1. Stray field measurement during power transformer energization Miroslav Novák Faculty of Mechatronics, Informatics and Interdisciplinary Studies Technical University of Liberec  +420 48 535 3626 e-  miroslav.novak@tul.cz

2. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 2/11 Transient phenomenon after transformer switch on Theoretical maximum of mag. flux can reach almost 3× of its nominal amplitude. It induces intensive inrush current with amplitude >50× of nominal current

3. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 3/11 Inrush current Construction and material of mag. circuit hysteresis loop remanent flux Working mag. flux reserve toward saturation Construction of winding coil diameter = magnitude of stray flux Coil resistance, lead-in and power supply impedance SkSk SpSp d

4. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 4/11 Theoretical evaluation Maximal inrush current Primary impedance important Coil diameter dependency Supply resistance Primary resistance Reserve of working flux to saturation Remanent flux Geometry Supply voltage

5. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 5/11 Measurements Samples 2 transformers UI core 1.2 kVA, 230//230 V coil gap 6 mm Hall probe positioning switch on transient recorded at each point Synchronous sampling current, voltage, stray flux Conditions U 1 = 190 V, B = 1.24 T, R net = 0.17  switch on angle 0° Remanent flux 0.6 T by controlled de-energization Load a) no load b) nominal resistive

6. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 6/11 Stray flux in time and position Radial stray flux Peak 106 A Primaryvoltage current flux Core flux

7. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 7/11 Stray flux in time and position 2 Radial stray flux Peak 106 A Primaryvoltage current

8. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 8/11 Stray flux in time and position 3

9. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 9/11 Inrush currents TransformerA p (m 2 ) R p (  ) I max Theory (A)I max Meas. (A)max B stray (mT) 13.1e -3 0.98159150120 15.8e -3 1.33107103133 23.2e -3 0.43216209172 24.9e -3 0.53161165200 4 Coil measured – different diameter = stray field Repeated measurement n = 50, variance <0.1 % Decreasing of inrush current due to coil diameter 26-29 % Decreasing of inrush current due to coil resistance 6-16 %

10. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 10/11 Conclusion Theoretical formula suits to practice Primary stray field limit inrush current 28 % Importance of primary circuit impedance confirmed Recommendations for inrush current decreasing Use outer winding as primary Increase primary diameter through spacers This work was supported by grant GAČR 102/08/P453 “Transformer inrush current suppression”.

11. Stray field measurement during Miroslav Novák MM2010 power transformer energization TU of Liberec 11/11 Thanks you for your attention