Appendix 9 Definitions
A 19
A
Unbalance
Factor
• Balanced (Symmetrical) Three-Phase Voltage (Current)
This term denotes three-phase alternating voltage or current when each
phase has the same voltage (or current) and a phase difference of 120
degrees between phases.
• Unbalanced (Asymmetrical) Three-Phase Voltage (Current)
Denotes three-phase alternating voltage or current when the voltages (or
c
urrents) of the phases are not the same, or when the phase difference
between the phases is not 120 degrees.
Although the following descriptions refer to voltage, they apply to current as well.
Degree of Unbalance in Three-Phase Alternating Voltage
Usually called the voltage unbalance factor, this is the ratio of negative-phase volt-
age to positive-phase voltage
Zero-Phase, Positive-Phase and Negative-Phase Voltage
The concept of zero-, positive- and negative-phase components in a three-
p
hase alternating circuit applies the method of symmetrical coordinates (in
which a circuit is thought of as divided into symmetrical components of zero
phase, positive phase, and negative phase).
• Zero-phase component: Voltage [V
0
] that is equal in each phase (the “0”
subscript denotes a zero-phase-sequence component).
• Positive-phase component: Symmetrical three-phase voltage [V
1
] in which
the value for each phase is equal, and each of the phases is delayed (lags)
by 120 degrees in the phase sequence a→b→c (the “1” subscript denotes a
positive-phase-sequence component).
• Negative-phase component: Symmetrical three-phase voltage [V
2
] in which
the value for each phase is equal, and each of the phases is delayed (lags)
by 120 degrees in the phase sequence a→c→b (the “2” subscript denotes a
negative-phase-sequence component).
If Va, Vb, and Vc are the three-phase alternating voltages, the zero-, positive- and
negative-phase voltages are formulated as follows:
Here, “a” denotes the “vector operator”, which is a vector with magnitude 1 and
phase angle of 120 degrees. Any given phase angle is advanced by 120 de-
grees when multiplied by a, and by 240 degrees when multiplied by a
2
.
When the three-phase alternating voltage is balanced, the zero- and negative-
p
hase voltages are 0, so only the positive-phase voltage (which in this case is
equal to the rms value of the three-phase alternating voltage) is displayed re-
mains.
Voltage Unbalance Factor =
Negative-Phase Voltage
Positive-Phase Voltage
x 100 [%]
Zero-phase voltage V
0
=
Va+Vb+Vc
3
Positive-phase voltage V
1
=
Va+aVb+a
2
Vc
3
Negative-phase voltage V
2
=
Va+a
2
Vb+aVc
3
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