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 testDefinition of symbols

C

= Number of conductors in series per phase

tp

N

= The number of turns per phase (i.e.

Z

´

2

)

p

N

= The number of parallel paths per phase

F

= Useful flux per pole

p

= Number of pole pairs

n

= Speed in r.p.s. (revolution per second)

f

= Frequency

d

K

=The winding distribution or spread factor

p

K

=The coil pitch or cording factor

Basis formula

The following formula forms the basis of theory behind the flux test.

p

tp

p

d

rms

N

N

K

K

f

E

F

´

´

´

´

´

=

44

,

4

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:

)

(

poles

of

Number

´

F

=

Step 2:

There are 2 poles in 1 pole pair. The formula therefore becomes:

p

´

´

F

=

2

Step 3:

The amount of magnetic flux that “cuts” a conductor in 1 second is therefore:

n

p

´

´

F

=

2

( the average e.m.f. generated per conductor is therefore:

pn

E

average

´

F

´

=

2

Step 4:

The average e.m.f. generated per phase therefore becomes:

C

pn

E

average

´

´

F

´

=

2

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:

Factor

RMS

Factor

Average

Factor

Convertion

=

635

,

0

707

,

0

=

11

,

1

=

( The R.M.S. voltage generated per phase is:

C

pn

E

rms

´

´

F

´

´

=

2

11

,

1

F

´

´

´

=

np

C

22

,

2

Step 6:

The numbers of conductors in series (

C

), can be replaced with the number of turns per phase (

tp

N

) in the formula. Since there are 2 conductors in series per turn, a factor of 2 should be used when using

tp

N

instead of

C

.

F

´

´

´

=

np

C

E

rms

)

(

22

,

2

F

´

´

´

=

np

N

tp

)

2

(

22

,

2

F

´

´

´

´

=

np

N

tp

2

22

,

2

F

´

´

´

=

np

N

tp

44

,

4

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:

np

f

=

When replacing

np

with

f

, the formula changes as follows:

F

´

´

´

=

tp

rms

N

np

E

44

,

4

F

´

´

´

=

tp

N

f

44

,

4

Step 8:

The winding distribution or spread factor (

d

K

) has the following ratio:

winding

ed

concentrat

a

with

f

m

e

winding

d

distribute

a

with

f

m

e

K

d

.

.

.

.

.

.

=

When the winding distribution is accommodated, the formula changes as follows:

F

´

´

´

´

=

tp

d

rms

N

K

f

E

44

,

4

Step 9:

The coil pitch or cording factor (

p

K

) is the following ratio:

coil

pitched

full

a

with

f

m

e

coil

pitched

long

or

short

a

with

f

m

e

K

p

.

.

.

.

.

.

=

The figure for

p

K

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:

F

´

´

´

´

´

=

tp

p

d

rms

N

K

K

f

E

44

,

4

Step 10:

The number of parallel paths per phase (

p

N

) must also be considered. The formula then becomes:

p

tp

p

d

rms

N

N

K

K

f

E

F

´

´

´

´

´

=

44

,

4

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:

tp

p

d

p

L

L

N

K

K

f

N

V

´

´

´

´

´

=

F

-

44

,

4

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” (

F

V

) required for rated flux in the back of the core is:

100

2

44

,

4

x

f

V

F

´

÷

ø

ö

ç

è

æ

F

´

´

=

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 (

S

V

).

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:

F

S

T

V

V

N

=

T

N

is the number of is turns,

S

V

is the test voltage and

F

V

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

length

core

Total

only

material

magnetic

lenght

Summated

factor

Stacking

"

"

=

Step 2:

The area mentioned in Fig. 6 is calculated as follows:

factor

Stacking

depth

Core

of

Back

length

Core

Area

´

´

=

Fig. 9

Step 3:

The flux density (

B

) in Tesla at the back of the core is calculated as follows:

Area

B

)

2

/

(

F

=

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:

p

´

=

diameter

core

of

back

Average

path

flux

of

Length

)}

2

(

{

depth

slot

diameter

Inside

diameter

Outside

diameter

core

of

Back

´

+

-

=

Step 3:

The total ampere-turns (

MMF

) required to induce the required flux density (

B

) in the back of the core area is:

fluxpath

of

length

H

MMF

´

=

Step 4:

The steady state supply current in ampere during the test is calculated as follows:

T

S

N

MMF

I

=

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

The initial current, immediately after the supply is switched on, will be higher than the steady state current (

S

I

) due to the transient inrush currents. The level of the inrush current is not predictable in practical terms. The reason for this is:

· The core’s remnant flux and its polarity are not known.

· 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)

6 turns

7 turns

X

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