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Power System Protection
Dr. Lionel R. Orama Exclusa, PEWeek 2
Jan 25/2006 Copyright L.R. Orama 2006 2
CT Performance
Readings-Mason Chapter 7,pgs 99-115• Steady State (Symmetrical)
– Basics– Accuracy Classification– Effects on Accuracy– Evaluating CT performance
• Transient (Asymmetrical)– Time to Saturation
Copyright L.R. Orama 2006 3
Current Transformers (CT)
• CT produces current proportional to the system conductor current
• Ideal CT has:
• Rated ICT typically 5A (called the CT 2ry
current)
CT
SYSCT N
II =
Copyright L.R. Orama 2006 4
Current Transformers (CT’s)
4002000:5
2001000:5
120600:5
80400:5
40200:5
20100:5
1050:5
TurnsCurrent
Common ratios Polarity dot convention
Copyright L.R. Orama 2006 5
Current Transformers (CT)
36-550KV4000A
12-40KV2500A
5-25KV4000A
600V2000A
Copyright L.R. Orama 2006 6
CT Steady State PerformanceEquivalent circuit of a
bushing CT• CT is a toroid, leakage
flux is minimum– No leakage reactance
in circuit equivalent
• ZB is called the Burden (load)– Impedance in the
internal circuits of the relay
100% ×=CT
E
I
IRatioError
BCTT ZIV =
EP
CT IN
II −=
Jan 27/2006 Copyright L.R. Orama 2006 7
CT Accuracy ClassificationWith 20 times rated 2RY current
(5A X 20 = 100A), CT is classified on a basis of the VMAXit can sustain without exceeding a specified Ratio Error (RE)
• Example using line 2 on the table (10T20):– 10 is the %RE (at 20 times
Rated Current-100A)– 20 is the VMAX it can maintain
without exceeding the 10% RE (VRATING)
• T is for tested device• C for calculated device• RE < 10% for ICT < 100A and
ZB< VT/100A
100% ×=CT
E
I
IRatioError
CalcTest
10C80010T800
10C40010T400
10C20010T200
10C10010T100
10C5010T50
10C2010T20
10C1010T10
Copyright L.R. Orama 2006 8
Copyright L.R. Orama 2006 9
CT Accuracy Classification
• Determination of CT accuracy class– From CT Saturation Curve (120 turns)
• ICT=100A, IE=10A, ES=500V• VT=ES-100RCT (sat curve determines the RCT)
– Ex., if RCT=0.372ohm, then
• VT=500V-100A(0.372ohm)=463V
– CT Accuracy Class would be C400• Since from last table class jumps from 400 to 800
– This is true assuming all I’s, V’s & Z’s are in phase
Jan 30/2006 Copyright L.R. Orama 2006 10
CT Accuracy Classification
• True error at VT = RatingES=VT+ICTRCT
• At VT=800V & ICT=100A• RCT=(.0031ohm/turn)X240turns=0.774ohm• ES=800+100(0.744)=874V (on the curve)• IE=0.4A• %RE= IE /ICT X100=0.4%<10% (OK!)
Copyright L.R. Orama 2006 11
CT Accuracy Classification
( )
100×=
+
−=
−==
−=
+=
CT
E
BCTEP
S
BEP
BCTT
EP
CT
TCTCTS
I
IRE
ZRIN
IE
ZIN
IZIV
IN
II
VRIE
Accu.REIEESN
Accu.REIEESZB
Accu.REIEESRCT
Accu.REIEES
upIP
Accu.REIEES
The higher the turns ratio of the CT, the better the accuracy.
Copyright L.R. Orama 2006 12
CT Accuracy Classification
Is the CT adequate?
%10
100,100
100,100
<
<=
≤=
≤
RE
then
AIA
VZ
orA
VZAI
or
VV
CTRATING
B
RATINGBCT
RATINGT
Copyright L.R. Orama 2006 13
Evaluating CT Performance
( )
( ) ( )
ES
BCTEBCTP
S
BCTEP
S
EP
CTBCTCTCTS
BCTTTCTCTS
IKKE
ZRIZRN
IE
ZRIN
IE
IN
IIZIRIE
ZIVVRIE
21 −=
+−+=
+
−=
−=+=
=+=
L
L
Given IP and a relay IPU, calculate weather or not the relay will operate(ICT>IPU)
Copyright L.R. Orama 2006 14
Evaluating CT Performance
( )
2
1
1
2
1
21
0
0
K
KIE
KEI
ZRK
ZRN
IK
IKKE
ES
SE
BCT
BCTP
ES
=→=
=→=+=
+=
−=
Copyright L.R. Orama 2006 15
Evaluating CT Performance
else
II
if
IN
II
puCT
EP
CT
≥
−=
IE is the operating point of the relay atthe above conditions, then
Try another IPU setting or another N
IPU setting is OK!
Copyright L.R. Orama 2006 16
Transient Performance
Copyright L.R. Orama 2006 17
Transient Performancev t( )
V
10sin ω t⋅ θ+( )⋅:= i t( )
V
Zsin ω t⋅ θ+ φ−( ) sin θ φ−( ) exp
t−τ
⋅−
⋅:=
0 0.01 0.02 0.03 0.04 0.05 0.06
1000
500
500
1000Short Circuit Current (5mi dist. line)
time (s)
curr
ent (
A),
tent
h of
vol
tage
(V
)
i t( )
v t( )
t
3 Feb 2006 Copyright L.R. Orama 2006 18
Transient Performance• Offset fault current
* W.A. Elmore, Protective Relaying Theory & Application,Marcel Dekker, NY, 1982, pg. 80.
Copyright L.R. Orama 2006 19
Transient Performance
* W.A. Elmore, Protective Relaying Theory & Application,Marcel Dekker, NY, 1982, pg. 80. dt
dNe
φ−=
Copyright L.R. Orama 2006 20
Transient Performance
* W.A. Elmore, Protective Relaying Theory & Application,Marcel Dekker, NY, 1982, pg. 80.
Copyright L.R. Orama 2006 21
Transient Performance• Offset fault current
– CT response
* W.A. Elmore, Protective Relaying Theory & Application,Marcel Dekker, NY, 1982, pg. 80.
Copyright L.R. Orama 2006 22
Transient Performance
• CT Flux density for theasymmetrical fault current
−=
−
−⋅=
=
−
−
)cos(2
)sin(1
110
2
1
2
8
teIi
teAN
IRB
AB
DC
DC
t
t
DC
ω
ωω
τ
φ
τ
τ
B-Flux Density (lines/in2)
Total CT Burden (resistive)
Copyright L.R. Orama 2006 23
Transient Performance• Time to Saturation
2
8102
1ln
ANk
kIR
Bt
DC
SDC
⋅=
−−=
ττ BS-Saturation Flux Density
125,000 to 130,000 lines/in2
•States how long the CT will accurately reproduces the fault current•Time constant is that of the power system•R is the resistance of the CT + wiring
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