7. Leakage magnetic field of a transformer

AE1B38EMA

7. MEASUREMENT OF THE LEAKAGE MAGNETIC FIELD OF A TRANSFORMER Task of the measurement 1. Evaluate the search coil parameters: sensitivity constant C CH , self resonant circular frequency  r , simplified series equivalent circuit impedance components L S and R S . .2. Measure the leakage magnetic field of the transformer in the horizontal plane (perpendicular to the transformer core sheets, see Fig. 17b.5). 3. Using the results of measurement decide in which distance can the transformer magnetic field be considered to be of dipole-origin.

Schematic diagram – see Figs. 2 and 3 List of the used equipment Tr - a transformer – the source of the measured leakage magnetic field; G - RC-generator, producer: ..., model number: ...; V - low-frequency millivoltmeter, type ...; mA - milliammeter, type..., class of accuracy ... , range ... mA; HC - Helmholtz coils, C HC = ... A m-1 /A; MC - the search coil; R - the adjustable resistor ... , ... A; Source of AC voltage 48 V, 6 V.

Theoretical background An AC magnetic field in air at low frequencies can be most easily measured by a search coil (also called pick-up coil, induction coil, measuring coil). In most cases this coils is a cylindrical coil without any ferromagnetic core. If we measure periodic field waveforms having only one pass through zero during the period, magnetic flux density B (magnetic induction) can be calculated as: Bm 

where B m U RM f N S

U RM 4f S N

(1)

is the maximum value of measured magnetic induction B in the direction of the coil axis (T), is the rectified mean value (= arithmetic mean value) of the induced voltage (V), is the frequency of the fundamental harmonic component of the measured voltage (Hz), is the number of turns of the search coil, is the cross-sectional area of the search coil (m2). 1 of 5

7. Leakage magnetic field of a transformer

AE1B38EMA

The magnitude of the magnetic field strength H m can be calculated as Hm 

A m

Bm 0

-1

; T,  0  4  10 -7 H m -1



(2)

Equation (1) can be used even for non-sinusoidal waveforms supposing that the induced voltage is measured by an AC voltmeter with built-in rectifier - either moving coil or electronic. We can get the rectified mean value by dividing reading of these voltmeters by 1.11. (For non-sinusoidal voltage waveform it is NOT the voltage RMS value!) The measured object

Ii is possible to replace approximately the source of the magnetic field the magnetic path of which is mainly in the air by a magnetic field of a magnetic dipole (see Fig. 1). Hy y

-Q m

+Q m



Hx

x

Fig. 1 A coordinate system for measurement of the dipole magnetic field in a plane xy

Under the assumption that   x and   y, the magnetic field strength on axes x and y of the plane xy can be expressed by relations Hx 

mC 2 0 x

3

,

Hy 

mC 4 0 y 3

(3)

where mC

is Coulomb magnetic moment (Wb.m=T.m3),

 0 = 4 10-7 H/m

is permeability of the open space (vacuum),

x, y

are distances of the measuring points from the center of the dipole (m).

If it is possible by measurement of components H x and H y to prove that in a certain distance from the measured object the magnetic field is of dipole character, then the field in this area is fully determined by the value of m C .

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7. Leakage magnetic field of a transformer

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Hints for the measurement Finding parameters of the search coil Resistance of the coil winding R S = kΩ (can be measured by any DC method of resistance measurement). Total coil impedance can be measured e.g. using the V-A (Ohm) method. It is however necessary to know prior to this measurement the own resonant frequency of the coil f r . This frequency can be found using circuit from Fig. 17b.3. search coil Ls

Rs

I mA

Cp U

G

V

Fig. 2 Circuit for finding the own resonant frequency of the measured coil

This circuit is fed from the source of the constant voltage U. Impedance of this circuit is maximal at the resonant frequency f r , so the current I at this frequency is minimal. The resonant frequency is fr 

1

(4)

2 Ls C p

Note: Capacitor C p is a fictive element representing the effect of individual inter-turn capacitances. The circuit from Fig. 2 can be used for finding the lowest resonant frequency; capacitance C p is here mainly the capacitance of the connecting cable. Impedance of the search coil shall be measured on frequency lower than f m = 0,1 f r , where the influence of the capacitance C p can be disregarded. The impedance at the frequency f m is Zm 

where U m Im

Um 1  Rs2  ωm2 L2s , Ls  Im ωm

Z m2  Rs2

(5)

is voltage measured at the frequency f m , is current measured at the frequency f m .

The value of C p can be calculated from the relation (4), where the measured resonance frequency f r and the self inductance L s are known. b) Finding the constant of the search coil The constant K CH of the measured coil can be found by measurement of the output voltage of the measured coil in the known magnetic field of the Helmholtz coils in circuit according to Fig. 3. Since the magnetic field strength of coils has the same frequency (50 Hz) and the same waveform (harmonic, i.e. sinusoidal) as the leakage magnetic field of the transformer, there is

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7. Leakage magnetic field of a transformer

K CH 

AE1B38EMA

H max  U RMS

2 I RMS K HZ

(17b.10)

U RMS

where K HZ is constant of the Helmholtz coils pair (m-1), I RMS is the Helmholtz coils current (A), U RMS is the RMS value of the voltage induced in the measuring coil (V).

R A

HC

Ief

Helmholtz coils

Hm V 6 V, 50 Hz

MC

U ef

Fig. 3 Circuit for finding the constant of the measuring coil (search coil)

Measurement of the magnetic field strength of the leakage magnetic field Measurement of the leakage magnetic field of transformer will be performed using arrangement according to Fig. 4. The transformer is fed by voltage at power line frequency 50 Hz. Both the x and y axes pass through the center of the transformer ground-plan. The voltage induced in the measuring coils shall be measured in several points on axes x and y at known (measured) distances from the transformer center. The values of the magnetic field strength can be found using the relation (3) as H xmax = K CH  U Hx = f(x) and H ymax = K CH  U Hy = f(y). The value of the m C can be found from the relation of the (3) and from the measured values of m C we find which distances the measured field corresponds to the dipole field (in this region there is m C = konst). Note: Value of voltage induced at the search coil by switched-off transformer should be checked before measurement for each position of the measuring coil. Its value should be negligible compared to the measured voltage induced by transformer leakage magnetic field.

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7. Leakage magnetic field of a transformer

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U Hy

Hy

axis y y D

U Hx

Hx

axis x

x

Fig. 4 Search coil positioning for the leakage field measurement

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