App-27
IM 253710-01E
Appendix
App
Vector Display of an AC signal
In general, the instantaneous values of voltage and current are expressed by the
following equations.
Voltage : u = U
m
sin
ω
t
Current : i = I
m
sin(
ω
t –
φ
)
The time offset of the voltage and current is called the phase difference, and
φ
is
called the phase angle. This time offset is mainly created by the load that is supplied
with power. In general, when there is only resistance in the load, the phase difference
is zero; when there is inductance (coil) in the load, the current lags behind the voltage;
when there is capacitance in the load, the current leads the voltage.
0
π
2
π
i
u
ω
t
φ
When the current lags the voltage
0
π
2
π
i
u
ω
t
φ
When the current leads the voltage
The vector display is used to show the amplitude and phase relationships of the
voltage and current. Taking the positive vertical axis to be the reference, an angle in
the counter clockwise direction is taken to be positive.
To clearly indicate that the graph is showing a vector, a dot is placed on the top of the
symbol representing the value. The amplitude of the vector represents the rms value.
φ
U
I
When the current lags the voltage
φ
U
I
When the current leads the voltage
The vector display of the voltage and current of a three-phase AC signal would look
something like the following figure.
φ
U
1
I
1
φ
φ
I
3
I
2
U
3
U
2
Appendix 7 Power Basics (Power/Harmonics/Three Constants Related to the AC Circuit)
