1566 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 3, JULY 2007 Asymmetry During Load-Loss Measurement of Three-Phase Three-Limb Transformers R. Escarela-Perez, Senior Member, IEEE, S. V. Kulkarni, Member, IEEE, N. K. Kodela, and J. C. Olivares-Galvan, Member, IEEE Abstract—When the load-loss measurement test is conducted on three-phase transformers, an appreciable asymmetry is observed among the power readings of the three phases. This asymmetry is the result of two causes, viz. asymmetrical disposition of phases in space with respect to each other and unequal stray losses produced by phases. The disposition of phases leads to asymmetrical mutual impedances between phases and this is the principal contributor to the phenomenon. Another factor that may have an important con- tribution to the phenomenon is the deviation of the phase angle difference between the voltages of the three phase source (used during the test) from 120 . The causes are analyzed using a de- tailed three-dimensional (3-D) finite-element (FE) simulation of a 31.5 MVA, 132/33 kV transformer. In addition, a six-port network impedance model is deduced from open-circuit 3-D FE simulations. The impedance model is able to reproduce any condition of the transformer (e.g., open-circuit, short-circuit or on-load conditions) since it captures all the transformer electromagnetic phenomena. The six-port network results are discussed in order to elaborately clarify the intriguing problem of asymmetrical load-loss distribu- tion, which is important for both transformer manufacturers and users. The results are further explained through sequence compo- nents of currents. Index Terms—Asymmetry, load loss, finite element analysis, mu- tual inductance, transformer. I. INTRODUCTION T HE transformer is a complex three-dimensional (3-D) piece of electromagnetic equipment. Various phenomena occurring inside the transformer continue to attract the attention of researchers due to the need to give a comprehensive expla- nation or to give practical solutions for them. The continuous development of numerical techniques have enabled researchers to simulate the electromagnetic phenomena in transformers with great detail, which were previously analyzed by semi-em- pirical (or approximated analytical) formulations. One of such phenomena is the asymmetry observed during the load-loss measurement test in three-phase transformers. The load losses in a transformer are commonly measured by a three-wattmeter method. It is generally found that the three readings are appreciably different, even though the total losses Manuscript received April 24, 2006; revised August 11, 2006. Paper no. TPWRD-00222–2006. R. Escarela-Perez is with the Departamento de Energia, Universidad Autonoma Metropolitana, Mexico City C.P. 02200, Mexico (e-mail: r.escarela@ieee.org). S. V. Kulkarni and N. K. Kodela are with the Electrical Engineering Depart- ment, Indian Institute of Technology-Bombay, Mumbai 400076, India (e-mail: svk@ee.iitb.ac.in). J. Olivares-Galvan is with the Instituto Tecnologico Superior de Zapopan, Jalisco 45019, Mexico (e-mail: jolivare_1999@yahoo.com). Digital Object Identifier 10.1109/TPWRD.2007.899248 (addition of the three readings) are near to the design value. This asymmetry raises doubts in the minds of transformer users, and test engineers find it difficult to give a convincing explanation for the phenomenon. The stray loss may form an appreciable part of the total load loss in power transformers. Hence, the simplest explanation which may normally be given is that the stray loss for each phase could be different due to the asymmetry of tank and other structural parts. However, this explanation is marginally true. The major reason contributing to the phenom- enon is the asymmetry of the mutual magnetic couplings be- tween phases. The asymmetry observed during the no-load test has been elaborately discussed in the literature [1]–[4]. This magnetizing asymmetry, which results in different currents and powers of the three phases, occurs due to asymmetry in magnetic reluctances offered to the three phase fluxes. It has been observed that the no-load loss is even negative in one of the phases sometimes. The literature published on the asymmetry observed during the load-loss test is almost nonexistent, although there could be classified documents and analysis reports available internally with transformer manufacturers. An interesting work [5], that sheds light on this subject, has been presented until very re- cently. Magnetic circuit theory is used there for explaining the asymmetry phenomenon. However, the numerical model is not rigorously deduced from transformer geometry and material properties. In order to obtain correct results, the reluctances are adjusted to reproduce test results. Hence, the work presented in this paper is motivated by the lack of adequate published analysis on this phenomenon which continues to intrigue transformer users and manufacturers. This work attempts to give a comprehensive explanation for the asymmetry in the loss values of the three phases during the load-loss test. A 31.5 MVA, kV three-phase transformer has been analyzed using a comprehensive 3-D time-harmonic finite-element (FE) analysis. The 3-D FE model is first used to simulate the load-loss test, this way obtaining stray losses, winding currents and voltages. Then, six open-circuit simula- tions are performed to establish a six-port impedance network model, which is capable to encapsulate all the electromagnetic details of the 3-D FE model. Hence, any operating condition can be accurately obtained without resorting to the 3-D FE model any longer. Moreover, the impedance model gives clear insight into the asymmetry phenomenon. II. LOAD LOSS ASYMMETRY When a three-phase three-limb core type transformer is subjected to the load-loss measurement test, it is found that the 0885-8977/$25.00 © 2007 IEEE