True, Reactive, and Apparent power
We know that reactive loads such as
inductors and capacitors dissipate zero power, yet the fact
that they drop voltage and draw current gives the deceptive
impression that they actually do dissipate power.
This "phantom power" is called reactive power, and it
is measured in a unit called Volt-Amps-Reactive
(VAR), rather than watts. The mathematical symbol for
reactive power is (unfortunately) the capital letter Q. The
actual amount of power being used, or dissipated, in a
circuit is called true power, and it is measured in
watts (symbolized by the capital letter P, as always). The
combination of reactive power and true power is called
apparent power, and it is the product of a circuit's
voltage and current, without reference to phase angle.
Apparent power is measured in the unit of Volt-Amps
(VA) and is symbolized by the capital letter S.
As a rule, true power is a function of a
circuit's dissipative elements, usually resistances (R).
Reactive power is a function of a circuit's reactance (X).
Apparent power is a function of a circuit's total impedance
(Z). Since we're dealing with scalar quantities for power
calculation, any complex starting quantities such as
voltage, current, and impedance must be represented by their
polar magnitudes, not by real or imaginary
rectangular components. For instance, if I'm calculating
true power from current and resistance, I must use the polar
magnitude for current, and not merely the "real" or
"imaginary" portion of the current. If I'm calculating
apparent power from voltage and impedance, both of these
formerly complex quantities must be reduced to their polar
magnitudes for the scalar arithmetic.
There are several power equations relating
the three types of power to resistance, reactance, and
impedance (all using scalar quantities):
Please note that there are two equations
each for the calculation of true and reactive power. There
are three equations available for the calculation of
apparent power, P=IE being useful only for that
purpose. Examine the following circuits and see how these
three types of power interrelate:
Resistive load only:
Reactive load only:
These three types of power -- true,
reactive, and apparent -- relate to one another in
trigonometric form. We call this the power triangle:
Using the laws of trigonometry, we can solve
for the length of any side (amount of any type of power),
given the lengths of the other two sides, or the length of
one side and an angle.
Power dissipated by a load is referred to
as true power. True power is symbolized by the
letter P and is measured in the unit of Watts (W).
Power merely absorbed and returned in load
due to its reactive properties is referred to as
reactive power. Reactive power is symbolized by the
letter Q and is measured in the unit of Volt-Amps-Reactive
Total power in an AC circuit, both
dissipated and absorbed/returned is referred to as
apparent power. Apparent power is symbolized by the
letter S and is measured in the unit of Volt-Amps (VA).
These three types of power are
trigonometrically related to one another. In a right
triangle, P = adjacent length, Q = opposite length, and S
= hypotenuse length. The opposite angle is equal to the
circuit's impedance (Z) phase angle.