Formula Sheets Measurement of Power & Energy - Electrical and Electronic Measurements

 Page 1


Electrical and Electronic Measuremen ts:
Measuremen t of P o w er & Energy F orm ula Sheet for
Electrical GA TE
P o w er M easuremen t
• Instan taneous P o w er : P o w er in a circuit at an y instan t.
P =VIcos?
where P is p o w er (W ), V is RMS v oltage (V ), I is RMS curren t (A ), ? is phase angle
b et w een v oltage and curren t.
• Electro dynamometer W attmeter : Deflection torque for p o w er measuremen t.
T
d
=kI
1
I
2
cos?
where T
d
is deflection torque ( Nm ), k is a constan t, I
1
is curren t in fixed coil, I
2
is
curren t in mo ving coil (prop ortional to v oltage).
• W attmeter Reading : F or single-phase A C circuit.
P =VIcos?
where V is v oltage across pressure c oil, I is c urren t through curren t coil.
• Three-Phase P o w er (Balanced Load) : Using t w o-w attmeter metho d.
P
total
=W
1
+W
2
where W
1
,W
2
are readings of t w o w attmeters.
• P o w er F actor (T w o-W attmeter Metho d) :
cos? = cos
[
tan
-1
(
v
3·
W
1
-W
2
W
1
+W
2
)]
• Three-Phase P o w er (Star/Delta, Balanced) :
P =
v
3V
L
I
L
cos?
where V
L
is line v oltage (V ), I
L
is line curren t (A ).
Energy Measuremen t
• Energy Consumed : Energy o v er time.
E =P ·t
where E is energy (Wh or kWh ), P is p o w er (W ), t is time (h ).
1
Page 2


Electrical and Electronic Measuremen ts:
Measuremen t of P o w er & Energy F orm ula Sheet for
Electrical GA TE
P o w er M easuremen t
• Instan taneous P o w er : P o w er in a circuit at an y instan t.
P =VIcos?
where P is p o w er (W ), V is RMS v oltage (V ), I is RMS curren t (A ), ? is phase angle
b et w een v oltage and curren t.
• Electro dynamometer W attmeter : Deflection torque for p o w er measuremen t.
T
d
=kI
1
I
2
cos?
where T
d
is deflection torque ( Nm ), k is a constan t, I
1
is curren t in fixed coil, I
2
is
curren t in mo ving coil (prop ortional to v oltage).
• W attmeter Reading : F or single-phase A C circuit.
P =VIcos?
where V is v oltage across pressure c oil, I is c urren t through curren t coil.
• Three-Phase P o w er (Balanced Load) : Using t w o-w attmeter metho d.
P
total
=W
1
+W
2
where W
1
,W
2
are readings of t w o w attmeters.
• P o w er F actor (T w o-W attmeter Metho d) :
cos? = cos
[
tan
-1
(
v
3·
W
1
-W
2
W
1
+W
2
)]
• Three-Phase P o w er (Star/Delta, Balanced) :
P =
v
3V
L
I
L
cos?
where V
L
is line v oltage (V ), I
L
is line curren t (A ).
Energy Measuremen t
• Energy Consumed : Energy o v er time.
E =P ·t
where E is energy (Wh or kWh ), P is p o w er (W ), t is time (h ).
1
• Single-Phase Energy Meter : Energy measured b y meter.
E =
N
K
where N is n um b er of disc rev olutions, K is meter constan t (revolutions/kWh ).
• Three-Phase Energy Meter : T otal energy in a three-phase system.
E = (W
1
+W
2
)·t
where W
1
,W
2
are w attmeter r eadings, t is time.
• Meter Constan t Calculation :
K =
3600
VIcos?
where K is meter constan t for one rev olution p er second, assuming rated v oltage and
curren t.
Errors in P o w er Measuremen t
• W attmeter Error : Due to pressure coil inductance.
T rue P o w er = W attmeter Reading·cos?/cos(?+ß)
where ß = tan
-1
(?L
p
/R
p
) , L
p
is pressure coil inductance (H ), R
p
is pressure coil
resistance (? ), ? is angular fre quency (rads
-1
).
• Creeping Error in Energy Meter : Un w an ted disc rotation at no load.
A djust friction comp ensation t o ensure no creeping.
Instrumen t T ransformers in P o w er Measuremen t
• Curren t T ransformer (CT) : Curren t ratio.
I
p
I
s
=
N
s
N
p
whereI
p
,I
s
are primary and sec ondary curren ts (A ),N
p
,N
s
are primary and secondary
turns.
• P oten tial T ransformer (PT) : V oltage ratio.
V
p
V
s
=
N
p
N
s
where V
p
,V
s
are primary and se condary v oltages (V ).
• W attmeter Reading with CT/PT :
P =V
s
I
s
cos?·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
2
Page 3


Electrical and Electronic Measuremen ts:
Measuremen t of P o w er & Energy F orm ula Sheet for
Electrical GA TE
P o w er M easuremen t
• Instan taneous P o w er : P o w er in a circuit at an y instan t.
P =VIcos?
where P is p o w er (W ), V is RMS v oltage (V ), I is RMS curren t (A ), ? is phase angle
b et w een v oltage and curren t.
• Electro dynamometer W attmeter : Deflection torque for p o w er measuremen t.
T
d
=kI
1
I
2
cos?
where T
d
is deflection torque ( Nm ), k is a constan t, I
1
is curren t in fixed coil, I
2
is
curren t in mo ving coil (prop ortional to v oltage).
• W attmeter Reading : F or single-phase A C circuit.
P =VIcos?
where V is v oltage across pressure c oil, I is c urren t through curren t coil.
• Three-Phase P o w er (Balanced Load) : Using t w o-w attmeter metho d.
P
total
=W
1
+W
2
where W
1
,W
2
are readings of t w o w attmeters.
• P o w er F actor (T w o-W attmeter Metho d) :
cos? = cos
[
tan
-1
(
v
3·
W
1
-W
2
W
1
+W
2
)]
• Three-Phase P o w er (Star/Delta, Balanced) :
P =
v
3V
L
I
L
cos?
where V
L
is line v oltage (V ), I
L
is line curren t (A ).
Energy Measuremen t
• Energy Consumed : Energy o v er time.
E =P ·t
where E is energy (Wh or kWh ), P is p o w er (W ), t is time (h ).
1
• Single-Phase Energy Meter : Energy measured b y meter.
E =
N
K
where N is n um b er of disc rev olutions, K is meter constan t (revolutions/kWh ).
• Three-Phase Energy Meter : T otal energy in a three-phase system.
E = (W
1
+W
2
)·t
where W
1
,W
2
are w attmeter r eadings, t is time.
• Meter Constan t Calculation :
K =
3600
VIcos?
where K is meter constan t for one rev olution p er second, assuming rated v oltage and
curren t.
Errors in P o w er Measuremen t
• W attmeter Error : Due to pressure coil inductance.
T rue P o w er = W attmeter Reading·cos?/cos(?+ß)
where ß = tan
-1
(?L
p
/R
p
) , L
p
is pressure coil inductance (H ), R
p
is pressure coil
resistance (? ), ? is angular fre quency (rads
-1
).
• Creeping Error in Energy Meter : Un w an ted disc rotation at no load.
A djust friction comp ensation t o ensure no creeping.
Instrumen t T ransformers in P o w er Measuremen t
• Curren t T ransformer (CT) : Curren t ratio.
I
p
I
s
=
N
s
N
p
whereI
p
,I
s
are primary and sec ondary curren ts (A ),N
p
,N
s
are primary and secondary
turns.
• P oten tial T ransformer (PT) : V oltage ratio.
V
p
V
s
=
N
p
N
s
where V
p
,V
s
are primary and se condary v oltages (V ).
• W attmeter Reading with CT/PT :
P =V
s
I
s
cos?·
(
N
p
N
s
)
PT
·
(
N
s
N
p
)
CT
2
Key Notes
• Standard units: P o w er (W ), Energy (Wh or kWh ), V oltage (V ), Curren t (A ), F re-
quency (Hz ).
• T w o-w attmeter metho d is standard for three-phase p o w er measuremen t in GA TE.
• Ensure CT/PT ratios are applied correctly for accurate p o w er readings.
• P o w er factor cos? ranges from 0 to 1; negativ e W
2
indicates lo w p o w er factor.
• Use SI units for GA TE calculations.
3