Environmental Engineering Reference
In-Depth Information
Alternating current, AC
Three-phase machines work with a three-phase AC. Before three-phase
machines can be explained in detail, a short introduction into AC calculations
is given here.
An alternating voltage dependent on time is defined as:
(5.47)
with amplitude
^
, zero phase angle
ϕ
v
of the voltage and the angular
frequency
ω
given by:
(5.48)
The associated
current i
with the zero phase angle
ϕ
i
and the amplitude
î
is:
(5.49)
The phase angle
ϕ
between current and voltage is:
(5.50)
If the phase angle is positive, the voltage is ahead of the current (leading). If
the phase angle is negative, the voltage is behind (lagging). Figure 5.16 shows
the curve of current and voltage as a function of time. With zero phase angles
ϕ
v
= 0 and
ϕ
i
=-
π
/4, the phase angle of this example is
ϕ
=+
π
/4, i.e. the
voltage is ahead of the current.
Another common description is the vector diagram of the amplitudes.
Here, the amplitude of the voltage is usually the vertical reference vector. The
other amplitudes are added relatively with their phase angle. The amplitudes
of the current and voltage of the example above are shown in the vector
diagram of the amplitudes in Figure 5.16.
Figure 5.16
Current and Voltage as a Function of Time and Vector Diagram
of the Amplitudes
î
and
^
(
ϕ
=
π
/4)
