Considerations about Maximum Temperature of Toroidal Transformers in Steady-State Conditions


Toroidal transformers, Maximum temperature, Thermal analysis.

How to Cite

Adrian Pleșca. Considerations about Maximum Temperature of Toroidal Transformers in Steady-State Conditions. J. Adv. Therm. Sci. Res. [Internet]. 2020 Oct. 16 [cited 2022 May 23];7(1):22-9. Available from:


 In this paper, a novel method based on a thermal mathematical model which includes the main geometrical, physical and thermal parameters of the toroidal transformer has been developed in order to obtain the maximum temperature inside the transformer during steady-state operating conditions. The influence of electric current and ambient temperature on the maximum temperature has been investigated. To validate the proposed method, some experimental tests have been done. The analyzed transformer had a rated power of 2kVA and the rated primary voltage of 230V. There is a good correlation between experimental and theoretical results with a maximum difference of 3°C.


Hernandez I, de Leon F and Gomez P. Design formulas for the leakage inductance of toroidal distribution transformers. IEEE Transactions on Power Delivery 2011; 26: 2197-2204.

Askari M, Kadir Ab and Izadi M. On the trend of improvement of thermal model for calculating the TOT and HST. Przegląd Elektrotechniczny 2012; 88: 297-301.

Madžarević V, Kapetanović I, Tešanović M and Kasumović M. Different approach to thermal modeling of transformers - a comparison of methods. International Journal of Energy and Environment 2011; 5: 610-617.

Popescu M, Mastorakis N and Popescu-Perescu L. New aspects providing transformer models. Int. Journal of Systems Applications, Engineering & Development 2009; 2: 53-63.

Amoiralis E, Tsili N and Kladas A. Transformer design and optimization: a literature survey. IEEE Transactions On Power Delivery 2009; 24: 1999-2024.

Folvarcny A and Marek M. Experimental analysis of temperature influence on the parameters of the current load type toroidal transformers, compared with conventional types of transformers. 11th Int. Sci. Conf. on Electric Power Engineering, (Brno) 2010; 727-731.

Hwang C, and Jiang Y. Thermal analysis of high-frequency transformers using finite elements coupled with temperature rise method. IEE Proceedings - Electric Power Applications 2005; 152: 832-836.

Lefevre A, Miegeville L, Fouladgar J and Olivier G. 3-D computation of transformers overheating under nonlinear loads. IEEE Transactions on Magnetics 2005; 41: 1564- 1567.

Koizumi K and Ishizuka M. Thermal modeling of toroidal inductor. Nihon Kikai Gakkai Nenji Taikai Koen Ronbunshu 2005; 6: 299-300.

Galdi V, Ippolito L, Piccolo A and Vaccaro A. Parameter identification of power transformers thermal model via genetic algorithms. Electric Power Systems Research 200; 60: 107-113.

Tutkun N. Genetic estimation of iron losses in strip wound toroidal cores under PWM flux conditions. Journal of Magnetism and Magnetic Materials 2006; 300: 506–518.

Nimet O, Grellet G, Morel H, Rousseau J and Ligot D. Optimal design of a toroidal transformer fed by nonsinusoidal high frequency currents. 8th Int. Conf. on Power Electronics and Variable Speed Drives 2000; 57-62.

Sullivan C, Li W, Prabhakaran P and Lu S. Design and fabrication of low-loss toroidal air-core inductors. IEEE Power Electronics Specialists Conference 2007; 1754-1759.

Moses A and Tutkun N. Investigation of power loss in wound toroidal cores under PWM excitation. IEEE Transactions on Magnetics 1997; 33: 3763-3765.

Turchi P, Reass W, Rousculp C, Oro D, Merrill F, Griego J and Reinovsky R. Evaluation of conductor stresses in a pulsed high-current toroidal transformer. 17th IEEE International Pulsed Power Conference 2009; 372-377.

Purushothaman S and de Leon F. Heat-transfer model for toroidal transformers. IEEE Transactions on Power Delivery 2012; 27: 813-820.

Saket M, Jandaghi B, Moghaddami M and Oraee H. Thermal lumped parameter modeling of a toroidal transformer. Electric Power Engineering & Control Systems 2011; 1-6.

Serikov A and Gerasimenko T. Thermal calculation of transformer-type radiator. Russian Electrical Engineering 2011; 82: 371-376.

Folvarčný A, Marek M and Holčáková R. Magnetic properties of types of core for toroidal transformers made from thin lowloss sheets and thermal influence on resulting transformer idle current. Journal of Electrical Engineering 2010; 61: 137- 140.

Grzesik B, Stepien M and Jez R. Toroidal HTS transformer with cold magnetic core – analysis with FEM software. Journal of Physics: Conference Series, 9th European Conference on Applied Superconductivity 2010; 1-8.

Luciano B, Cavalcante de Albuquerque J, Benício de Castro W and Afonso C. Nanocrystalline material in toroidal cores for current transformer: analytical study and computational simulations. Materials Research 2005; 8: 395-400.

Van der Veen M, de Leon F, Gladstone B, Tatu V. Measuring acoustic noise emitted by power transformers. AES 109th Convention 2000; 1-19.

Turkyilmazoglu M. Heat transfer from moving exponential fins exposed to heat generation. International Journal of Heat and Mass Transfer 2018; 116: 346-351.

Turkyilmazoglu M. MHD natural convection in saturated porous media with heat generation/absorption and thermal radiation: Closed-form solutions. Archives of Mechanics 2019; 71: 49-64.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2021 Journal of Advanced Thermal Science Research