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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AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor
AC POWER CALCULATION Instantaneous, average and reactive power Apparent Power and Power Factor Complex Power. SEE 1023 Circuit Theory. Dr. Nik Rumzi Nik Idris. i(t). Passive, linear network. Instantaneous, Average and Reactive Power. + v(t) . - PowerPoint PPT Presentation
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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 FactorComplex 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
vi
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
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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)
t2sin)sin(2IVt2cos)cos(
2IV)cos(
2IV
ivmm
ivmm
ivmm p =
p = P + Pcos(2t) Qsin(2t)
Using trigonometry functions, it can be shown that:
)cos(2IVP ivmm = AVERAGE POWER (watt)
)sin(2IVQ ivmm = REACTIVE POWER (var)
Which can be written as
5
t2sin)sin(2IVt2cos)cos(
2IV)cos(
2IV
ivmm
ivmm
ivmm p =
6
t2sin)sin(2IVt2cos)cos(
2IV)cos(
2IV
ivmm
ivmm
ivmm 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(2IVt2cos)cos(
2IV)cos(
2IV
ivmm
ivmm
ivmm 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