App-13
IM 760201-01E
Appendix
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App
Index
Appendix 3 Power Basics (Power, harmonics, and
AC RLC circuits)
This section explains the basics of power, harmonics, and AC RLC circuits.
Power
Electrical energy can be converted into other forms of energy and used. For example,
it can be converted into the heat in an electric heater, the torque in a motor, or the light
in a fluorescent or mercury lamp. In these kinds of examples, the work that electricity
performs in a given period of time (or the electrical energy expended) is referred to as
electric power. The unit of electric power is watts (W). 1 watt is equivalent to 1 joule of
work in 1 second.
DC Power
The DC power P (in watts) is determined by multiplying the applied voltage U (in volts) by
the current I (in amps).
P = UI (W)
In the example below, the amount of electrical energy determined by the equation above
is retrieved from the power supply and consumed by resistance R (in ohms) every
second.
R
I
U
Alternating Current
Normally, the power supplied by power companies is alternating current with sinusoidal
waveforms. The magnitude of alternating current can be expressed using instantaneous,
maximum, rms, and mean values. Normally, it is expressed using rms values.
The instantaneous value i of a sinusoidal alternating current is expressed by Imsin
ω
t
(where Im is the maximum value of the 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.
*
* Thermal action is the phenomenon in which electric energy is converted to heat energy when
a current flows through a resistance.
p
2p
W
t
i = I
m
sin
W
t
i
2
I
m
I
m
2
Rms value I
Average of i
2
The areas are the same
The rms value (effective value) is the DC value that generates the same thermal action
as the alternating current. With I as the DC value that produces the same thermal action
as the alternating current:
I =
The average of i
2
over one cycle =
=
1
2
P
0
2
P
i
2
d
W
t
I
m
2
Because this value corresponds to the root mean square of the instantaneous values
over 1 period, the effective value is normally denoted using the abbreviation “rms.”
