Download Rationale for the power flux test

Power flux test on a stator core
by Kobus Stols
Rationale for the power flux test
The purpose of a power flux test is to test the integrity of the insulation between the lamination plates in
the core of a stator. The EL-CID (electromagnetic core imperfection detection) is the preferred test, but
it was found that in some cases, there is still a need for a power flux test. The resistance between
laminations is not always linear under different voltage levels. A power flux test with a higher axial
potential difference between laminations may therefore yield core faults that may not detectable by an
EL-CID test.
The axial potential differences between adjacent lamination plates are explained with the aid of Figs.1
and 2.
Fig. 1
Fig. 2
The relevant polarity of the voltages that drive the Eddy current is shown in the Figure 2. Note the
opposing polarities on two adjacent sides of the insulation.
Fig. 3
Flux between 80% and 105% of rated flux are normally used to perform a power flux test. The % flux
level refers to the flux in the back of the core and not to the flux per pole.
Test equipment setup
The ideal setup to perform the test is illustrated in Fig. 4.
Fig. 4
The following provides the essential calculations regarding a power flux test
Definition of symbols
C
=
Number of conductors in series per phase
N tp
=
The number of turns per phase (i.e. 2  Z )
Np
=
The number of parallel paths per phase

p
=
Useful flux per pole
=
Number of pole pairs
n
=
Speed in r.p.s. (revolution per second)
f
=
Frequency
Kd
=
The winding distribution or spread factor
Kp
=
The coil pitch or cording factor
Basis formula
The following formula forms the basis of theory behind the flux test.
E rms 
4,44  f  K d  K p  N tp  
Np
This steps that follows illustrates step-by-step, based on first principles, where the formula originated
from.
Step 1:
The amount of magnetic flux that “cuts” a conductor in 1 revolution:
   ( Number of poles )
Step 2:
There are 2 poles in 1 pole pair. The formula therefore becomes:
   2 p
Step 3:
The amount of magnetic flux that “cuts” a conductor in 1 second is therefore:
 2pn
 the average e.m.f. generated per conductor is therefore:
E average  2    pn
Step 4:
The average e.m.f. generated per phase therefore becomes:
Eaverage  2    pn  C
Step 5:
If a sinusoidal waveform is assumed, the average e.m.f. can be converted to an R.M.S. value by
multiplication with the following factor:
Convertion Factor 

Average Factor
RMS Factor
0,707
0,635
 1,11
 The R.M.S. voltage generated per phase is:
Erms  1,11 2    pn  C
 2,22  C  np  
Step 6:
The numbers of conductors in series ( C ), can be replaced with the number of turns per phase ( N tp )
in the formula. Since there are 2 conductors in series per turn, a factor of 2 should be used when
using N tp instead of C .
Erms  2,22  (C )  np  
 2,22  (2 N tp )  np  
 2,22  2  N tp  np  
 4,44  N tp  np  
Step 7:
Convert the speed and the number of poles to frequency. Note that " n " is already expressed in
revolutions per second, and not per minute:
f  np
When replacing np with f , the formula changes as follows:
E rms  4,44  np  N tp  
 4,44  f  N tp  
Step 8:
The winding distribution or spread factor ( K d ) has the following ratio:
Kd 
e.m. f . with a distributed winding
e.m. f . with a concentrated winding
When the winding distribution is accommodated, the formula changes as follows:
E rms  4,44  f  K d  N tp  
Step 9:
The coil pitch or cording factor ( K p ) is the following ratio:
Kp 
e.m. f . with a short or long pitched coil
e.m. f . with a full pitched coil
The figure for K p is 1,0 if the coil is fully pitched (i.e. 180º electrical).
When the coil pitch or cording factor is accommodated, the formula changes as follows:
E rms  4,44  f  K d  K p  N tp  
Step 10:
The number of parallel paths per phase ( N p ) must also be considered. The formula then becomes:
E rms 
4,44  f  K d  K p  N tp  
Np
Flux in the back of the core
It is important to know the rated flux in the back of the core before the number of turns for the test
can be calculated.
Step 1:
The rated flux per pole when the formula in step 10 of the previous section is manipulated to extract
the flux element:

VL  L  N p
4,44  f  K d  K p  N tp
Step 2:
The flux from a pole divides into 2 as soon as it enters the stator core. This is illustrated in Figure 4.
The flux in the circumferential direction of the stator core yoke is therefore half of the flux per pole.
Fig. 5
The “flux voltage” ( VF ) required for rated flux in the back of the core is:
 x
VF  4,44  f    
 2  100
The figure “ x ” in the formula is the % flux level chosen for the test. Good results can be obtained
when the test is performed at flux levels that vary between 75% and 105% of the rated flux level.
The sinusoidal voltage of a given magnitude and frequency dictates the magnitude of the steady
state flux regardless of the core dimensions and the property of the core material.
Test voltage
The ideal is to have a variable supply, but since this is seldom available, a fixed voltage is normally
used.
Any of the readily available supplies can be used for the test. This chosen supply is referred to the
test voltage ( V S ).
The effect of the different voltage sources is the number of turns and the current required for the test.
The availability of a specific cable for the test normally dictates the voltage source.
Number of turns
The number of turns for the rated flux test can be calculated as follows:
NT 
VS
VF
N T is the number of is turns, VS is the test voltage and VF is the “flux voltage”.
Flux density calculation
The flux is distributed through the cross-sectional area as shown by the light red colour in the
simplified figure below.
Fig. 6
The slots in the core cause a high reluctance path in the inner path of the core. This high reluctance
path is shown in a light yellow colour in the illustration.
Fig. 7
The flux during the test will tend to follow the path with the least reluctance i.e. the path shown in red.
The high reluctance path (the yellow area) should therefore be ignored when the cross-sectional area
is calculated. The length of the core is determined by the following:

Lamination thickness

Number of laminations

Ventilation space distance

Number of ventilation spaces

The thickness of interlamination insulation
Step 1:
The total core length is not made of magnetic material. The stacking factor is basically used to obtain
the effective length of the core from a magnetic material perspective.
Fig. 8
Stacking factor 
Summated " lenght " magnetic material only
Total core length
Step 2:
The area mentioned in Fig. 6 is calculated as follows:
Area  Core length  Back of Core depth  Stacking factor
Fig. 9
Step 3:
The flux density ( B ) in Tesla at the back of the core is calculated as follows:
B
( / 2)
Area
Test current calculation
The magnetising current depends on the size of the core and the type of material used. It is important
to know how many amperes will be drawn by the winding in order to size the cable correctly.
Step 1:
Take the flux density ( B ) calculated previously and read the corresponding magnetic field intensity
( H ) from the B-H curve that is relevant to the specific core material.
Fig. 10
Step 2:
The magnetic field intensity ( H ) is expressed in ampere-turns/meter. It is therefore required to
calculate the length of the magnetic path before the magneto magnetic force ( MMF ) can be
calculated.
The length of the flux path is calculated as follows:
Length of flux path  Average back of core diameter  
Back of core diameter  Outside diameter  {Inside diameter  (2  slot depth)}
Step 3:
The total ampere-turns ( MMF ) required to induce the required flux density ( B ) in the back of the
core area is:
MMF  H  length of fluxpath
Step 4:
The steady state supply current in ampere during the test is calculated as follows:
IS 
MMF
NT
The test current will decrease with an increase in the number of turns as can be seen in the example
shown in Figure 11.
Fig. 11
X the steady state
The initial current, immediately after the supply is switched on, will be higher than
current ( I S ) due to the transient inrush currents. The level of the inrush current is not predictable in
practical terms. The reason for this
is:
6 turns

The core’s remnant flux and its polarity are not known.
7 turns

The point of the sine wave, where the supply voltage will be switched on, is not predictable. In
the worst condition, the newly applied voltage may attempt to set up a flux in the same direction
of the remnant flux, thereby driving the core into saturation with a significant increase in
magnetising current being a result.
Test duration
The duration of the test depends on the size of the core and whether the stator bars are still fitted.
The duration of the test can typically vary between 30 and 70 minutes.
Core evaluation
The temperatures in the core depend on the flux density. The temperature in the teeth will therefore be
lower than the temperature in the area at the back of the core as can be seen in the infrared picture
shown in Fig. 12.
Fig. 12
The influence of the emissivity of the core material and the reflection of light from external sources
should be considered when using an infrared temperature measuring device. A calibrated temperature
meter that utilises a different technology can be used to confirm the temperature of a suspected
“hotspot”.
It is important to compare areas with similar flux density levels when evaluating the core. A difference in
“hot spot” versus average core temperature of less than 10º Celsius is normally acceptable when the
test is performed at flux levels between 85% and 100% of the rated level.
Disclaimer
It should be noted that a power flux test has the potential to destroy a stator core if not performed
correctly or if any test values are incorrectly calculated. The author of this article therefore does not take
any responsibility if the information provided in the article is used, perused, disseminated, copied or
stored as a reference by anybody.
References

ISBN 0-471-61447-5, Operation and Maintenance of Large Turbo-Generators (by Geoff Klempner
& Isidor Kerszenbaum)

ISBN 0-582-41144-0, Electrical Technology (by Edward Hughes)