App-25
IM 253710-01E
Appendix
App
Appendix 7 Power Basics (Power/Harmonics/Three
Constants Related to the AC Circuit)
This section describes the basic concepts of power, harmonics, and the three constants
related to the AC circuit.
Power
Electrical energy is transformed and used in different forms such as heat in an electric
heater or an electric furnace, rotational power to drive motors, and light in fluorescent
and mercury lamps. Power (electric power) represents the amount of work that the
electricity (electrical energy) performs on these types of loads over a unit amount of time.
The unit of power is W (watts). When 1 joule of work is done over a period of 1 second,
the electrical power is equal to 1 W.
DC power
DC power P[W] can be determined by the product of the applied voltage U(V) and the
current I[A].
P = UI [W]
In the following figure, electrical energy indicated in the above equation is taken from
the power source and dissipated at R[
Ω
] (load).
R
I
U
AC (alternating current)
The electricity supplied by the power company is an alternating current. The
waveform is sinusoidal. The amplitude of an AC signal an be expressed in terms of
the instantaneous values, maximum values, rms values, and mean values. In
general, it is expressed in terms of rms values.
The instantaneous value of the current of a sine wave, i, is expressed as I
m
sin
ω
t (I
m
:
max. value of current,
ω
: angular velocity where
ω
= 2
π
f, f : frequency of the AC
signal). The heating effect of the AC signal is proportional to i
2
and varies as shown in
the following figure.
*
Refers to the electrical energy being converted to heat energy due to current flowing
through the resistor.
π
2
π
ω
t
i = I
m
sin
ω
t
i
2
I
m
I
m
2
Mean of i
2
Same area
Rms value I
Rms value (effective value)
The rms value (effective value) is the value of the DC signal that generates the same
heating effect as the AC signal. If the value of the DC signal that generates the same
heating effect is expressed as I, then
I =
Mean over one period of i
2
=
=
1
2
π
0
2
π
i
2
d
ω
t
I
m
2
Because this value is equal to the square root of the mean of the square of the
instantaneous values (i) over one period (in short, rms), the symbol “rms” is generally
used to denote the effective value.