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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
Sizing Current Transformers Rating To Enhance
Digital Relay Operations Using Advanced Saturation
Voltage Model
*J.O. Aibangbee1 and S.O. Onohaebi 2
*Department of Electrical &Computer Engineering, Bells University of Technology, Ota, Nigeria
Department of Electrical / Electronic Engineering, University of Benin, Nigeria
Current transformers for transmission lines are rated to
avoid saturation during the asymmetrical portion of the
maximum fault current. The selection of current transformers
(CTs) rating to maximize microprocessor-based (MPB) relay
operations was investigated.
This paper examines the effects of saturation on protection
relays, and developed an advanced saturation voltage (VS)
algorithm for the selection of CT rating for Microprocessorbased relays applications in transmission lines with high short
circuit levels.
Results show that Instantaneous MPB relay operation using
C400, 1200:5A ratio can be guaranteed with Voltage burden of
525, within 1-cycle trip time as compared to Voltage burden of 20
times rated voltage at standard burden to avoid saturation
specified by IEEE standard for EMR. A criterion for selecting
minimum CT rating for MPB overcurrent relay operations in
transmission lines to avoid saturation using the developed voltage
saturation (VS) algorithm is presented. It allows protection
engineers to determine the limits of high current applications in
terms of the fault current magnitude, the X/R ratio, and relay
burden. The criteria address the limitation of CT ratings used in
line protections. Small cores, long leads, high burdens, high
currents, and dc offset lead to saturated CTs. Improper selection
of CTs results in CT’s saturation during fault conditions and this
causes relay mal-operation or fail-to-trip.
Keywords: Microprocessor-based relays, Relay burden,
EMR, Current Transformers, Relay burden, Saturation
Voltage (VS), dc offset, Fault current.
1. Introduction
Most of the generating stations in Nigeria are retrofitted with
Microprocessor-based (digital) relays and protection
equipment with the rest of the installation such as Current
transformers (CTs) and control cables (lead) remaining
unchanged. In the past, due to the high burden of
electromechanical relays (EMRs), it was the rated power of
the CTs and potential transformers (PT) that was the crucial
parameter. In recent time, it is the transient performance of
instrument transformers that has become the over-riding
influence within the digital relays, measuring and controlling
devices. It is utmost important therefore to evaluate the
dimensioning of CTs while planning such up-grade. The
existing CT sizes and lead sizes of EMRs may not be adequate
for the latest protective relays which might demand a different
CT performance [1, 2, 4]. CTs are the basic interconnection
ISSN: 2231-5381
between the power system networks and protective relays.
CTs step the primary current down to a nominal secondary
level for use by protective relays, meters, and other
monitoring devices. CTs perform reasonably in most
operating scenarios, faithfully reproducing primary current as
a secondary current, with little distortion or error CTs for
transmission lines are rated to avoid saturation during the
asymmetrical portion of the maximum fault current.
Saturation is avoided by selecting the voltage rating larger
than the maximum fault burden voltage with the (X/R+1)
factors applied according to [3]. This is possible in line
protection applications since large load currents result in the
use of high ratio CTs, and fault currents are typically limited
from 5 to 7, and rarely exceed 10 times the CT primary
current rating. In this paper, the relationship between the flux
density and the time integral of the voltage is examined. Using
this as a basis, the relationship between fault current, CT
burdens, and system X/R ratio is established and this
ultimately determines the useful range of any CT.
II. Current Transformers Burden and Accuracy Class
The burden of current transformers is the property of the
circuit connected to the secondary winding, which determines
the active and reactive power at the secondary terminals [3].
The external load applied to the secondary of a CT is called
the “burden” The total burden is the combination of internal
CT burden and the external burden connected to the CT
terminals. In selecting CT, the process is to minimize the total
burden that consists of the internal resistance of the CT
winding itself, the resistance of the leads from the CT to the
relay including the return path, and the burden of the
connected relays.
The accuracy of CT’s is defined as the extent to which the
current in the secondary circuit reproduces the current in the
primary circuit as stated by the marked ratio. In many
applications the use of the ANSI/IEEE accuracy class
designation is adequate to assure satisfactory relay
performance. The accuracy class can be obtained by
calculation or by test, followed by the minimum secondary
terminal voltage that transformer will produce at 20 times
rated secondary current with one of the standard burdens
without exceeding the accuracy class limit of 10%. The
secondary voltage rating is the voltage the CT will deliver to a
standard burden at 20 time’s rated secondary current without
exceeding 10% ratio correction. The standard burden values
Page 298
International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
for relaying are 1.0, 2.0, 4.0, and 8.0 ohms all with an
impedance angle of 600 [4,5,6]. Consequently, at 20 times
the rated current of 5 amperes the standard voltage ratings
are 100, 200, 400, and 800 volts respectively. Table 1
presents standard current transformers burdens with 5A
secondary windings.
Table 1: Standard burdens for current transformers with 5A Secondary [6]
III. System X/R Ratio on CT’s Saturation
CT performance is affected significantly by the D.C
component of the ac current. When a current change occurs in
the primary ac system, one or more of the three-phase currents
may obtain some D.C offset. This results from the necessity to
satisfy two conflicting requirements that may occur [7].
In a highly inductive network, the current wave must be
near maximum when the voltage is at or near zero, and
The actual current at the time of the change, which is
determined by the prior networks conditions.
During asymmetrical faults, the fault current can be represents
by two parts, namely the d.c and ac components as follows:
Figure 1 shows the shaded volt-time area produced by
asymmetrical fault current. Where If is the magnitude of the
fault current in the secondary; Zb is the burden impedance,
and L/R is the time constant of the primary fault current. The
sine wave and the exponential components of the wave are
shown dashed for comparison. The plot shows the change of
burden voltage with the time. The volt-time area of the
asymmetrical fault is increases compared to the normal sine
wave and hence will affect the performance of the CT and the
relay [8].
Figure 1: Burden Voltage for Asymmetrical Fault current
Using the asymmetrical burden voltage equation (3) and
substituting in equation (5) will result in the following
The total fault current can be rewritten as:
The burden voltage can be expressed as follows:
In equation (6), the limit of the integral of the exponential term
is the X/R ratio of the primary circuit.
Since the limit integral of the cosine term is unity, we can write
the equation as follows:
The burden voltage V is related to the core turn (N) of the CT
and the rate of change of the core flux by the induction Equation (7) expresses the CT-rating voltage in terms of the
physical parameters of the CT, namely the saturated flux
density Bs, system turns ratio N, the core cross – sectional
areas A; and angular frequency w.
A different form of Equation (7) can be derived by recognizing
that the rating voltage is 20 times the voltage across the
Integrating equation (4) show that the flux density in the core standard burden at rated current. If we then express the fault
is represented by the area under the voltage waveform.
current If in per unit of the rated current and the burden Zb in
In other words, for a given secondary fault current, more per unit of the standard burden, equation (8) becomes the
burden voltage from the CT will be required and the core simple criterion to avoid saturation.
density is proportional to the time – interval of this voltage.
Therefore the flux linkages in the core are given by the
20 ≥ (X/R + 1).* IF * Zb
interval of equation (5) where the flux is expressed as flux
density B times the core cross – sectional area A
Where VS = 20
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
= the maximum fault current in per unit of CT rating,
= the CT burden in per unit of standard burden and
= the system X/R ratio, that is the primary system
reactance and resistance up to the point of fault.
However, most times, these rules result in impractically large
CTs, which are not economically acceptable.
CT Selection Procedures
The algorithms for the selection of current transformers in a
given transmission line relay application is outline as follows
(IEEE standard C37.110-1996).
Determine the maximum fault current If in primary
Determine the corresponding primary circuit X/R ratio.
Select the CT voltage rating based on the load
Determine the total burden in per unit of the CT
standard burden.
Divide the maximum primary fault current If by the per
unit current to determine the CT nominal current rating.
Select the nearest standard rating greater than the
calculated value.
Calculate the saturation voltage VS.
Finally, compare VS to the current transformer rating.
If the voltage rating is greater than or equal to the
calculated secondary voltage, the current transformer is
acceptable for the application.
IV. Methodology Description
Advanced Saturation Voltage Model
Microprocessor-based (MPB) relays have a relatively small
burden of 0.2 VA (0.008 Ω). The secondary burden is the
impedance of the CT windings and cables (leads) full circuit
runs; and it is purely resistive. In this paper, the CT selection
criteria are based on the degree of saturation voltage produced
by the 120KA fault in the C400, 1200:5 CT primary rating.
Evaluation of the effects of asymmetrical faults with DC
offset on operation of instantaneous microprocessor-based
relay is considered.
In order to avoid DC saturation, the saturation voltage
equation VS is as expressed in equation 9.
VS ≥
undistorted CT secondary current to perform phasor
measurement in the presents of the dc offset.
Using class C400, 1200:5 CT ratio with standard burden of
4Ω, the calculated total burden is express as:
CT cables of 121.92m full circuit run of #10 AWG
(1.0 Ω/1000 feet)
= 0.40
CT winding of 240 turns at 0.0025Ω/turn
= 0.60
Total burden
= 1.00 Ω
The burden is primarily due to the CT winding and external
cables to the relay. Equation (10) determines the maximum
burden in per unit of the standard burden:
Zb =
With an X/R ratio of 20, the saturation voltage can be
calculated using equation (9) as follows:
Vs ≥ [20+1]* 100 * 0.25 = 525
Consequently, CTs used with the microprocessor relays
should meet the criteria in equation 11;
Calculated maximum load current of the protected line is
1049.76A, so select CT of C400, 1200:5A, being the nearest
CT standard rating greater than the calculated value. Also, the
calculated Voltage Saturation of CT 1200:5A rating from the
enhanced model is 302 Volts. This is less than the 400 Volts
rating of CT 1200:5A ratio, hence the selected CT rating of
C400, 1200:5A is thus adequate and suitable for protection
For evaluation purposes, microprocessor overcurrent relay
with a 240A instantaneous setting and X/R ratio of 20 (worst
case) is considered. The equation for maximum fault current
in terms of primary CT and ANSI voltage rating, burden in
ohms, and X/R ratio is as express in equation 12,
Imax =
The acceptable calculated saturated voltage VS is 525 volts,
substituting equation (12) above, the maximum fault current
for secure operation can be calculated as follows:
Where If = the maximum faults current in per unit of CT rating,
Imax =
is the CT burden in per unit of standard burden,
is the CT saturation voltage in per unit,
X/R is the X/R ratio of the primary fault current.
B. Simulation:
* 1200 = 120,000 A for MPBRs
Evaluation of CT Secondary Burden:
A . CTs Selection for line Protection
Modern Microprocessor-based relays clear faults
cycles to preserve stability, accurately identify fault
single-pole reclosing applications, and determine an
fault location. To accomplish this, line relays
ISSN: 2231-5381
in few
type for
In the simulation conducted at BELLS University of
Technology, Power Laboratory, different secondary burdens
of 1.0, 3.0, 5.0, and 10Ω were injected at different times into
the SEL-551 MPB instantaneous overcurrent relay by the
secondary test equipment ISA T2000, using a CT of C400,
1200:5A ratio. Starting from a burden of 1.0 Ω; the burden is
Page 300
International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
primary due to CT winding itself, and external leads (a wire
size of #10 AWG) of a total length of 400ft (121.92m) from
CTs to the relay including the return path. With total burden
of 1.0 ohm, secondary current waveform results was obtained
from ATP simulations base on transmission network
parameters as shows in Figure 2; it indicates an undistorted
waveform throughout the duration of the simulation.
When secondary burden of 3.0 ohm was injected into the
secondary circuit, the CT core saturates for at least four (4)
cycles after the fault occurs. Subsequently increasing the
burden to 5.0 ohm, and then 10 ohms respectively, the
waveform distortion became more present (visible) during the
entire simulation. The severe CT saturation (distortions)
caused by the heavy fault current (115 KA) with maximum
offset and different values of secondary burden (3, 5, and 10
ohms) is shown in Figure 3; these caused RMS current to be
smaller than in fact it was, i.e. the secondary current is
substantially reduced under severe saturation of main CTs.
This proves that relative small burden can influence CT
accuracy if the fault current is not correctly anticipated.
Conclusively, proper selection of a CT is required for a better
protection scheme operation.
Figure 3: Severe CT Saturation (Distorted Waveforms) due to varying burden
(3, 5, and10Ω).
V. Case Study and Application
A case study is considered to show the area of application of
the work. A transmission line under protection with MPB
overcurrent relay installed at the source of the busbar to
protect against over load and short circuits is rated 600 MVA,
three phase, 330 KV, 50Hz, line reactance (X) and resistance
(R) of 0.32735Ω/km and 0.0288 Ω/km (i.e, X/R of 11.4
ratios). A CT rating of C400, 1200:5A ratio is selected based
on the full load current of 1049.76A. Short circuit faults
occurred at 5km away from source, with maximum fault
current calculated to be 115996A. The CT performance data is
shown in table 2.
Table 2: CT Performance Data
Current transformer in used
Class C400,1200:5
Instantaneous element pickup
240A secondary
setting (1200:5)
Figure 2: Non-saturated Waveform secondary burden (1.0 ohm).
Since MPB instantaneous relays operates within one cycle (1)
and that the CTs operation was accurate from one to four
cycles of its operation before saturation start to occurs, this
proved that MPB instantaneous relays operation is not
affected by CT saturation. Thus the trip time of MPB relay is
unimpaired by CT saturation due to DC offset with extremely
high fault currents.
X/R ratio (0.32735 / 0.0288)
11.4 (85º)
Maximum fault current at 5 km
Using C400, and a total burden of 1.0 ohms, the minimum CT
rating can be determine in terms of maximum fault current,
X/R ratio, ANSI rating, and burden as in equation (13),
CT Rating
The parameters presented are the maximum fault current of
120 KA, X/R = 20 (worst case) and a total burden of 1.0 Ω.
CT rating
= 1200
Table 3 lists the maximum fault current versus X/R ratio for
which saturation is avoided. Using ANSI Class of C400, CT
ratio’s of 2000:5, 1500: 5, 1200: 5, or 1000: 5, with varying
burdens at various inception angles is presented.
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
Table 3: Maximum current (Amps) to avoid saturation using Microprocessorbased Relays
ZB =
1.5 Ω
ZB =
ZB =
1.2 Ω
1.0 Ω
ZB =
0.8 Ω
The CT primary current accuracy describes the highest fault
current magnitude at which the CT will fulfill the specified
accuracy. Beyond this level the secondary current of the CT
will be distorted and it might have severe effects to the
performance of the protective relay.
Compliance with saturation voltage equation depends on the
X/R ratio and the magnitude of the maximum fault current.
Either by calculation or measuring the burden and the X/R
ratio, the saturation voltage equation can be applied to
calculate the maximum fault current for a given CT ratio.
Thus, relay operations with 1200:5 CT can be selected and
guaranteed with a saturation voltage of 525 for the relay trip
operations as show in table 3.
b) Transient Behavior of CT during Faults.
The total secondary burden of the installation is 1.008 Ω
primarily due to the CT winding and external CT control wire
of (400ft) 121.92 m full circuit runs of #10 AWG to the relay.
From equation (11), saturation voltage
VS = 525 ≥ (X/R+I) * If * Zb
Fault current at 5 km away from source
If(5) =
= 96.66 A
Substitute these values into equation (11) to determine the
limit of saturation voltage.
525 ≥ (11.4+1) * 96.66 * 0.252 = 302 Volts
Result shows that the instantaneous operations of MPB relay
using C400, 1200:5A CT can be guaranteed with 302 times
CT rating with X/R ratio of 11.4. Figure 4 show the response
of the relay with 115996A short circuit fault currents for the
case presented. The thick line indicates the root mean
square current (IRMS) while the dash waveform is the
secondary currents. It confirmed that the MPB relay with
240A instantaneous setting will respond to the fault in this
case with no more than three cycles.
ISSN: 2231-5381
Figure 4: Case Study Test Result with X/R =11.4
microprocessor-based relays will operate properly with
1200:5A CT ratio and high short circuit levels. CT
performance will be satisfactory as the CT secondary
maximum symmetrical fault current multiplied by the total
secondary burden is less than the ANSI-class voltage rating of
the CT.
The criteria allow protection engineers to determine the limits
of high current applications in terms of the fault current
magnitudes, the X/R ratio and relay burden. The developed
algorithm has addressed the limitation of CT ratings used in
line protection where fault current exceed 525 times the CT
primary rating. As shown in equation (9), a smaller size CT
rating and accuracy class with adequate capability can be
employ for line protection. However, the CT ratings that avoid
saturation for asymmetrical current are impractical in
applications near a generator bus-bar where X/R ratio and the
fault current are both extremely high. A limit to the criterion is
shown in table 3 where the permissible maximum fault current
for a given CT rating is severely decreasing with increasing
X/R ratio. The limit occurs where high X/R ratio and high
fault current are experienced near the bus-bar.
VI. Conclusion
The effect of CT saturation on protective relays has been
The relation between the ANSI voltage rating, CT
burden, maximum fault current, and system X/R ratio
defines the threshold of CT saturation.
The derived equation provides the CT rating criteria for
line protection in new installations and can identify the
threshold of CT saturation in older installations.
CT rating is selected based on short circuit level
available, secondary burden connected, X/R ratio and
required relay trip time. Consequently, the need for
higher CT ratio with higher class could be eliminated.
Page 302
International Journal of Engineering Trends and Technology (IJETT) – Volume 23 Number 6- May 2015
CT of smaller size rating can be used for MPBR as
against the heavy and bulky type CT rating currently
used for electromechanical relays.
The criterion used CT selection procedure for line
protection which determined the CT ratio using the
maximum fault in amperes, the system X/R ratio and
the ct burden expressed in per unit of a CT rated
standard burden.
The instantaneous operations of microprocessor –
based relay can be guarantee with the advanced
saturation voltage Algorithm developed.
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ISSN: 2231-5381
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