# CT Saturation Tutorial

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CT Saturation TutorialPresented by Tony Giuliante

Bushing CT

IS

IP

N Turns

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Physical Properties of CoreLength L Area A

B-H Characteristic

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B-H CharacteristicB

H

Flux to Volts per Turn=

s B

dA

= B A sin (t) V = d = B A cos (t) N dt

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Flux to Volts per Turn

V = BA N

Electric Field to Ampere Turns =

H

dL

= H L

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Convert B-H CharacteristicB V = BA N

= H L

H

V/N vs. NIV N

NI

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CT Exciting Characteristic2000:5

300:5

VS

IS

Simplified Bushing CT CircuitIS

IPN

REB

REB = RLEADS + RDEVICES

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Simplified Bushing CT CircuitRCT IS

IPN

XM IM

REB

Simplified Bushing CT CircuitIS

IPN

XM IM

V = IS RTB

RTB

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Flux vs VoltageV = N d dt 1 = N 1 = N

V

dt

IS RTB

dt

Flux vs Voltage1 = N

IS RTB

dt

Flux equals the AREA under the Voltage

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Voltage Demand IS RTB

Voltage & Flux WaveformsIS RTB

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Flux Design Limits+ S

- S

Secondary CurrentNo Saturation

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Increased Voltage Demand Five times IS RTB5*IS RTB

Flux for Ideal CTNo Saturation

5*IS RTB

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Current Output for Ideal CTNo SaturationPrimary Current Secondary Current

Amperes

Time (Seconds)

Flux Design Limits+ S - S

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Flux Design Limits+ S - S

Flux Excursion

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Current vs Flux

AC Saturation

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AC Saturation Large Fault Current Large Burden Low CT Kneepoint Voltage

AC SaturationRelay Applications Large Fault Current Unit Auxiliary Transformers

Large Burden High Impedance Bus Differentials

Low CT Kneepoint Voltage Compact Distribution Switchgear

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Unit Auxiliary TransformersG

87UAT

DC OffsetTransformer

Fault current includes a dc component, or offset, that makes the current asymmetrical. L/R = 100 ms X/R = 37.7

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Offset Current vs FluxPrimary Current Flux Sec. Amperes or Flux Density

Time (Seconds)

Secondary CurrentPrimary Current Secondary Current

Amperes

Time (Seconds)

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Secondary Current Observations Secondary current is distorted due to the core flux saturation Secondary current distorts after a short time (time-to-saturation) Distortion slowly dissipates as primary dc offset decays

Secondary Current 100 Amps 50 0 -50 0 2 Tesla 1 0 -1 0 1 2 3 4 Cycles 5 6 7 I SEC 1 2 3 4 5 6 Magnetic Flux Density (B) 7 I PRIM

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Large Differential CurrentSecondary Current Primary Current

Amperes

Differential Current

Time (Seconds)

DC Saturation Factors Large DC Time Constant Large Burden Low CT Kneepoint Voltage High Remanent Flux

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Remanent Flux Trapped magnetic flux in core if a previous offset current is interrupted before reaching a symmetrical state High X/R ratios make remanent flux more likely due to the slow decay rates of offset current

Remanent Flux SurveyRemanent flux in % of saturation 0 - 20 21 - 40 41 - 60 61 - 80 Percentage of cts 39 18 16 27

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Remanent Flux Example CT data 1200:5, C800, burden = 1.6 +j 0.7 ohm

Fault current 24,000 amps with dc offset X/R ratio = 19 Display ct secondary output current for remanence of 0%, 50% and 75% of saturation

0% Remanent FluxPrimary Current Secondary Current

Amperes

Time (Seconds)

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50% Remanent FluxPrimary Current Secondary Current

Amperes

Time (Seconds)

75% Remanent FluxPrimary Current Secondary Current

Amperes

Time (Seconds)

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Remanent Flux ResultsRemanent flux 0% 50% 75% Time-to-saturation 1+ cycles 1/2 cycle 1/3 cycle

IEEE Guide for the Application of Current Transformers Used for Protective Relaying Purposes C37.110-1996

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CT Classification

CT Accuracy Class ANSI defines accuracy rating classes by a letter and number C100, C800 or T100, etc. Letter designates how the accuracy can be determined Number designates the minimum secondary terminal voltage under a standard burden

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Accuracy Class Letter C means by Calculation non-gapped cores with negligible leakage flux, such as bushing cts

T means by Test cts with leakage flux, such as cts with wound primaries

Old classes H and LH T and L C

Accuracy Class Number Minimum secondary terminal voltage produced at 20 times rated current into a standard burden without exceeding a 10% ratio correction factor

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What is a Standard Burden? IEEE Standard Requirements for Instrument Transformers C57.13-1993 the standard relaying burdens are 1, 2, 4 and 8 ohms at a lagging 0.5 p.f. 20 times rated secondary current of 5 A is 100 A, and 100 A times the standard burdens yield C ratings of 100, 200, 400 and 800 V

CT Knee Point Voltages45o Tangent A B 300:5 2000:5

VS

IS

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Knee Point Definitions Point A is the ANSI knee point voltage point tangent to 45 degree slope line

Point B is the IEC knee point where a 10% increase in voltage causes a 50 % increase in current

IEC knee point is higher than ANSI knee point

CT Excitation Impedance Excitation curve represents the exciting impedance in terms of voltage and current The ANSI knee point (A) represents the point of maximum permeability of the iron core

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Examples Determine Accuracy Class Selecting CT Ratings Calculating Time to Saturation

Example - Find Accuracy Class Find the approximate ct accuracy class from the excitation curve the C class is defined for a 10% ratio correction factor at 20 times rated current 10% of (20 X 5 A) is 10 A for IE = 10 A, use the excitation curve to find VS as about 500 V

next find the ct terminal voltage by subtracting the internal voltage drop from VS (continued)

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Example - Equivalent CircuitIP VS = 500 IS = 100 A IE = 10 A VB = ? ZB

Example - continued VB (voltage to the burden)VB = VS - (IS X RS) VB = 500 - (100 X 0.61) VB = 439 V

The approximate ct accuracy class is the next lowest ANSI class number (C400)

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Examples Determine Accuracy Class Selecting CT Ratings Calculating Time to Saturation

Avoiding CT SaturationVX > IS ZTB (1 + X/R)VX = saturation voltage IS = secondary current ZTB = total ct secondary burden

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CTs for Generator Differentials For generators, typically cts cannot be sized to avoid saturation because of: high fault current high X/R ratio

Common applications would: select adequate ct primary rating select highest practical C class match manufacturer and types of cts

Examples Determine Accuracy Class Selecting CT Ratings Calculating Time to Saturation

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Transient Response of Current TransformersPower Systems Relaying Committee

Time to Saturate Equation

VK I F R TB

( I - KR )

=

TCT TST CT - T S

{

e

-t TCT

-e

-t TS

}

+1

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VKVK 2000:5 Tangents Intersect 300:5

VS

IS

Saturation ParametersR TB = RCT + R LEADS +R DEVICES I F = FAULT CURRENT (SEC RMS AMPS) KR =

{

.5 - .75 IRON CORE .1 AIR GAP

= 377L TCT = M R TB

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VM & I M45o Tangent VM 300:5 2000:5

VS

IM

IS

CT InductanceLM TCT = RTB VM

XM =

IMXM

LM =

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DC Offsets

DC Offset Current Depends on where in the voltage wave the fault occurs. Fault time is defined as: F I A => Fault Initiation Angle

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Voltage WaveformFIA

0

45

90 4.16

135 180 225 270 345 360 8.33 12.5

Degrees

60 Hz

0

16.67 Time ms

Voltage WaveformFIA

0

45

90 5

135 180 225 270 345 360 10 15

Degrees

50 Hz

0

20 Time ms

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Power SystemR L

G

Z = R2 + X2 = ARCTAN ( L / R)

Power SystemR L

G

= Characteristic Angle

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Fault at FIA = No OffsetR L

G

Current Waveform No Offset FIA = 2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

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Fault at FIA = 90 Max OffsetR L

G

Current Waveform Max Offset FIA = + 902 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

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Total Current2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

Equationsv(t) = Vmax * sin ( Wt + Close_Ang ) i (t) = i ss (t) + i trans (t) i ss (t) = [ Vmax / Z ] * sin ( Wt + Alpha ) Alpha = Close_Ang - ArcTan ( WL/R ) i trans (t) = [ e^ (-R/L) t ] * [ -Vmax / Z ] * sin ( Alpha )

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Power System Time ConstantsL/R (MS) 1 2 5 10 30 100 200 400 1000 X/R 0.377 0.754 1.885 3.770 11.310 37.699 75.398 150.796 376.991 Ang (deg) 20.66 37.02 62.05 75.14 84.95 88.48 89.24 89.62 89.85 Power System High Fault Resistance Distribution Lines Subtransmission Lines EHV Lines Transformers Generators Large Generators

Subtransmission Line L/R = 10 ms2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

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Generator L/R = 200 ms2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

EHV Line L/R = 30 ms2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

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Distribution Line L/R = 5 ms2 1

0 Current

-1

-2

-3 0 10 20 Time - Milliseconds 30 40 50

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