Analytical Method for Calculating the Magnetic Flux in a High-Voltage Test Transformer’s Magnetic Circuit under Load

  • Lyudmila I. SAHNO
  • Evgeniy D. PARAMONOV
  • Ol’ga I. SAHNO
  • Stanislav O. POPOV
DOI: https://doi.org/10.24160/0013-5380-2025-11-39-48
Keywords: high-voltage test transformer, magnetic circuit, magnetic flux, magnetic induction, transformer equivalent circuit

Abstract

A feature of high-voltage test transformers is a capacitive nature of their load and high leakage inductance. According to the standard calculation procedure for transformers, the magnetic circuit cross-section is selected so that the induction amplitude would not exceed the permissible value in the no-load mode. However, in the nominal mode, this condition may be upset, as a result of which the permissible secondary voltage sinusoidal distortion coefficient becomes exceeded, thereby affecting the quality of measurements. The article proposes an analytical method for calculating the magnetic flux and magnetic induction in the magnetic circuit during the transformer operation on a capacitive load. The induction value obtained as a result of such calculation should be used to refine the magnetic circuit cross-section selected in the no-load mode. The analytical method is convenient to use both in designing a transformer using the standard methodology and in performing multi-criteria optimization of its design, because unlike numerical calculations, it provides significant time savings. According to the proposed method, an open thin winding is introduced in the analysis circuit diagram, which is tightly adjacent to the magnetic circuit in the place where the magnetic induction has to be determined. To reduce the calculation time, it is proposed to find the average value of induction in the magnetic circuit core and yoke. The formula used for calculating the leakage inductance takes into account the trapezoidal shape of the secondary winding. Expressions for the coefficient of magnetic flux change in the magnetic circuit under load have been obtained. The article presents dependences of the magnetic flux increase coefficient on the tested object capacitance for the core and yoke of a high-voltage test transformer for a secondary voltage of 100 kV. Recommendations on calculating the magnetic circuit cross-section area of a designed armored transformer are given.

Author Biographies

Lyudmila I. SAHNO

(Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia) – Senior Researcher, Professor of the Higher School of High-Voltage Energy, Dr. Sci. (Eng.).

Evgeniy D. PARAMONOV

(Mars-Energy SK LLC, St. Petersburg, Russia) – Design Engineer.

Ol’ga I. SAHNO

(Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia) – Senior Researcher, Docent of the Higher Mathematics Dept., Cand. Sci. (Eng.).

Stanislav O. POPOV

(Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia) – Docent of the Higher School of High-Voltage Energy, Dr. Sci. (Eng.), Docent.

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Published
2025-09-29
Issue
No 11 (2025): Вulletin № 11
Section
Article