IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010 1657 Numerical Method for the Investigation of Fault Containment and Tank Rupture of Power Transformers Jean-Bernard Dastous, Senior Member, IEEE, Jacques Lanteigne, and Marc Foata Abstract—This paper presents an analysis method based on ex- plicit dynamic analysis, enabling detailed and representative in- vestigations of the mechanical effects of low-impedance faults in power equipment. To illustrate the effectiveness of the proposed method, a given transformer design having caused the projection of a heavy chimney/bushing assembly over a significant distance is used as a case study. A comparison about the observed projection distance of this assembly shows that the method provides represen- tative results, thus offering the significant advantage of replacing costly and unpractical tests. The method is then used to study the retrofit measure proposed in this case to retain the chimney, further exemplifying its power to effectively study different design and ret- rofitting options. Index Terms—Arc containment, explicit dynamic anal- ysis, finite-difference methods, finite-element methods, finite volume methods, internal faults, pressure effects, tank rupture, transformers. I. INTRODUCTION L OW-IMPEDANCE faults in power equipment can lead to catastrophic tank ruptures, resulting in fires, oil spills, and projection of parts. The recent occurrence of these faults for a given transformer design led to the identification of an insulation defect in the chimney supporting the main high-voltage bushing. In some cases, the resulting overpressure caused the detachment of the chimney from the transformer wall, and its projection over a significant distance (Fig. 1). To prevent this hazard, a retrofit measure consisting of retaining the chimney with two belts made from hollow beams has been proposed (Fig. 2). In order to study the mechanical effects of faults within power equipment as well as the adequacy of retrofit measures, such as the one proposed before, a refined numerical simulation methodology was devised and is presented in this paper. This methodology is based on explicit dynamic analysis and permits numerically to simulate in “real time,” the pressure buildup during a fault by reproducing the formation of the gas bubble resulting from decomposition of oil by the arc, and its simul- taneous effects on the equipment item under study, such as the Manuscript received December 15, 2008; revised June 16, 2009. Current ver- sion published June 23, 2010. Paper no. TPWRD-00880-2008. J.-B. Dastous and J. Lanteigne are with the Institut de Recherche d’Hydro-Quebec (IREQ), Varennes, QC J3X 1S1, Canada (e-mail: dastous. jean-bernard@ireq.ca; lanteigne.jacques@ireq.ca). M. Foata is with the Hydro-Québec TransEnergie, Montréal, QC H5B 1H7, Canada (e-mail: foata.marc@hydro.qc.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2010.2047277 deformation of its walls, projection of parts, and oil outside as well as the failure of components, such as bolts and shear of material. This method thus permits replacing tests that are costly and often unpractical, and that are furthermore random in nature since due to the erratic nature of arcs, the amount of fault energy can vary considerably for tests under the same input conditions. Through the case study corresponding to Figs. 1 and 2, this paper presents a detailed description of this methodology, a comparison about the observed projection distance of the chimney which supports its predictive abilities, and the main results from investigating the effectiveness of the proposed retrofit measure, thus demonstrating its relevance for the anal- ysis of fault effects within power equipment. II. METHODOLOGY A. Analysis Method In the situation at hand, many complex phenomena occur within a short time, in the order of tens of milliseconds: • oil decomposition by the arc and interaction of the resulting gas bubble with the surrounding oil; • pressurization and displacement of the oil and its interac- tion with the transformer walls; • increase of mechanical stresses in the materials, up to rup- ture in some cases; • projection of the chimney and its interaction with the belts designed to retain it as well as the expulsion of oil and gas through the opening created. The modeling of these phenomena over time and their inter- action cannot be performed by using standard numerical tech- niques, such as the widely used implicit finite-element analysis method since: • the short duration of the phenomenon involves wave-prop- agation effects which cannot be treated adequately by implicit analysis, which is more appropriate for low-fre- quency structural dynamics; • large deformations at a high strain rate (material nonlin- earity) and large displacements (geometric nonlinearity) are involved, which make convergence difficult using im- plicit numerical schemes; • a small time step for accuracy and stability is necessary to address the above, and the use of these small time steps is not appropriate in implicit numerical schemes which then become costly in terms of computational time. The most appropriate numerical method to adequately ad- dress the aforementioned obstacles is transient explicit dynamic 0885-8977/$26.00 © 2010 IEEE