1 AC POWER CALCULATION AC POWER CALCULATION Instantaneous, average and reactive power Instantaneous, average and reactive power Apparent Power and Power Factor Apparent Power and Power Factor Complex Power Complex Power Dr. Nik Rumzi Nik Idris Dr. Nik Rumzi Nik Idris SEE 1023 Circuit Theory SEE 1023 Circuit Theory
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1 AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor Complex Power Dr. Nik Rumzi Nik Idris SEE 1023 Circuit.
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AC POWER CALCULATIONAC POWER CALCULATIONInstantaneous, average and reactive powerInstantaneous, average and reactive power
Apparent Power and Power FactorApparent Power and Power Factor
Complex PowerComplex Power
Dr. Nik Rumzi Nik IdrisDr. Nik Rumzi Nik Idris
SEE 1023 Circuit TheorySEE 1023 Circuit Theory
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Instantaneous, Average and Reactive PowerInstantaneous, Average and Reactive Power
+v(t)
i(t)
Passive, linear network
Instantaneous power absorbed by the network is, p =v(t).i(t)
Let v(t) = Vm cos (t + v) and i(t) = Imcos(t + i)
Which can be written as
v(t) = Vm cos (t + v i) and i(t) = Imcos(t)
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v(t) = Vm cos (t + v i) and i(t) = Imcos(t)
p = Vm cos(t + v – i ) . Im cos(t)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
-2
-1
0
1
2
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-0.5
0
0.5
1
1.5
2
v
i
Instantaneous Power (p)
Example when v i = 45o
positivepositive p p = power transferred from source to network
negativenegative p p = power transferred from network to source
45o
4
v(t) = Vm cos (t + v i) and i(t) = Imcos(t)
p = Vm cos(t + v – i ) . Im cos(t)
t2sin)sin(2
IVt2cos)cos(
2
IV)cos(
2
IViv
mmiv
mmiv
mm p =
p = P + Pcos(2t) Qsin(2t)
Using trigonometry functions, it can be shown that:
)cos(2
IVP iv
mm = AVERAGE POWER (watt)
)sin(2
IVQ iv
mm = REACTIVE POWER (var)
Which can be written as
5
t2sin)sin(2
IVt2cos)cos(
2
IV)cos(
2
IViv
mmiv
mmiv
mm p =
6
t2sin)sin(2
IVt2cos)cos(
2
IV)cos(
2
IViv
mmiv
mmiv
mm p =
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
0
1
2
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080
0.5
1
1.5
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
-0.5
0
0.5
1
Example for v-i = 45o
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t2sin)sin(2
IVt2cos)cos(
2
IV)cos(
2
IViv
mmiv
mmiv
mm p =
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
0
1
2
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080
0.5
1
1.5
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1
-0.5
0
0.5
1
P = average power
Q = reactive power
p = P + P cos(2t) Q sin(2t)
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P = AVERAGE POWER
Q = REACTIVE POWER
p = P + P cos(2t) Q sin(2t)
• Useful power – also known as ACTIVE POWER
• Converted to other useful form of energy – heat, light, sound, etc
• Power charged by TNB
• Power that is being transferred back and forth between load and source
• Associated with L or C – energy storage element – no losses