CT/PT Calculation

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Calculation example

Dimensioning of Current and Voltage Transformers

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RE COMMENTS DATE BY SIGNATURE

V.
00

1.0

2.0

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The specific and general settings suggested in this document were made based on data
supplied to GE Power Management that was used to perform the equipment electrical
analysis under load and fault conditions for this specific application, and under
applicable rules of protection.
This setting document does not cover, or purport to cover, all variations which may be
encountered in the installation, operation and maintenance of the related equipment.
Should the user encounter variations not addressed by this document, the matter should
be reported to GE Power Management.
GE Power Management shall have no liability for any claim of any kind, including
without limitation negligence, for any loss or damage, including without limitation
special incidental, indirect or consequential damages from use of the settings herein
included or from failure of them to perform as intended.

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Content

XXXX SUBSTATION-CURRENT AND VOLTAGE TRANFORMERS...............................................................5

XXXX -CURRENT AND VOLTAGE TRANFORMERS ...............................................14

COMMENTS AND CONCLUSIONS ......................................................................................................................24

CT DIMENSIONING - BASIS..................................................................................................................................27
1. TRANSIENTS ON CURRENT TRANSFORMERS - FUNDAMENTALS ............................................................................28
2. RESULTANT VOLTAGES ON CT SECONDARIES DURING FAULTS ..........................................................................29
3. TIME TO MAXIMUM FLUX – TIME TO SATURATION .............................................................................................31
4. TRIPPING TIMES OF PROTECTION DEVICES ...........................................................................................................34
5. RESULTANT FAULT VOLTAGES AND CT DIMENSIONING ......................................................................................35
6. TERMS AND DEFINITIONS .....................................................................................................................................36

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Current and Voltage Tranformers

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S/S S/S
Current Transformer Capacitive Voltage Transformer
Fault Location Fwd.-Close-in Instrument Transformer
Instrument Transformer Location
Location S/S XXXX Transmission Line XXXXX
Bay XXXX Rated Frequency (Hz) 50.00
Rated Frequency (Hz) 50.00 CVT Ratio 2200 ('220000/? 3:100/? 3)
SC Iac rms Value (kA) 40.00 CVT Rated Sec. Voltage (V) 57.73
SC IEffective Peak Value (kA) 69.28 CVT Actual Burden (VA) 50.00 **
CT Ratio 500.00 * CVT Class 3P **
CT Rated Sec. Current (A) 1.00 * Sec. Wiring Length (m) 48.00
CT Actual Burden (VA) 30.00 * Cable Material/Cross Area Cu/6 mm2
CT Class 5P20 * Cable Resistance (Ohms/km) 3.27
CT Actual Knee Point (V) 600.00 Sec. Wiring Resistance RW (Ohms) 0.16
Sec. Wiring Length (m) 48.00 Sec. Wiring Burden PW (VA) 0.04
Cable Material/Cross Area Cu/ 6mm2 Relays Total Burden Prelay (VA) 0.44
Cable Resistance (Ohms/km) 3.27 Others Burden Pother (VA) 5.00
Sec. Wiring Resistance RW (Ohms) 0.16 Total Burden Ptotal (VA) 5.48
Relays Resistance Rrelay (Ohms) 0.30
Terminals Resistance Rt (Ohms) 0.20
CT Sec. Resistance RCT (Ohms) 0.35
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.07
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 7.58
Resultant Fault Voltage (V) 610.62
Resultant CT Burden (VA) 30.18
Eq. Burden on one CT core CT's PT's
Relay P442 (connected to other CT core) 0.0000 0.0300 * As per Dwg. XXXX
Relay DBF 0.1000 0.0000 ** As per Dwg. XXXX
Relay D60 0.2000
Relay MIV 0.0000 0.2000 Does not impose load on CT
Relay DRS 0.0000 0.2000 Does not impose load on CT
Unit D25 UCL (connected to measure core) 0.0000 0.0000
Unit 0.0006 0.0100
Unit D25 OSC (connected to other CT core) 0.0000 0.0000
TOTAL (VA) 0.3006 0.4400
TOTAL (Ohms) 0.3006

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S/S XXXX
Current Transformer
Fault Location Fwd.-Close-in
Instrument Transformer XXXX
Location S/S XXXX
Bay XXXX
Rated Frequency (Hz) 50.00
SC Iac rms Value (kA) 40.00
SC IEffective Peak Value (kA) 69.28
CT Ratio 500.00 *
CT Rated Sec. Current (A) 1.00 *
CT Actual Burden (VA) 30.00 *
CT Class 5P20 *
CT Actual Knee Point (V) 600.00
Sec. Wiring Length (m) 98.00
Cable Material/Cross Area Cu/ 6mm2
Cable Resistance (Ohms/km) 3.27
Sec. Wiring Resistance RW (Ohms) 0.32
Relays Resistance Rrelay (Ohms) 0.35
Terminals Resistance Rt (Ohms) 0.20
CT Sec. Resistance RCT (Ohms) 0.35
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.10
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 7.92
Resultant Fault Voltage (V) 773.20
Resultant CT Burden (VA) 38.31
Eq. Burden on one CT core CT's PT's
Relay DTP 0.1500 0.0000
Relay SMOR1000(1) 0.1000 0.2000
Relay DBF 0.1000 0.0000
Unit D25 UCL (connected to measure core) 0.0000 0.0000
TOTAL (VA) 0.3500 0.2000
TOTAL (Ohms) 0.3500 Vsignal taken from CVT's
* As per Dwg.XXXX at Busbar 225kV Bay

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S/S XXXX S/S XXXX

Current Transformer Capacitive Voltage Transformer
Fault Location Fwd.-Close-in Instrument Transformer
Instrument Transformer XXXX Location XXXX
Location S/S XXXX Bay Transfer
Bay Trasnfer Rated Frequency (Hz) 50.00
Rated Frequency (Hz) 50.00 CVT Ratio 2200 ('220000/? 3:100/? 3)
SC Iac rms Value (kA) 40.00 CVT Rated Sec. Voltage (V) 57.73
SC IEffective Peak Value (kA) 69.28 CVT Rated Burden (VA) 50.00 **
CT Ratio 500.00 * CVT Class 3P **
CT Rated Sec. Current (A) 1.00 * Sec. Wiring Length (m) 48.00
CT Actual Burden (VA) 30.00 * Cable Material/Cross Area Cu/6 mm2

CT Class 5P20 * Cable Resistance (Ohms/km) 3.27

CT Actual Knee Point (V) 600.00 Sec. Wiring Resistance RW (Ohms 0.16
Sec. Wiring Length (m) 76.00 Sec. Wiring Burden PW (VA) 0.09
Cable Material/Cross Area Cu/ 6mm2 Relays Total Burden Prelay (VA) 0.69
Cable Resistance (Ohms/km) 3.27 Others Burden Pother (VA) 5.00
Sec. Wiring Resistance RW (Ohms) 0.25 Total Burden Ptotal (VA) 5.78
Relays Resistance Rrelay (Ohms) 0.40
Terminals Resistance Rt (Ohms) 0.20
CT Sec. Resistance RCT (Ohms) 0.35
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.07
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 7.58
Resultant Fault Voltage (V) 726.71
Resultant CT Burden (VA) 35.99
Eq. Burden on one CT core CT's PT's
Relay P442 (connected to other CT core) 0.00 0.0300 * As per Dwg.XXXX
Relay DBF 0.10 0.0000 ** As per DwgXXXX
Relay D60 0.20 0.2500
Relay MIV 0.10 0.2000
Relay DRS 0.00 0.2000 Does not impose load on CT's
Unit D25 UCL 0.00 0.0000 Connected to CT measure core
Unit D25 OSC (connected to other CT core) 0.00 0.0000
Unit AINRTAL 0.00 0.0100
TOTAL (VA) 0.40 0.6900
TOTAL (Ohms) 0.40

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S/S XXXX
Capacitive Voltage Transformer
Instrument Transformer XXXX
Location S/S XXXX
Transmission Line VBusbar 220kV Measuring
Rated Frequency (Hz) 50.00
CVT Ratio 2200 ('220000/? 3:100/? 3)
CVT Rated Sec. Voltage (V) 57.73
CVT Actual Burden (VA) 50.00 *
CVT Class 3P *
Sec. Wiring Length (m) 98.00
Cable Material/Cross Area Cu/6 mm2

Cable Resistance (Ohms/km) 3.2700

Sec. Wiring Resistance RW (Ohms) 0.3205
Sec. Wiring Burden PW (VA) 0.0000
Relays Total Burden Prelay (VA) 0.4000 TR-1 and TR-2 voltage loads
Others Burden Pother (VA) 5.0000 Estimated
Total Burden Ptotal (VA) 5.4000

Equipment Burden
- General Measuring
- Voltage Elements of TR-1 and TR-2
* As per Dwg. XXXX

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S/S XXXX S/S XXXX

Current Transformer Inductive Voltage Transformer
Fault Location Fwd.-Close-in Instrument Transforme
Instrument Transformer XXXX Loc at ion XXXX
Location S/SXXXX Bay XXXX
Bay XXXX Rated Frequency (Hz) 50.00
Rated Frequency (Hz) 50.00 CVT Ratio 600 ('60000/? 3:100/? 3)
SC Iac rms Value (kA) 25.00 CVT Rated Sec. Voltage (V) 57.73
SC IEffective Peak Value (kA) 43.30 CVT Actual Burden (VA) 50.00 *
CT Ratio 500.00 * CVT Class 3P *
CT Rated Sec. Current (A) 1.00 * Sec. Wiring Length (m) 68.00
CT Actual Burden (VA) 30.00 * Cable Material/Cross Area Cu/6 mm2

CT Class 5P15 * Cable Resistance (Ohms/km) 3.27

CT Actual Knee Point (V) 450.00 Sec. Wiring Resistance RW (Ohm 0.22
Sec. Wiring Length (m) 68.00 Sec. Wiring Burden PW (VA) 0.13
2
Cable Material/Cross Area Cu/ 6mm Relays Total Burden Prelay (VA) 0.69
Cable Resistance (Ohms/km) 3.27 Others Burden Pother (VA) 5.00
Sec. Wiring Resistance RW (Ohms) 0.22 Total Burden Ptotal (VA) 5.82
Relays Resistance Rrelay (Ohms) 0.24
Terminals Resistance Rt (Ohms) 0.50
CT Sec. Resistance RCT (Ohms) 0.50
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.02
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 5.46
Resultant Fault Voltage (V) 399.43
Resultant CT Burden (VA) 26.13
Equipment Burden (VA) CT's PT's
Relay P442 0.0400 0.0300
Relay D60 0.2000 0.2500
Relay MIV 0.0000 0.2000
Relay DRS 0.0000 0.2000
Unit D25 UCL 0.0000 0.0000 Connected to CT measure core
Unit AINRTAL 0.0006 0.0100
TOTAL (VA) 0.2406 0.6900
TOTAL (Ohms) 0.2406
* As per Dwg. XXXX

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S/S XXXX
Current Transformer
Fault Location Fwd.-Close-in
Instrument Transformer XXXX
Location S/S XXXX
Bay Transformer
Rated Frequency (Hz) 50.00
SC Iac rms Value (kA) 25.00
SC IEffective Peak Value (kA) 43.30
CT Ratio 1000.00 *
CT Rated Sec. Current (A) 1.00 *
CT Actual Burden (VA) 30.00 *
CT Class 5P15 *
CT Actual Knee Point (V) 450.00
Sec. Wiring Length (m) 68.00
Cable Material/Cross Area Cu/ 6mm2
Cable Resistance (Ohms/km) 3.27
Sec. Wiring Resistance RW (Ohms) 0.22
Relays Resistance Rrelay (Ohms) 0.47
Terminals Resistance Rt (Ohms) 0.50
CT Sec. Resistance RCT (Ohms) 0.50
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.10
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 7.92
Resultant Fault Voltage (V) 335.17
Resultant CT Burden (VA) 21.84
Equipment Burden (VA) CT's PT's
Relay SMO1000(2) 0.1000 0.2000
Relay MLJ 0.0000 0.1500
Unit KVGC 202 0.0200 14.0000
Unit D25 UCL 0.0000 0.0000 Connected to CT measure core
Relay MIFP 0.2000 0.0000
Unit AINRTAL 0.0006 0.0100
Relay DTP (Restraint for Sec. Wdg.) 0.1500 0.0000
TOTAL (VA) 0.4706 14.3600
TOTAL (Ohm,s) 0.4706 Vsignal taken from CVT's
* As per Dwg. XXXX at Bu sbar 60 kV Bay

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S/S XXXX S/S XXXX

Current Transformer Inductive Voltage Transformer
Fault Location Fwd.-Close-in Instrument Transforme 72,5
Instrument Transformer XXXX Loc atioXXXX
n S/S XXXX Bay Coupling
Bay Coupling Rated Frequency (Hz) 50.00
Rated Frequency (Hz) 50.00 CVT Ratio 600 ('60000/? 3:100/? 3)
SC Iac rms Value (kA) 25.00 CVT Rated Sec. Voltage (V) 57.73
SC IEffective Peak Value (kA) 43.30 CVT Rated Burden (VA) 50.00
CT Ratio 1000.00 * CVT Class 0.50
CT Rated Sec. Current (A) 1.00 * Sec. Wiring Length (m) 68.00
CT Actual Burden (VA) 30.00 * Cable Material/Cross Area Cu/6 mm2

CT Class 5P15 * Cable Resistance (Ohms/km) 3.27

CT Actual Knee Point (V) 450.00 Sec. Wiring Resistance RW (Ohms) 0.22
Sec. Wiring Length (m) 94.00 Sec. Wiring Burden PW (VA) 0.00
Cable Material/Cross Area Cu/ 6mm2 Relays Total Burden Prelay (VA) 0.01
Cable Resistance (Ohms/km) 3.27 Others Burden Pother (VA) 5.00
Sec. Wiring Resistance RW (Ohms) 0.31 Total Burden Ptotal (VA) 5.01
Relays Resistance Rrelay (Ohms) 0.10
Terminals Resistance Rt (Ohms) 0.50
CT Sec. Resistance RCT (Ohms) 0.50
Others Resistance (Ohms) 0.00
Primary Time Constant τP (s) 0.02
Secondary Time Constant τs (s) 3.00
Relay Tripping Time (s) 0.025
CT Dimensioning Factor Ks 5.46
Resultant Fault Voltage (V) 192.21
Resultant CT Burden (VA) 12.31
Equipment Burden (VA) CT's PT's
Relay SMO1000 0.1000 0.2000
Relay MLJ 0.0000 0.1500
Unit D25 UCL 0.0000 0.0000 Connected to CT measure core
Unit AINRTAL 0.0006 0.0100
TOTAL (VA) 0.1006 0.3600
TOTAL (Ohm,s) 0.1006
* As per Dwg. XXXX

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S/S XXXX
Inductive Voltage Transformer
Instrument Transformer XXXX
Location S/S XXXX
Bay VBusbar 60 kV Measuring
Rated Frequency (Hz) 50.00
CVT Ratio 600 ('60000/? 3:100/? 3)
CVT Rated Sec. Voltage (V) 57.73
CVT Actual Burden (VA) 50.00 *
CVT Class 3P *
Sec. Wiring Length (m) 68.00
Cable Material/Cross Area Cu/6 mm2

Cable Resistance (Ohms/km) 3.270

Sec. Wiring Resistance RW (Ohms) 0.222
Sec. Wiring Burden PW (VA) 0.055
Relays Total Burden Prelay (VA) 28.720 TR-1 and TR-2 voltage loads
Others Burden Pother (VA) 5.00
Total Burden Ptotal (VA) 33.775

Equipment Burdens
- General Measuring
- Voltage Elements of TR-1 and TR-2 in 60 kV
* As per Dwg. XXXX

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Comments and Conclusions

S/S XXXX

There are not specific plant drawings available for these substations. Therefore for the wiring resistance
calculation (in each typical bay) the distances from CT’s/PT’s to the relay houses are the same used in XXXX
substation (Substation Plant drawing available).
It was assumed that the cable from the CT’s/PT’s secondary winding up to the relays is 6 mm2 cross section area
(commonly used in substations).
The primary and secondary time constants were taken from typical values for installations of similar rated
voltages as follows:
• 220 kV Line Zone CT’s 70 ms
• 220 kV Power Transformer Zone CT’s 100 ms
• 220 kV Transfer Zone CT’s 70 ms
• 60 kV Feeder Zone CT’s 20 ms
• 60 kV Coupling Zone CT’s 20 ms
• 60 kV Power Transformer CT’s 100 ms
•
The departure values of three-phase short-circuit fault values were:
• 40 kA for 220 kV
• 25 kA for 60 kV
The CT secondary resistance value was taken from similar CT’s for the different rated voltages, since no
specific data was available at the date of this document.
Current and voltage signals for relays/control in 220 kV Lines are taken from their specific CT’s and CVT’s.
Voltage signals for relays/control in 220 kV Transfer and Couplings Bays are taken from their specific CVT’s.
Voltage signals for relays/control/Voltage regulation in 220 kV Transformer Bay are taken from the inductive
PT’s installed in 220 kV busbar.
Current and voltage signals for relays/control in 60 kV Transformer Bay are taken from its combine CT/PT
instrument transformer.
Current and voltage signals for relays/control in 60 kV Coupling and Feeders Bays are taken from their
combine CT/PT instrument transformers.
The power transformers are shown inside a dashed line square in the single line diagrams. It also is shown the
primary CT with a CT ratio (i. e 400/1A). These CT ratios does not match with the CT ratios
shown in TRENCH drawings (500/1 or 1000/1). In the spreadsheets
the value used was 500/1.
PT characteristics verification was done for 220 kV and 60 kV zones in both substations
The resultant or equivalent burden calculated at the end of each table is the burden to guarantee that
during faults with severe dc component, the CT’s will sustain the secondary current without distortion to
allow the relays to trip before to go into saturation. The factor Ks is therefore the over-dimensioning
factor to be used to choose the final equivalent burden of CT’s.
Recall that spite different filtering action in the relays (including Fourier Transform) allows to work only with
the fundamental component of current, the presence of dc offset in the current signal make the CT to saturate
early before than with equivalent pure ac component. The CT will saturate but also the dc exponential
component distorts the CT transformation ratio in such a way that:

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IPr imary ac
ISec ac ≠
CTratio
and therefore dependent measuring devices might not work properly due this external error.

From the spreadsheets the meaning of coloured cells is:

Values assumed or taken from similar installations.

Resultant burdens lower than the actual rated burden (CT/PT sufficiently dimensioned)

Resultant burdens higher than the actual rated burden (CT/PT under dimensioned). Need changes

Since the minimum CT ratio was used which is the worst case (except for couplings or PT), for the under
dimensioned CT’s it is suggested to:
• Check the real distances CT-Relay in order to reduce the wiring resistance.
• Check the CT secondary resistance regarding the real value provided by the manufacturer.
• Change the CT Class to the next standard step.
• Change the CT burden to the next higher rated burden.
By decreasing the cable, terminal and CT secondary resistances the resultant burden of CT’s in 220 kV lines will
be lower and therefore will match the actual rated burden. However for power transformer and couplings in 220
kV it will be required changes in the Class or the rated burden of CT’s.

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Table 1
Substation XXXX
Bay CT Ratio Resultant CT Burden Actions
220 kV - T. Line 500/1 22.33 VA No actions
220 kV - Transformer 500/1 31.33 VA Change to 5P30
220 kV - Transfer 500/1 28.94 VA No actions
60 kV - Feeder 500/1 18.28 VA No actions
60 kV - Transformer 1000/1 17.51 VA No actions
60 kV - Coupling 1000/1 8.35 VA No actions
Substation XXXX
220 kV – T. Line 500/1 24.14 VA No actions
220 kV – Transformer 500/1 38.56 VA Change to 5P30 or to 40 VA
220 kV - Coupling 1000/1 11.37 VA No actions
60 kV - Feeder 400/1 20.70 VA No actions
60 kV - Transformer 1000/1 13.86 VA No actions
60 kV - Coupling 1000/1 7.01 VA No actions
60 kV TR-3 PT 500/1 36.08 VA Change to 5P20

♦ The PT’s or CVT’s are not subjected to the effects of short-circuits, and therefore it is necessary only to consider
the maximum load connected to their secondary to define the burden without any over-dimensioning factor.
♦ The CT characteristics for other bays not shown in the table, must keep the same requirements if their secondary
burdens and CT ratios are the same.
♦ CT’s for 24 kV zones

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CT Dimensioning - Basis

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DIMENSIONING OF CURRENT TRANSFORMERS FOR PROTECTION

APPLICATION
1. Transients on Current Transformers - Fundamentals
More than the steady state under load conditions of the CT’s, the main concern is about the fault conditions when the
protections installed in their secondaries must respond correctly to the short-circuit transient, specially during the first
cycles. Because of this, it is necessary to define how much a CT must be oversized in order to avoid the saturation
due to the asymmetrical component of the fault current (the dc offset or exponential component).

The initial value of this dc offset depending on the voltage incidence angle (the voltage value when the fault occurs), and the line
parameters may be between 0 and √2*Isc, being Isc the rms value of the short-circuit symmetrical current.

Considering this maximum value, the transient short-circuit current is defined by the following equation:

−t
i ( t ) = I* Sin (ωt + α − θ ) − I * Sin (α − θ ) * e τ 1 (1)

Where:

I= Peak value of current

ω= 2*π*f
α= angle on voltage wave at which fault occurs
θ= arctan (ω*X/R)
T1 = X/R (of power system)

Assuming that the secondary load is essentially resistive, the necessary flux in the CT to avoid saturation is defined
by the following expression:

ϕT = ϕA [ ωT1T2  e T − e T 
]
−ts −ts
1 2  − Sin ωt (2)
T1 −T2  

Where:
T1 = Line time constant or primary time constant = L/R
T2 = CT time constant or secondary time constant
ϕA = Peak value of symmetrical ac flux
ts = Any given time during which maximum transient flux will remain
without CT saturation, or the time after which saturation is permitted.

For T2 >> T1 (the case of TPY and TPX class CT’s – with and without air gaps),

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the equation (2) turns to:

 −t s

ϕT = ϕA [ ωT1 1 −

e T1  − Sin ωt ]

(3)

As the load and wiring are mainly resistive, we can consider Sin ωt = -1; and then equation (3) is reduced to:
 −ts 
ϕ T = ϕ A [ ωT1 1 − e T  + 1] 1
 
Finally because Ts (relay response time + Circuit Breaker operating time) is normally much higher than T1, the expression can be
reduced as follows:

ϕ T = ϕ A (ωT1 + 1) (4)

During faults the CT’s will be forced to develop a flux necessary to feed fault current to the secondary with two components: the
exponential (dc offset asymmetrical component ) and the ac component (symmetrical component). The resultant voltage must be
higher than that necessary to feed the load connected in the secondary side of CT’s without distortions caused by saturation.
Hence, the necessary oversize factor Ks is defined by:

ϕ transient = ϕ dc + ϕ ac = * Ks ϕ ac
where the overdimensioning or transient factor is:

 −ts

Ks = ω T1 1 −

e T1  − Sin ω t

(5)

2. Resultant Voltages on CT Secondaries During Faults

In general, testing and experience have shown that the performance of many relays will not be adversely affected by moderate
degrees of CT saturation. However, since it is not economically feasible to test and determine the performance of all types of
relays with different degrees of saturation, it is common practice to specify CT requirements for various protective schemes. The
requirement generally specified is that the CTs should not saturate before the relays operate for some specified fault location.
To meet this criteria, the required transient performance for a current transformer can be specified by calculating the minimum
required saturation voltage. In general different standards as IEC 185, BS3938 or ANSI/IEEE C5713 fix this voltage by the
general expression:

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V s = k 0 k s kR I2 R 2 (6)

where:

Vs = Saturation voltage as defined by the intersection point of the extensions of the straight line portions (the unsaturated
and the saturated regions) of the excitation curve

I2 = Symmetrical fault current in secondary Amperes

R2 = Total secondary resistance burden including CT secondary, wiring loop resistance, lead resistance and load resistance.

ω T1 T2  −Tt1s −t s

ks = Saturation or transient factor =  e − e T 2  + 1 (as per Eq. 2)
T1 − T2  

where

T2 = Secondary time constant

T1 = Time constant of the dc component of fault component. It is proportional to the X/R ratio of the system.

ω= System angular frequency

ts = Time to saturation. This is equal or greater than the relay operating time.

K0 = Represents the effect of the offset present during the fault. This offset is a function of the time when the fault occurs,
being maximum at zero voltage (0º or 180º). Experience states that the incidence angle of the faulted voltage is near
90º that produce a lower offset effect. Therefore this factor will apply in those cases where offset exceeds 0.5 p.u

KR = Remanent flux factor. The remanent flux can remain in the core due to the following:

• The excitation current leads the load current by 90º and thereby under normal control open commands,
the load current is cut near or at zero crosses, but the excitation current in the CT has significant value.

• DC tests performed on the CT’s

• The effect of the dc component on offset fault currents (exponential component) which is interrupted
when tripping the circuit breaker.

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Equation (2) is valid for CTs with air-gapped cores because of their low magnetizing impedance and then with low secondary time
constant T2. The air-gaps used in CTs tends to reduce drastically the effect of the remanent flux left in the core due to its lower
magnetizing impedance and therefore much lower secondary time constant. The effect of the remanent flux is also to reduce the
time to saturation. This factor may vary from 1.4 to 2.6 times the rated flux in the core.

For a closed-core CTs (normal CT’s), the secondary time constant T2 is too high (Lmagnetizing ≈ ∞ before saturation), equation (5)
does not include it, and then a conservative value for time to saturation will result.

3. Time to Maximum Flux – Time to Saturation

After the initiation of the short-circuit the flux β0 and the corresponding magnetizing current I0 will reach a maximum at a time
defined by:

 T1 ∗T2   T1 
t φ m a x =   l n   (7)
 T1 −T2   T2 

Finally the time to saturation is given by the following expression:

X / R  K s − 1
ts = − ln  1−  (8 )
2 π f  X / R 

Where:

Ks = VSaturation/( Ifault * R2)

VSaturation = Saturation voltage as defined in page 5

Ifault = Secondary fault current

R2 = Total loop resistance as defined in page 5

X/R = Reactance to resistance ratio of any given circuit, generator, etc. See Tables 1 or 2 and
specific curves herein enclosed.

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The decrement or rate of decay of the d-c component is proportional to the ratio of reactance to resistance of the complete circuit
from the generator (source) to the short-circuit.

If the ratio of reactance to resistance is infinite (i.e zero resistance), the d-c component never decays. On the other
hand, if the ratio is zero (all resistance, no reactance), it decays inmediately. For any ratio of reactance to resistance
in between these limits, the d-c component takes a definite time to decrease to zero.

In generators the ratio of subtransient reactance to resistance may be as much as 70:1; so it takes several cycles for the d-c
component to disappear. /*In circuits remote from generators, the ratio of reactance to resistance is lower, and the d-c
component decays more rapidly. The higher the resistance in proportion to the reactance, the more I2R loss from the d-c
component, and the energy of the direct current is dissipated sooner.

Often said that generators, motors, or circuits have a certain d-c time constant. This refers again to the rate of decay of the d-c
component. The d-c time constant is the time, in seconds, required by the d-c component to reduce to about 37% of its
original value at the instant of short circuit. It is the ratio of the inductance in Henrys [V*s/A] to the resistance in Ohms
(Ω) of the machine or circuit. This is merely a guide to show how fast the d-c component decays.

Typical values of X/R ratios of distribution and transmission lines depending on their rated voltages and geometrical configuration
are shown in Table 1.

TABLE 1

Sequence X/R Ratios for Distribution and Transmission Lines

69 kV (Avg.) 115 kV (Avg.) 138 kV (Avg.) 230 kV (Avg.) 380 kV (Line Type) 500 kV (Line Type)

X1/R1 2.30 3.40 3.98 7.36 9.80 (Hor.) 24.3 (Hor.)

9.6 (Delta) 18.5 (Vert.l)

X0/R0 1.95 3.05 4.23 4.08 3.2 (Hor.) 3.5 (Hor.)

3.3 (Delta) 5.0 (Vert.)

Table 2 shows X/R ratios for generators, transformers, etc. as a function of their rated power.

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TABLE 2
X/R Ratios for Other Power System Elements

Large Power Reactors

Generators Transformers 1.1.1.1.1 Utilities

40-120 See Curve 40-120 15-30

Typical 80 Typical 80 (near generating plant)

Power Transformer X/R Ratios

10
9
8
7
X/R Ratios

6
5
4
3
2
1
0
0 0.5 1 1.5 2 2.5 3 3.5

ONAN MVA Rating (0.03-3 MVA)

Power Transformer X/R Ratios

50

40
X/R Ratio

30

20

10

0
0 50 100 150 200 250

ONAN MVA Rating (3-200 MVA)

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4. Tripping Times of Protection Devices

Instantaneous units of overcurrent (50) and distance protections normally operates in 15 to 30 ms, and therefore dimensioning
factors must consider that the relay tripping times should be lower than time to saturation ts Therefore to guarantee the correct
operation of protection devices the equation (2) must be applied choosing as parameter t the instantaneous operating times of the
different relays. Table 3 shows typical tripping times for different GE relays and the necessary overdimensioning factor Ks using
CT class TPX with a secondary time constant T2 = 3 seconds.

TABLE 3

Relay Instantaneous Primary Time Constant Overdimensioning

Operating Time T1 Factor
(s) (after which saturation is permitted) Ks

MIC/MRC 25 ms 40 ms 6.81

“ “ 60 ms 7.39

“ “ 70 ms 7.57

“ 80 ms 7.72

DLP 20 ms 70ms 6.45

ALPS 10 ms 70ms 3.92

DGP 25 ms 70ms 7.57

SR489 45 ms 70ms 11.34

SMOR 25ms 70ms 7.57

DTP 45ms 70ms 11.34

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5. Resultant Fault Voltages and CT Dimensioning

With results shown in TABLE 3 and neglecting factors K0 and KR for equation (6), the next lines describe the way to find the
resultant “Precision Limit” and the necessary overdimensioning of the CT core (rated power dimensioning) to avoid saturation
previous to the tripping time of relays under consideration.

If assumes that the phase-to-phase short-circuit current is of the same order of magnitude than the phase-to-ground short-circuit
current, then a single equation should be used. If not Ks factor must be verified for both situations: the positive sequence
component during three-phase faults as well as the zero sequence component for phase-to-ground faults. In the present case
will use equation (6) for all:

Example

Being:

Ks = 6.18 Vrated = 13.8 kV, 50 Hz

Relay Resistance: 0.04Ω Pshortcircuit = 0.597 GVA (assumed)

CT Ratio: 600/1 CT Class: 5P20

CT Secondary Winding Resistance: 1.5Ω (assumed)

Lwiring: 2 * 10m (6 mm2 cross section cable) (assumed)

Rwiring = 0.059Ω

K0 not considered KR not considered

V s = k 0 k s kR I 2 R 2

PSC
3 V rated
Vs = K s (RC T +R W +RR ) = 24976/600 (1.5Ω + 0.059Ω + 0.04Ω) = 411 V
CTratio

 411 
 
. Ω ∗ (1) = 19 VA
Equivalent Power:  20 − 15
2

 1A 
 

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6. Terms and Definitions

6.1 Rated Primary Short-circuit Current (IPrimarysc)

RMS value of the primary symmetrical short-circuit current on which the rated accuracy performance of the
current transformer is based.
6.2 Instantaneous Error Current (Iε)

Difference between instantaneous values of the primary current and the product of the turns ratio times the
instantaneous values of the secondary current. When both alternating current and direct current
components are present, Iε must be computed as the sum of both constituent components:

Iε = Iε ac + Iε dc = ( n * ISecondary ac - IPrimary ac ) + (n * ISecondary dc - IPrimary dc )

6.3 Peak Instantaneous Error (ξi)

Maximum instantaneous error current for the specified duty cycle, expressed as a percentage of the peak
instantaneous value of the rated primary short-circuit current
6.4 Peak Instantaneous Alternating Current Component Error (ξac)

Maximum instantaneous error of the alternating current component expressed as a percentage of the peak
instantaneous value of the rated primary short-circuit current.

ξac = 100 * Iε ac / (√2 * IPrimary Short-circuit) (%)

6.5 Accuracy Class

Defined by the “Class Index” followed by the letter P

6.6 Class Index

Accuracy limit defined by composite error (ξc) with the steady state symmetrical primary current. This number indicates the upper
limit of the composite error at the maximum accuracy current feeding the accuracy load. The standard class indexes are 5 and
10.
No limit for remnant flux.
6.7 Limit Factor

Is the ratio between the limit accuracy current and the rated primary current. For protection applications this factor normally is 10
or 20

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6.8 Class P Current Transformer

Indicates “Protection” current transformers destined to feed protection relays. Accuracy limit is defined by
composite error ξac with steady state symmetrical primary current. There is no limit for remanent flux.
6.9 Class TPS Current Transformer

Low leakage flux current transformer for which performance is defined by the secondary excitation
characteristics and turns ratio error limits. There is no limit for remanent flux.
6.10 Class TPX Current transformer

Accuracy limit defined by peak instantaneous error (ξi) during specified transient duty cycle. There is no limit for remanent flux.
6.11 Class TPY Current Transformer

Accuracy limit defined by peak instantaneous error (ξi) during specified transient duty cycle. Remanent flux does not exceed
10% of the saturation flux.
6.12 Class TPZ Current Transformer

Accuracy limit defined by peak instantaneous alternating current component error (ξac) during single energization with maximum
dc. offset at specified secondary loop time constant. No requirements for dc. component error limit. Remanent flux to be
practically null.
6.13 Primary Time Constant (T1)

That specified value of the time constant of the dc. component of the primary current on which the
performance of the current transformer is based.
6.14 Secondary Loop Time Constant (T2)

Value of the time constant of the secondary loop of the current transformer obtained from the sum of the magnetizing and the
leakage inductance (Ls) and the secondary loop resistance (Rs).
Normally this value is higher as compared with T1 in TPS class current transformers (about 10s).
T2 will depend on the precision requirements but normally oscillates between 0.3 and 1 seconds for TPY class current
transformers.
Finally T2 is much more lower in TPZ class current transformers (about 0.07 seconds).
6.15 Time to Maximum Flux (t ϕ max)

Elapsed time during a prescribed energization period at which the transient flux in a current transformer
core achieves maximum value, it being assumed that saturation of the core does not occur.

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6.16 Secondary Winding Resistance (RCT)

Secondary winding dc. resistance in Ohms, corrected to 75º C, unless otherwise specified, and inclusive of
all external burden connected.
6.17 Secondary Loop or Burden Resistance (RB)

Total resistance of the secondary circuit, unless otherwise specified, and inclusive of all external burden
connected.
6.18 Low Leakage Flux Current Transformer

Current transformer for which a knowledge of the secondary excitation characteristic and secondary winding
resistance is sufficient for an assessment of its transient performance. This is true for any combination of
burden and duty cycle at rated or lower value of primary symmetrical short-circuit current up to the
theoretical limit of the current transformer determined from the secondary excitation characteristic.
6.19 Saturation Flux(ΨS)

That peak value of the flux which would exist in a core in the transition from the non-saturated to the fully
saturated condition. This regards to the point on the B-H characteristic of the core at which a 10% increase
in B causes H to be increased by 50%.
6.20 Remanent Flux (ΨR)

That value of flux which would remain in the core three minutes after the interruption of an exciting current
of sufficient magnitude as to induce the saturation flux (ΨS).

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