Hioki 3196 - Unbalance(I)

Appendix
221
Unbalance factor
If the phases of the three-phase alternating voltage (current) each
have the same voltage and deviate from each other by 120 degrees,
the voltage (current) is referred to as “balanced (symmetrical) three-
phase voltage (current).” If the voltages (currents) of the three phases
differ or if the difference between each of the phases is not 120
degrees, the voltage (current) is referred to as “unbalanced (asymmet-
rical) three-phase voltage (current).” Though all of the following
descriptions refer to voltage, they apply to current as well.
Degree of unbal-
ance in three-
phase alternating
voltage
Normally described as the voltage unbalance factor, which is the ratio
of negative-phase voltage to positive-phase voltage
Zero-phase/
positive-phase/
negative-phase
voltage
The concept of a zero-phase-sequence/positive-phase-sequence/neg-
ative-phase- sequence component in a three-phase alternating circuit
applies the method of symmetrical coordinates (a method in which a
circuit is treated so as to be divided into symmetrical components of a
zero phase, positive phase, and negative phase).
• Zero-phase-sequence component: Voltage that is equal in each phase.
Described as V
0
. (Subscript 0: Zero-phase-sequence component)
• Positive-phase-sequence component: Symmetrical three-phase voltage
in which the value for each phase is equal, and each of the phases is
delayed by 120 degrees in the phase sequence a->b->c. Described as V
1
.
(Subscript 1: Positive-phase-sequence component)
• Negative-phase-sequence component: Symmetrical three-phase volt-
age in which the value for each phase is equal, and each of the phases is
delayed by 120 degrees in the phase sequence a->c->b. Described as V
2
.
(Subscript 2: Negative-phase-sequence component)
If Va, Vb, and Vc are given as the three-phase alternating voltage, the
zero-phase voltage, positive-phase voltage, and negative voltage are
formulated as shown below.
a is referred to as the “vector operator.” It is a vector with a magnitude
of 1 and a phase angle of 120 degrees. Therefore, the phase angle is
advanced by 120 degrees if multiplied by a, and by 240 degrees if
multiplied by a
2
. If the three-phase alternating voltage is balanced, the
zero-phase voltage and negative-phase voltage are 0, and only posi-
tive-phase voltage, which is equal to the effective value of the three-
phase alternating voltage, is described.
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