YOKOGAWA WT500 - Appendix 3 Power Basics (Power, Harmonics, and AC RLC Circuits)

App-14
IM 760201-01E
To determine the mean value, the average is taken over 1 period of absolute values,
because simply taking the average over 1 period of the sine wave results in a value of
zero. With I
mn
as the mean value of the instantaneous current i (which is equal to I
m
sin
ω
):
Imn = The average of i over one cycle =
1
P
0
2P
i dWt
Im
2
=
2
P
These relationships also apply to sinusoidal voltages.
The maximum value, rms value, and average value of a sinusoidal alternating current are
related as shown below. The crest factor and form factor are used to define the tendency
of an AC waveform.
Crest factor =
Maximum value
Rms value
Form factor =
Rms value
Average value
Vector Display of Alternating Current
In general, instantaneous voltage and current values are expressed using the equations
listed below.
V
oltage: u = U
m
sin
ω
t
Current: i = I
m
sin(
ω
t –
f
)
The time offset between the voltage and current is called the phase difference, and
f
is
the phase angle. The time offset is mainly caused by the load that the power is supplied
to. In general, the phase difference is zero when the load is purely resistive. The current
lags the voltage when the load is inductive (is coiled). The current leads the voltage when
the load is capacitive.
0
P
2
P
i
u
Wt
F
When the current lags the voltage
0
P
2P
i
u
Wt
F
When the current leads the voltage
Vector display is used to clearly convey the magnitude and phase relationships between
the voltage and current. A positive phase angle is represented by a counterclockwise
angle with respect to the vertical axis.
Normally, a dot is placed above the symbol representing a quantity to explicitly indicate
that it is a vector. The magnitude of a vector represents the rms value.
F
U
I
When the current lags the voltage
F
U
I
When the current leads the voltage
Appendix 3 Power Basics (Power, harmonics, and AC RLC circuits)