Power Real and Otherwise

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Power Real and Otherwise
The terms real power and active power mean the
same thing. This is a topic that only pertains
to AC Power. In a DC system, voltage and current
are always in phase (of course, there is no
phase in a DC system) so real, apparent, and
reactive power are equal. In an AC system, there
can be a phase difference between voltage and
current, due to a reactive load. Well only
consider sinusoidal AC power.
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Power Real and Otherwise
Consider a power system with a source and a
resistive load. The source supplies 60 Hz AC
power to the load, with a peak value (amplitude)
of 120 V, and an effective (rms) value of 85 V
Lets say the peak current is 1 A (rms current
0.7071 A). Because the load is resistive, the
current is in phase with the voltage wave
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The power delivered by the source to the load at
any instant (the instantaneous power) is equal to
the source voltage times the current
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Power Real and Otherwise
By a common trig identity,
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Power Real and Otherwise
The instantaneous power varies sinusoidally,
between a minimum of zero and a maximum of 120
Watts. Peak power is equql to voltage amplitude
times current amplitude, when voltage and current
are in-phase. Average power is equal to rms
voltage times rms current,
or ½ the peak power.
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Power Real and Otherwise
Now lets see what happens when voltage and
current are not in phase. This can only happen
if the load is not purely resistive it must
have a reactive component. Let the voltage be
the same as before
Let the current also be the same as before, but
with a 45 deg. (p/4 radian) phase lag
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The phase lag means the load is no longer purely
resistive, it has an inductive component. The
product of voltage and current (power) is
E
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Power Real and Otherwise
By another common trig identity,
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Power Real and Otherwise
Notice that instantaneous power is less than
zero (i.e., negative) for part of each cycle.
This means that for that portion of each cycle,
the load is delivering power to the source! This
is due to the fact that the load now has a
reactive component, which behaves like an
inductor.
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Power Real and Otherwise
Reactive elements (inductors and capacitors)
store energy during part of the cycle, and return
it during the remainder of the cycle. In other
words, during the part of the cycle when the
instantaneous power is greater than zero, a
portion of the energy delivered to the load is
stored in reactive elements and the rest does
work (is dissipated as heat).
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Power Real and Otherwise
During the part of the cycle when the
instantaneous power is less than zero, the
energy that was previously stored in reactive
elements is returned to the system Notice that
the average power is reduced by an amount equal
to cos(p/4)
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Reactive Power
Now lets see what happens when the load is
purely inductive. This is an approximation to
many real-world loads, such as AC induction
motors. In this case, the current would lag the
voltage by 90 degrees, or p/2 radians
I
The power delivered by the source to the load at
any instant (the instantaneous power) is equal to
the source voltage times the current
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Reactive Power
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Reactive Power
Now power is positive for ½ cycle, and negative
for ½ cycle. While the power is positive, the
energy delivered to the load is all stored. The
load does not have a real (resistive) component,
so no work is done.
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Reactive Power
During the negative half of the power cycle, the
stored energy is all returned to the system.
Notice that the average power is zero, which
makes sense because no work is done.
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Reactive Power
Recall that power is formally the rate at which
work is done. In this situation, no work is done
power just goes back and forth between
source and load, so the power (the product
of voltage and current) isnt really power. To
keep things straight, its called reactive power.
The units of
reactive power are volt-amperes reactive.
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Reactive Power
Since in this case energy moves back and forth
between the source and the load, one could
ask reasonably which is the source and which is
the load. By convention, in the circuit shown
here the load current lags voltage, so energy is
said to flow from left to right. The inductor
absorbs reactive power.
A reactive load which absorbs reactive power is
called a reactor.
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Reactive Power
Since in this case energy moves back and forth
between the source and the load, one could
ask reasonably which is the source and which is
the load. By convention, in the circuit shown
here the load current lags voltage, so energy is
said to flow from left to right. The inductor
absorbs reactive power.
A reactive load which absorbs reactive power is
called a reactor.
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Reactive Power
Suppose a capacitor is connected in parallel with
the inductor, and the capacitance is chosen so
the reactances of the two elements are equal and
opposite. Since the voltage across the inductor
is unchanged, the inductor current is the same as
it was before
The capacitor current has the same magnitude, but
leads the voltage by p/2 radians (90 deg.)
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The source current is the sum of these two
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Reactive Power
The net source current is now zero, so the source
does not deliver any power. However, the
inductor voltage and current are exactly the same
as they were before the capacitor was added, so
the inductor must absorb the same reactive power
as it did before. This reactive power must come
from somewhere, but clearly doesnt come from the
source. It must come from the capacitor, which
acts as a reactive source.
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Reactive Power
Now lets remove the inductor. The voltage
across the capacitor remains unchanged, so the
capacitor current still leads voltage by 90
degrees
Since the capacitors behavior is unchanged, one
must conclude that it still acts as a reactive
source. The difference between reactive source
and reactive load (reactor) is the reactive
source current leads
voltage, while the reactor current lags. In this
case, the voltage source actually is a reactive
load, or receiver of reactive power. These
definitions are, of course, somewhat arbitrary
but are generally accepted.
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Reactive Power
In the real world, most loads are partly
resistive (using energy to do work) and partly
inductive. This was the case in the first
example, in which current lagged voltage by 45
deg. The resistive and reactive (inductive)
components of the load were equal.
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Reactive Power
The resistor current, Ip, is in phase with the
source voltage
The inductor current, Iq, lags the source voltage
by 90 deg
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The source current I is the vector sum of Ip and
Iq. The magnitude of I is
Iq
Ip
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Real, Reactive and Apparent Power
We can illustrate the relationship between E, I,
Ip and Iq by drawing a phasor diagram. Obviously,
the real power (dissipated by the resistor) is
EIp. The reactive power, absorbed by the
inductor and denoted Q, is EIq. Reactive power
is measured in units of Volt-Amperes Reactive
(VAR). The vector sum of real and reactive power
is apparent power, denoted S and measured in
units of Volt-Amperes (VA).
E
Ip
I
Iq
Ip
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I
Iq
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Real, Reactive and Apparent Power
Apparent power is called apparent, because if
we measured the peak (or rms) voltage across the
wires connecting the source and load, we would
measure E volts. If we measured the peak or rms
current flowing from the source to the load, wed
measure I amperes. It seems apparent that the
power transmitted from source to load is EI, the
apparent power.
E
Ip
I
Iq
Ip
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Iq
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Real, Reactive and Apparent Power
Of course, part of the apparent power is
reactive, which does no work. Because no work is
done by it, it does not require a transmission of
energy from the source to the load. So it costs
nothing, right? Wrong. The transmission system
must still be designed for a voltage E (which
imposes requirements on the insulators) and a
current I (which determines conductor size), so
reactive power isnt free.
E
Ip
I
Iq
Ip
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Iq
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Real, Reactive and Apparent Power
Lets take the circuit weve been considering,
and insert a Voltmeter, an Ammeter, a Wattmeter
(to measure real power) and a varmeter (to
measure reactive power. If the Voltmeter reads E
volts, and the varmeter reads Q vars, then
So
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Ip
A
W
VAR
Ip
E
Iq
V
R
L
I
Iq
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Real, Reactive and Apparent Power
If the Wattmeter reads P Watts, then
At the same time, the Ammeter reads I Amperes, so
the apparent power S is
So
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Ip
A
W
VAR
Ip
E
Iq
V
R
L
I
Iq
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Real, Reactive and Apparent Power
The phasor diagram makes it clear that
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Ip
A
W
VAR
Ip
E
Iq
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Iq
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Real, Reactive and Apparent Power
And the angle q is
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E
Ip
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VAR
Ip
q
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Iq
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Iq
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Power Factor
Power factor is defined as the ratio of real
power to apparent power
A power factor can never be greater than 1,
because real power can never exceed apparent
power.
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Ip
A
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VAR
Ip
q
E
Iq
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I
Iq
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Power Factor
Where q is the angle between Voltage and current.
If current lags voltage (as in an inductive
load, or reactor) the power factor is said to be
lagging, and if current leads voltage the power
factor is said to be leading.
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Ip
A
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VAR
Ip
q
E
Iq
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I
Iq
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Power Triangle
The geometric relationship between real, apparent
and reactive power is best illustrated by the
power triangle. The real power delivered to a
load is represented by the length of a horizontal
line. Reactive power is symbolized by a vertical
line. These two lines are the sides of the power
triangle the hypotenuse represents apparent
power. Geometrically, the power factor is
I
Q
S
A
W
VAR
Ip
E
Iq
V
q
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P