Formula Sheets: Instrument Transformers | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

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Electrical an d Electronic Measuremen ts: Instrumen t
T ransformers F orm ula Sheet for Electrical GA TE
Curren t T ransformer (CT)
• Curren t Ratio : Relationship b et w een primary and secondary curren ts.
I
p
I
s
=
N
s
N
p
where I
p
is primary curren t (A ), I
s
is secondary curren t (A ), N
p
is primary turns, N
s
is secondary turns.
• Nominal Ratio : Ideal turns ratio.
K
n
=
N
s
N
p
where K
n
is nominal curren t ratio.
• A ctual Ratio : A ccoun ts for losses and magnetizing curren t.
K
a
=
I
p
I
s
• Ratio Error : Deviation from nominal ratio.
Ratio Error (%) =
K
n
-K
a
K
a
×100
• Burden : Load on secondary in V A.
Burden =I
2
s
·Z
b
where Z
b
is burden imp edance (? ), t ypically including secondary circuit resistance
and reactance.
• Phase Angle Error : Angle b et w een primary and secondary curren ts.
?˜
I
m
sin?
I
s
where I
m
is magnetizing curren t (A ), ? is phase angle of burden imp edance (
?
).
P oten tial T ransformer (PT)
• V oltage Ratio : Relationship b et w een primary and secondary v oltages.
V
p
V
s
=
N
p
N
s
where V
p
is primary v oltage (V ), V
s
is secondary v oltage (V ), N
p
is primary turns, N
s
is secondary turns.
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Page 2


Electrical an d Electronic Measuremen ts: Instrumen t
T ransformers F orm ula Sheet for Electrical GA TE
Curren t T ransformer (CT)
• Curren t Ratio : Relationship b et w een primary and secondary curren ts.
I
p
I
s
=
N
s
N
p
where I
p
is primary curren t (A ), I
s
is secondary curren t (A ), N
p
is primary turns, N
s
is secondary turns.
• Nominal Ratio : Ideal turns ratio.
K
n
=
N
s
N
p
where K
n
is nominal curren t ratio.
• A ctual Ratio : A ccoun ts for losses and magnetizing curren t.
K
a
=
I
p
I
s
• Ratio Error : Deviation from nominal ratio.
Ratio Error (%) =
K
n
-K
a
K
a
×100
• Burden : Load on secondary in V A.
Burden =I
2
s
·Z
b
where Z
b
is burden imp edance (? ), t ypically including secondary circuit resistance
and reactance.
• Phase Angle Error : Angle b et w een primary and secondary curren ts.
?˜
I
m
sin?
I
s
where I
m
is magnetizing curren t (A ), ? is phase angle of burden imp edance (
?
).
P oten tial T ransformer (PT)
• V oltage Ratio : Relationship b et w een primary and secondary v oltages.
V
p
V
s
=
N
p
N
s
where V
p
is primary v oltage (V ), V
s
is secondary v oltage (V ), N
p
is primary turns, N
s
is secondary turns.
1
• Nominal Ratio : Ideal turns ratio.
K
n
=
N
p
N
s
where K
n
is nominal v oltage ratio.
• A ctual Ratio : A ccoun ts for losses and excitation curren t.
K
a
=
V
p
V
s
• Ratio Error : Deviation from nominal ratio.
Ratio Error (%) =
K
n
-K
a
K
a
×100
• Burden : Load on secondary in V A.
Burden =
V
2
s
Z
b
where Z
b
is burden imp edance (? ).
• Phase Angle Error : Angle b et w een primary and secondary v oltages.
?˜
I
m
cos?
V
s
/Z
b
where I
m
is excitation curren t (A ), ? is phase angle of burden imp edance.
P o w er M easuremen t with CT and PT
• W attmeter Reading : P o w er in a circuit using CT and PT.
P =V
s
I
s
cos?·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
where P is true p o w er (W ), V
s
is secondary v oltage, I
s
is secondary curren t, cos? is
p o w er factor.
• Three-Phase P o w er (T w o-W attmeter Metho d) :
P
total
=(W
1
+W
2
)·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
where W
1
,W
2
are w attmeter re adings.
Errors in Measuremen t
• T otal Error in P o w er Measuremen t : Com bines CT and PT errors.
T otal Error (%)˜ CT Ratio Error (%)+ PT Ratio Error (%)+ Phase Angle Error Effect
• Phase Angle Error Effect on P o w er :
P o w er Error (%)˜?
CT
+?
PT
·tan?
where ?
CT
,?
PT
are phase angle errors in radians.
2
Page 3


Electrical an d Electronic Measuremen ts: Instrumen t
T ransformers F orm ula Sheet for Electrical GA TE
Curren t T ransformer (CT)
• Curren t Ratio : Relationship b et w een primary and secondary curren ts.
I
p
I
s
=
N
s
N
p
where I
p
is primary curren t (A ), I
s
is secondary curren t (A ), N
p
is primary turns, N
s
is secondary turns.
• Nominal Ratio : Ideal turns ratio.
K
n
=
N
s
N
p
where K
n
is nominal curren t ratio.
• A ctual Ratio : A ccoun ts for losses and magnetizing curren t.
K
a
=
I
p
I
s
• Ratio Error : Deviation from nominal ratio.
Ratio Error (%) =
K
n
-K
a
K
a
×100
• Burden : Load on secondary in V A.
Burden =I
2
s
·Z
b
where Z
b
is burden imp edance (? ), t ypically including secondary circuit resistance
and reactance.
• Phase Angle Error : Angle b et w een primary and secondary curren ts.
?˜
I
m
sin?
I
s
where I
m
is magnetizing curren t (A ), ? is phase angle of burden imp edance (
?
).
P oten tial T ransformer (PT)
• V oltage Ratio : Relationship b et w een primary and secondary v oltages.
V
p
V
s
=
N
p
N
s
where V
p
is primary v oltage (V ), V
s
is secondary v oltage (V ), N
p
is primary turns, N
s
is secondary turns.
1
• Nominal Ratio : Ideal turns ratio.
K
n
=
N
p
N
s
where K
n
is nominal v oltage ratio.
• A ctual Ratio : A ccoun ts for losses and excitation curren t.
K
a
=
V
p
V
s
• Ratio Error : Deviation from nominal ratio.
Ratio Error (%) =
K
n
-K
a
K
a
×100
• Burden : Load on secondary in V A.
Burden =
V
2
s
Z
b
where Z
b
is burden imp edance (? ).
• Phase Angle Error : Angle b et w een primary and secondary v oltages.
?˜
I
m
cos?
V
s
/Z
b
where I
m
is excitation curren t (A ), ? is phase angle of burden imp edance.
P o w er M easuremen t with CT and PT
• W attmeter Reading : P o w er in a circuit using CT and PT.
P =V
s
I
s
cos?·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
where P is true p o w er (W ), V
s
is secondary v oltage, I
s
is secondary curren t, cos? is
p o w er factor.
• Three-Phase P o w er (T w o-W attmeter Metho d) :
P
total
=(W
1
+W
2
)·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
where W
1
,W
2
are w attmeter re adings.
Errors in Measuremen t
• T otal Error in P o w er Measuremen t : Com bines CT and PT errors.
T otal Error (%)˜ CT Ratio Error (%)+ PT Ratio Error (%)+ Phase Angle Error Effect
• Phase Angle Error Effect on P o w er :
P o w er Error (%)˜?
CT
+?
PT
·tan?
where ?
CT
,?
PT
are phase angle errors in radians.
2
Key Notes
• Standard units: Curren t (A ), V oltage (V ), P o w er (W ), Imp edance (? ), Burden (VA ).
• CT secondary is t ypically 5 A or 1 A; PT secondary is t ypically 110 V.
• Nev er op en CT secondary circuit to a v oid high v oltage buildup.
• Ratio and phase angle errors affect accuracy in p o w er measuremen ts.
• Use SI units for GA TE calculations.
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