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Chapter 11
AC Power Analysis
Chapter Objectives:
 Know the difference between instantaneous power and average
power
 Learn the AC version of maximum power transfer theorem
 Learn about the concepts of effective or Rms value
 Learn about the complex power, apparent power and power factor
 Understand the principle of conservation of AC power
 Learn about power factor correction
Huseyin Bilgekul
Eeng224 Circuit Theory II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
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Power Factor Correction
 The design of any power transmission system is very sensitive to the magnitude of
the current in the lines as determined by the applied loads.
 Increased currents result in increased power losses (by a squared factor since P =
I2R) in the transmission lines due to the resistance of the lines.
 Heavier currents also require larger conductors, increasing the amount of copper
needed for the system, and they require increased generating capacities by the utility
company.
 Since the line voltage of a transmission system is fixed, the apparent power is
directly related to the current level.
 In turn, the smaller the net apparent power, the smaller the current drawn from the
supply. Minimum current is therefore drawn from a supply when S = P and QT = 0.
 The process of introducing reactive elements to bring the power factor closer to
unity is called power-factor correction. Since most loads are inductive, the process
normally involves introducing elements with capacitive terminal characteristics
having the sole purpose of improving the power factor.
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Power Factor Correction
Increasing the power
factor without altering
the voltage or current
to the load is called
Power Factor
Correction
Original Inductive Load
Inductive Load with improved power factor correction
Effect of capacitor on total current
Power triangle of power factor correction
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Power Factor Correction
 Increasing the power factor without altering the voltage or current to the load is
called Power Factor Correction.
Qc = Q1 – Q2
= P (tan θ1 - tan θ2)
= ωCVrms2
Q1 = S1 sin θ1
= P tan θ1
P = S1 cos θ1
C 
Qc
2
ωVrms

P (tan θ1  tan θ2 )
2
ω Vrms
Q2 = P tan θ2
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Power Factor Correction
 The process of increasing the power factor without altering the voltage or current to
the original load is called power factor correction.
 Power factor correction is necessary for economic reasons.
P1  P2  P
Real power stays same
P  S1 cos 1 Q1  S1 sin 1  P tan 1
Q2  P tan 2
QC  Q1  Q2  P(tan 1  tan 2 )
QC
P(tan 1  tan  2 )
C

2
Vrms
Vrms 2
• The capacitance value needed to change the pf angle from 1 to 2 .
• Similarly the inductance value needed to change the pf angle from 1 to 2 for a
capacitive load.
Vrms 2
L
QL
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Power
Factor
Correction
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Power
Factor
Correction
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Power Factor Correction
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 Practice Problem 11.15: Find the value of the capacitance needed to correct a load of
140 kVAR at 0.85 lagging pf to unity pf. The load is supplied by a 110 Volt (rms), 60
Hz line.
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Applications
Power Measurement
 Wattmeter is the instrument for measuring the average power. Two coils are
used, the high impedance Voltage coil and the low impedance Current coil.
Wattmeter measures the average power given by:
P  12 Vm I m cos(v i )  VRms I Rms cos(v i )
Wattmeter
Wattmeter connected to the load
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Problem 11-74
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