Chapter 9 Measurement Accuracy Of Core Loss; Phase Angle Θ And Core Loss Pc In Distorted Wave - Iwatsu SY-8218 Instruction Manual

Chapter 9 Measurement Accuracy of Core Loss

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9.1 Phase angle θ and core loss Pc in distorted wave
● The following describes the relationship between the phase angle θ and the core loss Pc when a primary exciting current i
induced voltage V is a distorted wave.
2
If a B-H curve enter a saturated area; i.e. a primary exciting current i
between the phase angle θ and the core loss Pc is not necessarily expressed as "When θ is large, Pc is small" which is used at the time
when i and V are the single sine wave and it is proper to consider that discussion of the core loss Pc using the phase angle θ is used as a
1 2
standard.
Fig.9-1 shows the power vector. If a measured current and a measured voltage
are the single sine wave, the phase angle θ can be expressed using the apparent power VA
and the Active power (core loss) Pc, as shown in expression (2-14):
It apparently shows "When θ is large, Pc is small).
Next, consider the case where a measured current and a measured voltage are
distorted wave; not single sine wave. It corresponds to the case where B-H loop enters
a saturated area. The fact that the waveform of a current or voltage is distorted means
that the wave includes other frequency ingredient than sine wave of a basic frequency.
Consider the phase angel θ at that time.
Actually, a limitless number of frequency ingredients are included. However, to simplify
the explanation here, assume that only one frequency ingredient in addition to a basic
ingredient (hereinafter called "high-harmonic ingredient") is included.
Fig.9-2 is the vector diagram indicating the case where the apparent power of the
basic wave is VA and the apparent power of the high harmonic wave is va.
Generally, since a magnetic material has a different core loss and permeability in a
different frequency from the basic wave, the direction and intensity of va is different
from those of VA. The composed vector of va and VA is the apparent power VA of the
distorted wave. The diagram apparently shows that the phase angel θ' at that time
is larger than θ only for the basic wave.
Next, see another power vector diagram: i.e. Fig.9-3. The direction and intensity
of va in this diagram are different from those in Fig.9-2, and as a result, the phase
angle θ´ of the composed apparent power VA' is smaller than θ only for the basic wave.
In either case, the core loss Pc increases to Pc' but the increment of the phase angle is
different from that only for the basic wave. It is considered that which type is used is
determined by whether increment of the reactive power or the core loss only for the basic
wave is larger than that for the high harmonic wave. The increment of the reactive power
is considered to be controlled by the inductance (i.e. permeability) or capacitance.
On the other hand, the increment of the core loss is considered to be controlled by
hysteresis loss or eddy current loss.
As described above, if a B-H loop enters the saturated area; i.e, the single sine wave is not used
for explanation, it is proper to consider that discussion of the core loss Pc using the
phase angel θ is used as a standard.
 
P
 

 
1 c
cos
 
VA
or a secondary induced voltage V
1
(2.14): listed again
Fig.9-1 Phase angle of single sine wave
Fig.9-2 Phase angle of non-single sine wave (1)
Fig.9-3 Phase angle of non-single sine wave (2)
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B-H ANALYZER SY-8218 / SY-8219
or a secondary
1
is a distorted wave, the relationship
2
Apparent power
皮相電力
θ
Active power
有効電力
VA ´
va
va
VA
θ ´
θ
´
Pc Pc
Active power
有効電力
va
VA ´
VA
θ ´
θ va
Pc Pc
VA
Pc
´