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9.2 Relationship between measurement error of core loss Pc and phase angel θ (1)
● The following describes the relationship between the measurement error of the core loss Pc and the phase angle θ when a primary exciting
current i
and a secondary induced voltage V
1
As described in Section 9.1, if both a primary exciting current i
angle θ is large is equal to the fact that a core loss Pc is small. As the phase angle θ becomes close to 90°, the measurement accuracy of the
core loss Pc becomes worse. Finally, at θ=90°, the measurement accuracy of the core loss Pc is dispersed and cannot be specified. This
cannot be escaped from the pure mathematical principle.
If both the primary exciting current i
phase angel between them is θ, the core loss Pc is expressed in expression 9.1):
The expression apparently shows that calculation of the core loss Pc includes ① amplitude measurement error of current and voltage and ②
phase measurement error between current and voltage. The amplitude measurement error of ① is the same as the measurement error in a
general current/ voltage instrument. The phase measurement error of ② is the relative phase difference of current or voltage waveform and
corresponds to the time gap of the measured waveform.
Here, assume that real effective values of the current and voltage are i and V, the real value of the phase angle of a sample is θ. In addition, if
each measurement error is ⊿i, ⊿V, or ⊿θ, the measurement error of the core loss is expressed by expression (9.2):
The 1st term indicates the measurement error of the current, the 2nd term indicates that of the voltage, and the 3rd term indicates that of the
phase. The core loss measurement error ⊿Pc is more controlled by the 3rd term as the phase angle θ is closer to 90 .
Fig.9-4 shows the core loss measurement error when the phase measurement error ⊿θ varies within the range of 0.4 at the phase angel of
θ 89.0° 89.8° (amplitude measurement error not included). For example, when the phase angle is θ 89.6°, the core loss measurement error
can be 50% when the phase measurement error is 0.2°
Fig.9-4 Phase measurement accuracy and core loss measurement error for single sine wave
It can be easily understood that for the same phase measurement error⊿θ, the core loss measurement error is dispersed closer to ∞ as the real
value θ become close to 90°.
Even if both the primary exciting current i
loss Pc with high accuracy in the higher phase angle area.
are a single sine wave.
2
and the secondary induced voltage V
1
V
P
i
cos
c
(
i
i
)
(
V
P
c
i
i
V
V
i
V
100
89.6
89.7
80
89.4
60
89.2
40
89
20
0
-0.4
-0.3
-0.2
-20
-40
-60
-80
-100
and the secondary induced voltage V
1
and a secondary induced voltage V
1
are a single sine wave, effective values for both are i and V, and the
2
(9.1)
V
)
cos(
)
i
V
i
V
cos
cos(
)
1
cos
89.8
-0.1
0
0.1
Phase measurement error⊿θ [ ]
位相測定誤差⊿θ[°]
are the single sine wave, it is very difficult to measure the core
2
62
B-H ANALYZER SY-8218 / SY-8219
are a single sine wave, the fact that a phase
2
cos
(9.2)
0.2
0.3
0.4
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