App-16
IM 760301-01E
Appendix 4 Power Basics (Power, Harmonics, and
RLC of AC Circuits)
This chapter describes the basics of power, harmonic, and RLC of AC circuits.
Power
Electrical energy is converted into other types of energy for use such as in the form of
heat for electrical heaters and furnaces, turning force for motors, and light for fluorescent
lamps or mercury lamps. Electric power refers to the work that electricity performs on
these types of loads expressed in terms of the quantity per unit time. The unit is watts
(W), and electric energy that performs 1 joule of work in 1 second equals 1 W.
• DC Power
DC power P [W] is determined by the product of the applied voltage U [V] and the
current I [A] that flows.
P = UI [W]
In the example below, this amount of electric energy is retrieved from the power
supply and consumed by resistance R [
Ω
] every second.
R
I
U
• Alternating Current (AC)
Normally, the power supplied by the power company is alternating current, and the
waveform is sinusoidal. The size of alternating current can be expressed in terms of
the instantaneous value, maximum value, rms value, and mean value. Normally, it is
expressed in terms of the rms value.
The instantaneous value i of the sinusoidal alternating current is expressed by I
m
sin
ω
t
(where Im is the maximum value of current,
ω
is the angular velocity defined as
ω
=
2
π
f, and f is the frequency of the sinusoidal alternating current). The thermal action of
this alternating current
*
is proportional to i
2
, and varies as shown in the figure below.
*
The phenomenon in which electric energy is converted to heat energy due to the current
flowing through the resistor.
π
2
π
ω
t
i = I
m
sin
ω
t
i
2
I
m
I
m
2
Rms
value I
Average of i
2
Same are
The rms value (effective vale) is the DC value that generates the same thermal action
as the alternating current. If we denote the DC value of the same thermal action as I, we get
I =
The average of i
2
over one cycle
=
=
1
2
π
0
2
π
i
2
d
ω
t
I
m
2
Because this value corresponds to the root mean square of the instantaneous values
over 1 period, normally the effective value is denoted using the abbreviation
rms
.