF >K2×IBIAS–(K2−K1)×IS2 +IS1 where IBIAS>IS1

TABLE I. PARAMETERS OF BUON TUA SRAH HYDROPOWER PLANT

Parameters Values

Rated capacity 50.6 MVA

Normal Current IG.N 2116.5A

Rated Voltage 13.8kV

Frequency 50Hz

PT ratio of the terminal of the

generator

13.8 0.11 0.11
0.11

3 3 3
Line CT ratio 2500/1

Neutral CT ratio 2500/1

Rated current secondly 0.8466A

Synchronous reactance Xd 99.28%

Transient reactance X’d 28.27%

Sub Transient reactance X’’d 20.93%

Synchronous reactance Xq 62.88%

Negative reactance X2 23.60%

Static negative current I2∞ 250A

Transient negative current I
2
2t 40s

KRELAY_ERR
SEL300G is 2%, G60 is 1%,

P434 is 5%, and REG670 is 2%

B. ABB REG670 [9, 10]

The pick-up value (Idmin) is:

. .
min

1.5 (2 0.05) 2116.5
0.127

2500

REL ERR CT G N
d

K K I
I

× × × × ×
= = =

We set Idmin=0.2IG.N.

In Section1, the risk of false differential current is very low.
This is the case, EndSection 1 is set to experience value:

.
0.5 0.5 2116.5

Sec 1 0.4233
2500

G N
I

End tion
CT

× ×
= = =

A SlopeSection2 is proposed to be set to 30%. Breakpoint 2
set to experience value:

.
3 3 2116.5

Sec 2 2.5398
2500

G N
I

End tion
CT

× ×
= = =

SlopeSection3=80%. It is supposed to cope with false
differential currents related to current transformer saturation.
The F87G operates when IDIFF exceeds a threshold Idmin and a
percentage of IBIAS:

( )2 1
when 1 2

DIFF dmin BIAS

BIAS

I I SlopeSection I EndSection

Endsection I EndSection

> + × −

≤ ≤

 
 

( )
( )

2 2 S 1

3 2 ]

when 2

[
DIFF dmin

BIAS

I I SlopeSection EndSection End ection

SlopeSection I EndSection

I EndSection

> + × −

+ × −

≥

C. SEL300G [13, 14]

The Slope1 setting can be calculated as:

1 2
_ _CT ERR RELAY ERR MARGIN

SLP I K K= × + + (4)

SLP1=2×5%+2% +5%=17%, so 20% is proper. O87P
setting is calculated using the guidance shown in equation:
O87P=0.5∗SLP1=0.1

The SLP2 setting is fixed to 100%, the turning point
between Slope1 and Slope2 defined by the value IRS1 is fixed
to 3.0 per unit. The purpose of the Unrestrained Differential
Element Pickup Setting (U87P) is to detect the very high
differential current that clearly indicates a fault inside the
differential protection zone. The U87P setting is set to 10 per
unit as recommended by the relay manufacturer. The criteria
for internal and external faults can be seen from the differential
characteristic and are described below:

87 where 87 1/
DIFF BIAS
I O P I O P SPL> ≤

1
1 when 87 1/

DIFF BIAS BIAS RS
I I SLP O P SPL I I> × < <

( ) 12 1 2 when DIFF BIAS B RBI S SA IASI I SLP SLP SLP I I I> × + − × ≥

D. GE Multilin G60 [15, 16]

. . 1.5 0.02 2116.5 0.025398
2500

REL er n G NK I IPickup
CT

× × × ×
= = = , so

0.1A is proper. Slope1 is set at 15% starting from 0.04 (RC).
The Break1 setting should greater than the maximum overload
expected for the machine:

.1.05 1.05 2116.51 0.88893
2500

G NIBreak
CT

× ×
= = = , so it is set at 1.2

Slope2 is set at 80 %.

The Break2 setting is set at 3 or 4. It provides security from
misoperation for maximum fault and resulting maximum CT
error condition. The criteria for internal and external faults can
be seen from the differential characteristic and are described
below:

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www.etasr.com Le & Vu: Performance Evaluation of a Generator Differential Protection Function for a Numerical Relay

where 1/
DIFF BIAS
I Pickup I Pickup Slope> ≤

1 when 1 1 /
DIFF BIAS BIAS
I Slope I Pickup Slope I Break> × < <

2 3
0 1 2 3 ≥ + × + × + ×DIFF BIAS BIAS BIASI C C I C I C I

when 1 2, where:< <BIASBreak I Break

2 2

0 3

2 ( 1 2) 1 2

( 1 2)

Slope Slope Break Break
C

Break Break

× − ×
=

−

2 2

1 3

2 1 ( 1 1 2 4 2 )

( 1 2)

Slope Break Break Break Break Break
C

Break Break

× × + × + ×
=

−

2 2

1 2 (4 1 1 2 2 )

( 1 2)

Slope Break Break Break Break Break

Break Break

× × × + × +
−

−

2 2

2 3

2 ( 1 2) ( 1 1 2 2 )

( 1 2)

Slope Slope Break Break Break Break
C

Break Break

× − × + × +
=

−

( ) ( )
3 3

2 1 1 2

( 1 2)

Slope Slope Break Break
C

Break Break

− × +
=

−

and IDIFF>Slope2×IBIAS when IBIAS≥Break2

All setting parameter results are calculated based on the
best manufacturer practices that are adjusted to compensate for
CT ratio error mismatch and CT response via a dual slope
characteristic typically as shown in Figure 7.

Review: The numerical algorithm of the F87G is very
similar to motor differential protection. It is also principally
simpler than that of the power transformer differential
protection. No phase shifts, and no transformation ratios, typical
for power transformers, must be numerically allowed for. The
suggested protection for instantaneous and sensitive protection
for generator internal faults is presented in [17]. The variable
slope percentage differential relay is a widely used form of
differential relaying for generator protection. In this type of
relay, the percentage slope characteristic may vary from about
10% at low values of through current up to 100% or more at
high values of through current. A P434 is more sensitive than
another relay with K1=0% during light internal faults and
relatively low sensitivity (K2=20%) during heavy external
faults.

III. POWER SYSTEM UNDER STUDY

Matlab/Simulink tool is useful for the basic understanding
of power system protection, particularly for new engineers. It
helps them to model the F87G system behavior under normal
and fault conditions. In this section, the F87G performance is
tested on the 13.8kV, 50.6MVA synchronous generator,
connected with 220kV through a 51MVA, D11Yn step-up
transformer as shown in Figure 3.

A. The Generator

The generator is represented by its impedance and an AC
source, required for the system supply. It is located at the point
where one side can easily be grounded. A resistor of 0.5Ω,

which exists in the actual grounded generator neutral, is not
represented. This assumption does not have a significant
influence on the study.

Fig. 3. Power system model

B. Current Transformer Models

Current phasors at both ends of stator windings are
2500/1A 5P20 30VA which are performed the current
transformer excitation test, measured the CT winding resistance
and CT current-ratio automatically by The Vanguard EZCT-
2000 test set in Central Electrical Testing Company Limited.
All of the EZCT’s test leads can be connected to the CT output
terminals, eliminating the need for lead switching during
testing. Test voltage output is automatically raised and lowered
by the EZCT without any operator intervention. Once the test is
completed, test results can be printed and excitation curves can
be plotted on the built-in 4.5-inch wide thermal printer as in
Figure 4.

Fig. 4. V-I curve of CT 2500/1 A

Knee Type IEC 10/50 standard [18]: Vpk=1401.44V,
Ipk=0.0124A, CT ratio: 2485.885/1A, Error: 0.5646%, Ex
V=99.6V, Ex I=0.02A, Phase angle: 0.120, CT Pole: In Phase,
and Winding Res: 13.94Ω.

The proposed mathematical current transformer model is
shown in Figure 5 and is based on the CT Saturation Theory
and Calculator presented by the IEEE Power System Relaying
and Control Committee (PSRC) and the practical testing results
of CT by Vanguard EZCT-2000 test set above (See [19] for
more details).

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Fig. 5. A mathematical current transformer model

C. Different Protection Relay Model

By performing the essential computations given in Section
II, we got the four models of F87G relay (P343, REG670,
SEL300G, G60) which are connected on CT’s secondary side
at both ends of the generator (IL, IN). After that, these signals
were calculated using recursive discrete Fourier transform
algorithm. These are combined with setting parameters
sending to S-function block. This block has been developed
for detecting generator stator winding internal faults. If the
output from the S-function block is equal to zero, this means
that there is no fault in the stator winding of the generator,
otherwise, the stator winding of the generator has a fault. The
inside Simulink model of F87G block is shown in Figure 6.

Fig. 6. Differential protection relay P434 block

D. Three Phase Fault Block

Three phase fault block F1 and F2 generate fault types and
fault resistance varying from 1Ω to 35Ω which are inside the
protected zone, and out of the protected zone, respectively.

IV. SIMULATION RESULTS

After the building of the proposed model has been
completed, it is ready to analyze the operation of F87G applied
under three cases below. In the first case, the normal condition
shows the phase current waveforms captured at both terminal
IN=IL=2200A, CT Error ≈0%, IDIFF≈0A and all relays have not

generated trip signal. The trajectory of the operating point can
be seen by the relay lied the restrain zone (Figure 7).

Fig. 7. Current waves, CT error, trip signals and trajectory of operating

point for normal condition

In the second case, the internal fault occurs at 0.16s on the
terminal of phase ‘ABG’ stator winding as shown in Figure 8.
The phase currents captured at both terminals IN=2kA, IL=1kA
and remain in the same phase, CT Error ≈0%, IDIFF≈8A.
According to change in current waveforms during the fault, the
trajectory of the operating point moves quickly into trip zone,
which results in a tripping at 0.178s (REG670), 0.1832s
(SEL300G and G60), 0.1835s (P434). In the third case, a three-
phase fault occurs at 0.1s on the terminal of a synchronous
generator that is external to the stator winding. If the CTs have
no error, then currents at both ends of stator windings remain in
the same value and opposite phase, and IDIFF≈0A.
Unfortunately, during fault conditions as shown in Figure 9,
CTs do not always perform ideally, since core saturation may
cause a breakdown of a ratio (IN=20kA, IL=1.8kA). Such core
saturation usually from 0.13s to 0.15s is the result of a DC
transient in the primary fault current, total burden impedance
ZB=150Ω and may be aggravated by the residual flux left in the
core by a previous fault. The trajectory of the operating point
moves into the trip zone of P434, SEL300G, and REG670.
After that, it comes back to the restrain zone at 0.23s.
Therefore, in order to provide additional security against
maloperations during this event, the relay incorporates
saturation detection logic. When saturation is detected, the

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element will make an additional check on the angle between
the neutral and line current. If this angle indicates an internal
fault then tripping is permitted. In this case, the generator does
not trip because the differential relay does not a response to the
fault since the fault happens out of the protected zone.

Fig. 8. Current waves, CT error, trip sinals and and trajectory of operating

point for internal fault condition (ABG fault)

Review: The simulation results show that under the no-fault
condition and external fault then the relay does not trip; under a
fault condition, the trip signal is taken. In another way the
characteristic results are very sensitive to internal faults and
insensitive to CT error currents during severe external faults.

V. CONCLUSIONS

In order to verify the deployed generator protection scheme
is working as designed after field installation, this paper is
discussed with a Buon Tua Srah Hydropower plant example.
The paper provides calculation on appropriate a pickup
threshold, slope and breakpoint settings for an F87G function
available from today’s modern multifunctional generator
protection IEDs such as P434, REG670, SEL300G, and G60. It
also presents important aspects of generator protection system
analyzing at different conditions which are simulated on a
synchronous machine stator winding in Matlab/Simulink. This
software shows the two CTs’ current waves, and the different
and restraint current trajectories on the relay characteristics. It
tells the user how far the different locus intrudes into the trip
zone. According to the obtained results, it has been shown that
the IEDs operate safe and reliable.

Fig. 9. Current waves, CT error, trip sinals and and trajectory of operating

point for external fault condition (ABC fault)

ACKNOWLEDGMENT

The authors would like to thank the Central Electrical
Testing Company Limited, Vietnam for allowing the use of the
test record of current transformer, setting the calculations of
Hydropower Plants used in this study.

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Thai Nguyen University, Vol. 189, No. 13, pp. 129-134, 2018 (in
Vietnamese)