On the Use of the Ultimate Current Transformer Ratio in Design and Analysis of the Behavior of Differential Protections of Transformers .pdf
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Title: On the Use of the Ultimate Current Transformer Ratio in Design and Analysis of the Behavior of Differential Protections of Transformers
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Power Technology and Engineering
Vol. 37, No. 1, 2003
ON THE USE OF THE ULTIMATE CURRENT TRANSFORMER RATIO
IN DESIGN AND ANALYSIS OF THE BEHAVIOR
OF DIFFERENTIAL PROTECTIONS OF TRANSFORMERS
A. M. Dmitrenko1
Translated from Élektricheskie Stantsii, No. 2, February 2003, pp. 41 – 44.
A reduced ultimate ratio is used as a generalized parameter for describing current transformers (CT). This parameter is used to formulate the requirements to CT under steady state and transient operating conditions. It is
shown that the performance of differential protections under transient conditions of short circuits in the protected zone can be considerably increased by increasing the values of the reduced ultimate ratio of CT. This
will also reduce the transient imbalance currents at low through currents that appear, for example, upon
startup of a powerful engine.
Keywords: current transformer, differential protection, ultimate ratio, and through current.
The ultimate ratio K10 is the greatest ratio (I1/I1rat.ct,
where I1rat.ct is the primary rated current of the current transformer) of the primary current at which the total error å at the
specified secondary load does not exceed 10% . According to , a current transformer (CT) used in differential protection circuits of a transformer should have an error of at
most 10% at maximum short circuit (SC) current outside the
protected zone. With the use of the parameter K10 this requirement can be formulated as
¢ ³ I sc.ex.max
¢ ³ (I1rat.ctK10)/Irat.t,
grid, w2 is the number of coils of the secondary winding, sc is
the cross sectional area of the core (m2), I2rat is the secondary
rated current of the CT, Zw2 is the resistance of the secondary
winding of the CT in the T-connected equivalent circuit, and
Zl is the resistance of the load.
For circular cores produced from cold-rolled steel of
grades 3411 – 3413 Bmax » 1.8 T.
It can be seen from Eq. (3) that the parameter K10 can be
treated as a generalized parameter of a CT with connected
¢ will be a generalized parameter in a specific differload. K 10
ential protection circuit. Using this ratio we can approximately determine (accurate to the period of commercial frequency T) the time ts before saturation of the core of the CT
under transient operating conditions , i.e.,
¢ is the reduced ultimate ratio, I sc.ex.max
where K 10
= Isc.ex.max/Irat.t; Irat.t is the rated current of the protected transformer.
The rated current of the protected transformer (autotransformer) can be calculated by the formula
I rat.t =
t s = T a ln
where m is the ratio of the power of the winding to the rated
power Srat.t of the transformer (autotransformer) and Urat.tap is
the rated voltage of the tap at the zero position of the VR.
The ultimate ratio K10 can be calculated by an approximate formula
K 10 =
4.44 B max fw 2 s c
I 2rat | Z w2 + Z l |
(1 - B r* )K 10
|cos a |
2 pT a* I sc
B r* = Br/Bmax, Br is the residual induction of the core of the
CT, Ta is the time constant of damping of the aperiodic com*
= Isc/Irat.t, and á is
ponent of the SC current, T a* = Ta/T, I sc
the voltage phase at the moment of the SC.
It follows from expressions (4) and (5) that the increase
¢ leads to an increase in the parameter F and hence to
in K 10
an increase in the time before saturation ts in the transient
Russian powermen chiefly use sensitive differential relays that react in this or that way to distortions of the form of
the curve of the differential current and (or) the arm currents
where Bmax is the maximum value of induction in the CT
core at the ultimate ratio K10, f is the voltage frequency in the
Chuvashia State University, Cheboksary, Russia.
1570-145X/03/3701-0065$25.00 © 2003 Plenum Publishing Corporation
in the transient mode (DZT-21 and DZT-23 relays produced
by the Cheboksary Electric Equipment Plant, SPAD346C relay and RET316 terminal produced by the “ABB Avtomatizatsiya” Company of Cheboksary, etc.).
From the standpoint of high-speed operation of such differential protections under transient SC conditions in the protected zone we should know whether the time ts exceeds the
commercial frequency period under SC currents that are
lower than the setting current of the differential cutoff. In the
case of ts ³ T there will be no delay in the transient SC mode
in the protected zone. At ts < Ta a certain delay is possible,
¢ . For
but it also decreases with increase in the parameter K 10
example, according to the data of  the delay time of relay
DZT-21 in the transient SC mode in the zone at I sc
= 10 and
á = 0 decreases by about a factor of 3.5 when the parameter
¢ increases from 10 to 20.
With allowance for the facts presented above it is expedient to stop the choice of the transformation ratio for CT with
secondary rated current of 5 A, which are mounted on the
side of the highest (HV) and intermediate (IV) voltages, on
the highest value of the transformation ratio (if the CT has
several ratios like, for example, the TVT-type current transformers incorporated into a line transformer).
Equations (3) and (2) can be used to show that at the
maximum transformation ratio of a CT the value of the pa¢ is the highest. This creates no obstacles from the
rameter K 10
standpoint of the possibilities of the DZT-21 relay, because
the AT-31 current autotransformer provides a wide range of
The RET316 terminal is rated for currents of 1, 2, and
5 A, which also (together with the digital leveling) provides
successful functioning in the mentioned cases. The RET316
terminal is used on any side of the protected transformer with
groups of CT connected by the “star with neutral conductor”
pattern. As compared to the CT groups connected into a
delta, which are traditionally used on the HV and IV sides,
this reduces the design load of the CT by about a factor of 3
in three-phase SC and correspondingly increases the value of
the parameter K 10
At the same time, we should note that in the case of the
use of CT with a secondary rated current of 1 A and a high
I1rat.ct/Irat.t ratio there may arise problems with digital leveling of the currents. For such situations the “ABB Avtomatizatsiya” Company produces terminal RET316 with rated
currents of 0.2 or 0.333 A on special order.
On the side of the lower voltage (LV) of the protected
transformer the ratio I1rat.ct/Irat.t usually does not exceed 2 (in
many cases it is close to 1). Current transformers rated for
24 kV and lower voltages are produced in the Russian Federation only for a secondary rated current of 5 A. Such CT can
be saturated under transient operating conditions at low val*
ues of I sc
, which is responsible for the appearance of rela¢ on the
tively high imbalance currents (at a high value of K 10
side of HV). According to , a quasi-linear transient mode
of CT operation is possible at external SC and I sc
£ 2. In this
A. M. Dmitrenko
case the information parameters used for time grading (or
blocking) of the mentioned devices for differential protection
are usually not high, and the time grading can be performed
only by choosing appropriate parameters of the restraining
In a quasi-linear mode the time constant of the secondary
CT contour can be determined from the approximate relation
2 pI a0
B max I sc
= T2calc/T, â is a parameter characterizing the
where T 2calc
differential magnetic permeability of the electrotechnical
¢ m , and Ia0 is the
steel of the core of the CT, I a0
= Ia0/I sc
aperiodic component (the mean value for the period T) of the
magnetization current of the CT.
Knowing T 2calc
we find the relative value of the first har¢ is asmonics of the magnetization current I 0* (the current I cs
sumed to be the base), i.e.,
I 0* =
1 + ( 2 pT 2calc
Expressions (6) and (7) show that the time constant T 2calc
¢ , and the current I 0* deincreases with the growth in K 10
creases. Consequently, the first harmonics of the imbalance
current of the differential protection in the transient mode
can be decreased by raising the parameter K 10
Let us consider the protection of a TRDNS-25000/10
house transformer of a thermal power plant. We have the following parameters of the transformer and the CT: the range
of voltage regulation under load ±9%, the rated voltages
10.5/6.3 kV, the group of winding connection D/D-D-0-0,
the transformers of the protection current are connected into
a “star with neutral conductor” on all sides and have transformation ratios of 2000/5 on the HV side and 1500/5 on the
The load includes an asynchronous 5000-kW engine.
We find the rated current of the transformer on the HV
= 1376 A.
We take into account that the current Ist » 2675 A appears upon the startup of the asynchronous engine.
We find the ratio of the reduced startup current to the
rated current of the transformer on the HV side, i.e.,
6.3 ´ 2675
I rat.t 10.5 ´ 1376
which determines the ratio of the through current for the differential protection of the transformer.
On the Use of the Ultimate Current Transformer Ratio
¢ of the CT on the LV side has a lower
We assume that K 10
limiting value determined by inequality (1). In some cases
(more powerful CT, greater ratio I1rat.ct/Irat.t, etc.) the parame¢ on the HV side is considerably higher. In this case
ter K 10
and for the startup mode of the engine the CT is virtually not
saturated on the HV side. Then the imbalance current is determined by the magnetization current of the CT on the LV
side. A theoretical analysis and a study of actual oscillograms
of differential protection currents in the process of the engine
startup show that the current I 0* may attain 0.4. With allowance for this fact the coefficient Ktr that allows for the transient mode in the calculation of the imbalance current should
be assumed to be equal to 4.0.
It is known from  that the braking factor of the
DZT-21 relay can be calculated by the expression
k b ³ K cutoff I im.calc
K l.t - I t* - I t.i
the protection under coil short circuits in the transformer
windings, which appear under load.
It can be seen from Eq. (9) that the braking can be decreased by reducing Ktr. This can be provided by raising the
¢ . In the considered transient mode at
parameter K 10
¢ £ 25 we may choose Ktr = 2.5 and Kl.t = 1.0, which
20 £ K 10
will provide time grading at a braking factor v of at most 0.5.
The requisite values of K10 can be chosen from the
curves of ultimate ratios presented in  and other publications.
For CT of advanced design only the rated ultimate ratios
K10rat are often presented for the rated load power Sl.rat .
The rated load power has cos öl.rat = 0.8. Therefore, we use
Eq. (3) to obtain the following expression for the active load
of the CT:
K 10 =
K 10rat ( R w2 + 0.8 Z l.rat ) 2 + ( X w2 + 0.6 Z l.rat ) 2
( R w2 + R l ) 2 + X w2
is the relative initial differential pickup current
and Kl.t is the coefficient describing the lowering of the braking current in the transient mode.
Under the considered operating conditions we may chose
= I t* = 1.6, Kl.t = 0.95, DU reg
= 0.09, and Df lev
Since the value of Ktr is known quite exactly, we may assume that Kcutoff = 1.15. The settings of the DZT-21 relay are
chosen as follows: I d.i
= 0.3 and I t.i
Using the known formula for calculating the imbalance
= Ktrå* + DU reg
+ Df lev
. ( 4.0 ´ 01
. + 0.09 + 0.05) ´ 116
. - 0.3
0.95 ´ 116
. - 0.6
With a certain margin we may assume that kb = 0.9,
which is indeed used in practice. If we take I d.i
= 0.4, we will
obtain kb ³ 0.64. With a certain margin we choose kb = 0.7.
This variant of setting is used in practice.
The braking factor v of the RET316 terminal can be calculated by the formula
+ Df lev
K cutoff ( K tr e * + DU reg
= 0.02, and å* = 0.1.
where Kcutoff = 1.1 – 1.15, Df lev
For the braking mode employed in the RET316 terminal
we have Kl.t » 0.9 for the considered operating conditions.
At Kcutoff = 1.15 we find from Eq. (9) that
. ( 4.0 ´ 01
. + 0.09 + 0.2 )
The RET316 terminal has settings for a braking factor v
not exceeding 0.5, which provides enhanced sensitivity of
where Zl.rat = Sl.rat/I 2rat
It is rather difficult to calculate the dissipative reactance
of the secondary winding Xw2 of the CT with appropriate accuracy. At the same time, the analysis made in  shows that
for virtually every modern CT design used in circuits of differential protection the condition Xw2 < 0.5Rw2 is obeyed.
Taking this into account we may assume that Xw2 » 0 and
calculate K10 by an approximate formula
K 10 »
and assuming that å* = 0.1, we find from Eq. (8) that
. R w2 Z l.rat + Z l.rat
K 10rat R w2
R w2 + R l
The error in the calculation by formula (11) does not exceed 10%, and the calculated values are lower than the actual
The suggested method for calculating ultimate ratios has
constraints connected with the fact that the current transformers rated for primary currents ³6000 A function in the
transient mode at quite high intensities of the magnetic field
£ 2). This refers to CT of the
in the core (even at I sc
TShV-15, TSh-20 and other types operating on the generator
voltage. Equations (3) and (11) are not suitable for such current transformers because they may yield too high errors. A
more detailed consideration of this problem is outside the
framework of the present work.
The use of an ultimate ratio K ¢10 enhanced with respect
to the boundary values determined by expression (1) makes
it possible to raise the quality of operation of modern differential protections of transformers rated for a current of up to
1. V. V. Afanas’ev, N. M. Adon’ev, V. M. Kibel, et al., Current
Transformers [in Russian], Énergoatomizdat, Leningrad (1989).
2. Rules for Designing Electric Power Plants [in Russian], Énergoatomizdat, Moscow (1985).
3. A. M. Dmitrenko, “Time grading of the differential protection of
a transformer from transient imbalance currents under external
short circuits,” Élektrichestvo, No. 12 (1991).
A. M. Dmitrenko
4. A. M. Dmitrenko and M. G. Lint, “Effect of transient processes
on the performance of differential protection DZT-21,” Élektr.
Stantsii, No. 6 (1982).
5. A. M. Dmitrenko, “Allowance for transient processes in the
choice of parameters of pulse-time differential protections of
transformers (autotransformers),” Élektrichestvo, No. 1 (1995).
6. E. P. Korolev and E. M. Liberzon, Calculation of Permissible
Loads in Current Circuits of Relay Protection [in Russian], Énergiya, Moscow (1980).