S. E. Zirka, Y. I. Moroz, C. M. Arturi, D. Bonnman


Purpose. To show capabilities of topological models of three-phase, five-limb transformer to correctly represent transformer operation in regimes with high flux densities in the core. As a practically important example, time domain response of transformer subjected to geomagnetically induced currents (GIC) is analyzed and compared with results of a comprehensive field experiment.Methodology.  Transformer magnetic model, which takes into account geometry of the core and windings, is transformed in a dual electric equivalent scheme, whose transient is calculated by using EMTP-ATP. The results obtained demonstrate the importance of incorporating the positive and zero sequence impedances of power network.Findings. A simple and reliable model of five-limb transformer is proposed. It was found that the presence of the transformer tank can be effectively accounted for by linear inductances representing the paths of the off-core fluxes from yoke to yoke. The modeling of GIC events represented in the paper is the most accurate ever obtained for three-phase, five-leg transformers. The model is validated by close agreement of the predicted values and waveforms of the phase currents and reactive power with those measured in tests performed on two 400 MVA transformers connected back-to-back and to a 400 kV power network.
Originality. It is shown that a simplified non-hysteresis model developed portrays the behavior of the of five-limb transformer under GIC condition with the same good accuracy as its hysteresis model. Both the transformer models are well grounded. So, the paper dispels some misconceptions about the influence of the hysteresis properties of the core material and tank in transient modeling of five-leg transformers.Practical value. The practical value and significance of the paper is caused by the fact that the model proposed is a simple and reliable tool for power system studies. The paper warns of using unnecessary complicated models whose parameters are difficult to be estimated by experiments or calculations. 


five-limb transformer; topological transient models; transients; off-core magnetic fluxes; current waveforms; reactive power; experimental validation; back-to-back transformer test

Full Text:



Arturi, C. M. (1991). Transient simulation of a three phase five limb step-up transformer following an out-of-phase synchronization. IEEE Trans. Power Delivery, 6, 1, 196 – 207. DOI: 10.1109/61.103738.

Chen, X., Venkata, S.S. (1997). A three-phase three-winding core-type transformer model for low-frequency transient studies. IEEE Trans. Power Delivery, 12, 2, 775 – 782. DOI: 0885-8977/97/$10.00.

Mork, B. A., Gonzalez, F., Ishchenko, D., Stuehm, D. L., Mitra J. (2007). Hybrid transformer model for transient simulation – Part I: Development and parameters. IEEE Trans. Power Delivery, 22, 1, 248 – 255. DOI: 10.1109/TPWRD.2006.883000.

Zirka, S. E., Moroz, Y. I., Arturi, C. M. (2014). Accounting for the influence of the tank walls in the zero-sequence topological model of a three-phase, three-limb transformer. IEEE Trans. Power Delivery, 29, 5, 2172–2179. DOI: 10.1109/ TPWRD.2014.2307117.

Zirka, S. E., Moroz, Y.I., Høidalen, H. Kr., Lotfi, A., Chiesa, N., Arturi, C. M. (2017). Practical experience in using a topological model of a core-type three-phase transformer – No-load and inrush conditions. IEEE Trans. Power Delivery, 32, 4, 2081–2090. DOI: 10.1109/TPWRD. 2016.2618900.

Tikhovod, S.M. (2014). Modelirovanie perehodnyh processov v transformatorah na osnove magnitojelektricheskih shem zameshhenija. [Modeling transformer transients using magnitoelectric equivalent schemes]. Elektrotehnika i elektroenergetika, 2, 59-68, (in Russian).

Lahtinen, M., Elovaara, J. (2002). GIC occurrences and GIC test for 400 kV system transformer. IEEE Trans. Power Delivery, 17, 2, 555–561. DOI: 0885-8977(02)02750-4.

Rezaei-Zare, A. Marti, L., Narang, A., Yan, A. (2016). Analysis of three-phase transformer response due to GIC using an advanced duality-based model. IEEE Trans. Power Delivery, 31, 5, 2342–2350. DOI: 10.1109/TPWRD. 2015.2505499.

Rezaei-Zare, A. (2015). Enhanced transformer model for low- and mid-frequency transients–Part I: Model development. IEEE Trans. Power Delivery, 30, 1, 307–315. DOI: 10.1109/TPWRD.2014.2347930.

Rezaei-Zare, A. (2015). Enhanced transformer model for low- and mid-frequency transients–Part II: Validation and simulation results. IEEE Trans. Power Delivery, 30, 1, 316–325. DOI: 10.1109/TPWRD.2014.2347934.

Lambert, M., Mahseredjian, J. (2013) Electromagnetic transient type transformer models for geomagnetically-induced current (GIC) studies. EPRI Report 3002000832.

Zirka, S. E., Moroz, Y. I., Rahimpour, E. (2017). Towards a transformer transient model as a lumped-distributed parameter system. Compel, 36, 3, 741–750. DOI: 10.1108/COMPEL-09-2016-0389.

Zirka, S. E., Moroz, Y. I., Chiesa, N., Harrison, R. G., Høidalen, H. Kr. (2015). Implementation of inverse hysteresis model into EMTP – Part II: Dynamic model. IEEE Trans. Power Delivery, 30, 5, 2233–2241. DOI: 10.1109/TPWRD. 2015.2416199.

Moroz, Y. I., Zirka, S. E. (2014). Inverse models of magnetic hysteresis, [Online]. Available:

Alternative Transients Program, ATP-EMTP, (2016). [Online]. Available:

Tleis, N. D. (2008). Power systems modelling and fault analysis: Theory and practice. New York: Newnes/Elsevier, 625.

Evdokunin, G. A. (2016). Jelektricheskie sistemy i seti [Electrical systems and networks]. Saint Petersburg: Rodnaya Ladoga, 384, (in Russian).

GOST Style Citations


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Copyright (c) 2018 S. E. Zirka, Y. I. Moroz, C. M. Arturi, D. Bonnman

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

Address of the journal editorial office:

Editorial office of the the science journal "Electrical Engineering and Power Engineering" ("Electrotechnics and Electroenergetics")

Zaporozhye National Technical University, 

 Zhukovskiy street, 64, Zaporizhzhya, 69063, Ukraine. 

Telephone: +38-061-769-82-96 – the Editing and Publishing Department.


Reference to the journal is obligatory in the cases of complete or partial use of its materials.