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Analytical calculation of self Inductance of the secondary winding of a current transformer with a toroidal magnetic core

D.Yu. Vikharev, A.Yu. Murzin, N.A. Rodin

Vestnik IGEU, 2026 issue 1, pp. 49—58

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Abstract in English: 

Background. The study of steady‑state and transient processes in current transformers relies on constructing an equivalent circuit and calculating its parameters. One of the elements of the equivalent circuit is the leakage inductance of the secondary winding. Its value is primarily determined by the degree of the uniformity of the winding. The research results, as well as reference data indicate the necessity to take into account leakage inductance during engineering calculations. Currently, leakage inductance is determined experimentally. Existing analytical methods to calculate this parameter cannot be applied to obtain accurate results due to the assumption of uniformity of the winding when calculating the self‑inductance of the secondary winding. Thus, to develop a method for analytical calculation of the self‑inductance of the secondary winding considering the degree of its uniformity is an urgent task.

Materials and methods. To determine the leakage inductance, methods of mathematical modeling of electrical circuits have been used. The analytical expressions to calculate self‑inductance of the secondary winding are based on the use of the magnetic vector potential. Methods of vector analysis have been applied to transform the derived expressions into their final form.

Results. The authors have formulated an analytical expression to calculate the self‑inductance of the secondary winding of a current transformer considering the degree of the uniformity of the winding. The calculated expressions have been verified based on the experimental results obtained with a toroidal winding with an adjustable sector angle of the winding.

Conclusions. The analytical expressions obtained during the study can be used to calculate the leakage inductance of the secondary winding of a current transformer and to construct its equivalent circuit.

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Key words in Russian: 
трансформатора тока, индуктивность рассеяния, собственная индуктивность, векторный потенциал
Key words in English: 
current transformer, leakage inductance, self-inductance, magnetic vector potential
The DOI index: 
10.17588/2072-2672.2026.1.049-058
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