Transcript Reactive Power

JAMES W. NILSSON
&
SUSAN A. RIEDEL
ELECTRIC
CIRCUITS
EIGHTH EDITION
CHAPTER 10
SINUSOIDAL
STEADY – STATE
POWER
CALCULATIONS
© 2008 Pearson Education
CONTENTS
10.1 Instantaneous Power
10.2 Average and Reactive Power
10.3 The rms Value and Power Calculations
10.4 Complex Power
10.5 Power Calculations
10.6 Maximum Power Transfer
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10.1 Instantaneous Power

Instantaneous power is the product of the
instantaneous terminal voltage and current, or
p  vi
The black box representation of
a circuit used for calculating
power
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10.1 Instantaneous Power
 The
positive sign is used when the
reference direction for the current is
from the positive to the negative
reference polarity of the voltage.
 The
frequency of the instantaneous
power is twice the frequency of the
voltage (or current).
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10.1 Instantaneous Power
Instantaneous power, voltage, and current
versus ωt for steady-state sinusoidal operation
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10.2 Average and Reactive Power
Average Power
 Average power is the average value of
the instantaneous power over one period.
 It
is the power converted from electric to
non-electric form and vice versa.
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10.2 Average and Reactive Power
 This
conversion is the reason that
average power is also referred to as real
power.
 Average power, with the passive sign
convention, is expressed as
Vm I m
P
cos( v   i )
2
 Veff I eff cos( v   i )
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10.2 Average and Reactive Power
Reactive Power
 Reactive
power is the electric power
exchanged between the magnetic field of an
inductor and the source that drives it or
between the electric field of a capacitor and
the source that drives it.
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10.2 Average and Reactive Power
Reactive Power
 Reactive
power is never converted to
nonelectric power. Reactive power, with the
passive sign convention, is expressed as
Vm I m
Q
sin(  v   i )
2
 Veff I eff sin(  v   i )
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10.2 Average and Reactive Power
Instantaneous real power and average
power for a purely resistive circuit
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10.2 Average and Reactive Power
Instantaneous real power, average power, and
reactive power for a purely inductive circuit
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10.2 Average and Reactive Power
Instantaneous real power and average
power for a purely capacitive circuit
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10.2 Average and Reactive Power
Power Factor
Power factor is the cosine of the phase angle
between the voltage and the current:
pf  cos( v  i )
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10.2 Average and Reactive Power
The reactive factor is the sine of the phase
angle between the voltage and the current:
rf  sin(  v  i )
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10.3 The rms Value and Power
Calculations
A sinusoidal voltage
applied to the terminals
of a resistor
Average power
delivered to
the resistor
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10.3 The rms Value and Power
Calculations
2
rms
The average power
delivered to R is simply the
rms value of the voltage
squared divided by R.
V
P
R
If the resistor is carrying a sinusoidal
current, the average power delivered
to the resistor is:
PI
2
rms
.R
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10.4 Complex Power
 Complex
power is the
complex sum of real
power and reactive power.
S  P  jQ
| S | = apparent power
Q = reactive power
θ
P = average power
A power triangle
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10.4 Complex Power
Quantity
Units
Complex power
volt-amps
Average power
watts
Reactive power
var
Three power quantities and their units
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10.4 Complex Power
Apparent Power is the magnitude of
complex power.
S  P Q
2
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2
10.5 Power Calculations
The phasor voltage and current
associated with a pair of terminals
Complex power  V I
*
eff eff
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10.6 Maximum Power Transfer
A circuit describing
maximum power transfer
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10.6 Maximum Power Transfer
ZL  Z
*
Th
Condition for maximum
average power transfer
The circuit with the
network replaced by its
Thévenin equivalent
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10.6 Maximum Power Transfer
Example: Determining Maximum Power Transfer without
Load Restrictions.
a) For the circuit shown below, determine the impedance ZL
that results in maximum average power transferred to ZL.
b) What is the maximum average power transferred to the
load impedance determined in (a)?
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THE END
© 2008 Pearson Education