Analysis of Buckling Strength

Topics: Transformer, Buckling, Magnetic field Pages: 5 (3413 words) Published: October 29, 2014


Analysis of Buckling Strength of Inner Windings in
Transformers Under Radial Short-Circuit Forces
Amit Bakshi and S. V. Kulkarni, Senior Member, IEEE

Abstract—The buckling of conductors of inner windings in
transformers is one of the major causes of their failures. It can occur when a large magnitude of radial short-circuit electromagnetic force acts on them. In this paper, initially, mechanical strains developed during winding processes and due to radial short-circuit forces have been determined. The two mechanical strains viz. the short-circuit induced strain and the winding process-induced strain are algebraically added to obtain their resulting strain. The stress corresponding to the resulting strain has been determined by using the Ramberg–Osgood stress-strain relation. The critical buckling stress has been calculated and compared with the resulting stress. The analytically obtained result of the strain induced in the winding conductor during its winding process has been verified using the finite-element method. A case study has been described in which the factor of safety against the buckling strength is determined.

Index Terms—Buckling, short-circuit force, strain, stress, transformers.



OWER transformers should have sufficient mechanical
strength to withstand short-circuit forces. Due to growing
generating capacities and interconnections in power systems, the short-circuit duty of transformers becomes severe. A large amount of current flows in their windings during short-circuit events. The interaction of the circumferential component of the short-circuit current density with the axial component of the leakage flux density produces the radial component of the force density. For midheight conductors of an inner winding, the force density decreases from its outer surface to inner surface.

The effect of radial forces on an outer winding is to produce tensile hoop stresses in its conductors, and they produce compressive hoop stresses in an inner winding which must be adequately supported to avoid its failure [1], [2]. Inner windings generally fail due to a buckling phenomenon [3]–[5]. Buckling failures are of two types, viz. free buckling and forced buckling. The free buckling mode is considered as an unsupported type of failure, that is, there are no constraints present at the inner surface of the winding, which implies that the clearance between the axial-supporting spacers and the winding is appreciable. Also, the portion of conductor buckle does not have any Manuscript received January 01, 2013; revised April 11, 2013; accepted June 10, 2013. Date of publication July 18, 2013; date of current version January 21, 2014. Paper no. TPWRD-00001-2013.

The authors are with the Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai-400076, India (e-mail: amitbakshi@ee.;
Color versions of one or more of the figures in this paper are available online at
Digital Object Identifier 10.1109/TPWRD.2013.2272102

relation to the span of the spacers. In the forced buckling mode, considerable stiffness is provided by the inner support structure to the winding, and the conductor buckles between adjacent axial-supporting spacers are all along the circumference [6]–[9]. The supports can be considered as hinges, and the problem domain is considered as a uniformly compressed circular arch with hinged ends [6], [7], [10]–[12].

During the winding process, an appreciable strain is developed in conductors. This is due to the applied bending moment on the conductors during the process. The process-induced strain was not included in the analysis reported in the previous literature.

In this paper, the aforementioned strain has been taken into account along with the short-circuit-induced strain to determine the resulting stress in the winding...

References: [1] M. Waters, Short-Circuit Strength of Power Transformers. London,
U.K.: Macdonald, 1966, pp
[2] S. V. Kulkarni and S. A. Khaparde, Transformer Engineering: Design, Technology, and Diagnostics. Boca Raton, FL: CRC/Taylor &
Francis, 2012.
[3] Ability to Withstand Short Circuit, IEC 60076-5, 2006–02, 3rd ed.
of large power transformers,” in Proc. CIGRE 6th Southern Africa Regional Conf., Paper no. P 501, 2009, pp. 1–7.
Syst., vol. PAS-90, no. 5, pp. 2381–2390, Sep. 1971.
conditions,” CIGRE Paper No. 12-01, 1972.
no. 3, pp. 1091–1098, May/Jun. 1979.
rep. no. 147, 1962.
Transformers, 2nd ed. New York: Taylor & Francis/CRC, 2010.
Studies. ed. New York: McGraw-Hill, 1961, pp. 297–298.
[13] R. R. Craig Jr., Mechanics of Materials, 2nd ed. New York: Wiley,
2000, pp
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