Reactive, and Apparent power
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 for: a purely resistive load in Figure below, a purely reactive load in Figure below, and a resistive/reactive load in Figure below.
Resistive load only:
True power, reactive power, and apparent power for a purely resistive load.
Reactive load only:
True power, reactive power, and apparent power for a purely reactive load.
Resistive/reactive load:
True power, reactive power, and apparent power for a resistive/reactive load.
These three types of power -- true, reactive, and apparent -- relate to one another in trigonometric form. We call this the power triangle: (Figure below).
Power triangle relating appearant power to true power and reactive power.
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.
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