Analysis of Short-Circuit Forces at the Top of the Low Voltage U-Type and I-Type Winding in a Power Transformer Leonardo Štrac * , Franjo Kelemen * , Damir Žarko † * Kon ar Power Transformers, Research and Development department, Josipa Mokrovi a 6, 10000 Zagreb, Croatia, e-mail: leonardo.strac@siemens.com † University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Electrical Machines, Drives and Automation, Unska 3, 10000 Zagreb, Croatia, e-mail: damir.zarko@fer.hr Abstract— The aim of this study was to compare the short- circuit forces in the U-type and I-type low voltage winding of a large power transformer. The comparison of forces calculated using 2D Rabin’s method and 3D finite element method is conducted. The influence of the winding helix pitch on the winding forces calculated using 3D finite element method is also investigated. Keywords— Power transformer, short-circuit force, finite element method, Rabin’s method. I. INTRODUCTION Every large power transformer can be exposed to short- circuit conditions during its lifecycle. Therefore, large power transformers have to be designed to endure the time limited short circuit. The low-voltage windings are particularly exposed to high forces during short-circuits due to their high current. Two most common types of low voltage windings in a large three phase power transformer are I-type and U-type helix winding. The I-type winding has an entry at the top and an exit at the bottom of the winding. The U-type winding consist actually of two I- type windings connected at the bottom and has an entry and an exit both at the top of the winding. While U-type has some advantages in better cooling and easier connectivity, there is a question which type of winding better handles short-circuit forces. The calculation of radial and axial forces on transformer's winding coils is performed in many papers using different analytical and numerical methods in 2D and 3D geometry [1-2]. The advantages of 2D method are high calculation speed and low consumption of computer resources. While 2D method can describe the transformer windings and related core limbs correctly, it fails to model the transformer yoke properly. This occurs due to the fact that the winding and the core limb on one hand and the yoke on the other hand have mutually perpendicular axes of rotational symmetry. This paper analyzes axial and radial forces on the first wire of the top turn, forces on every turn, force on transformer clamping system as well as the maximal force on the winding. For each case there were three different calculations used: 2D Rabin’s method, 3D finite element method on the cylinder-shaped winding and 3D finite element method on the helix-shaped winding. Two different comparisons are actually shown here, one between I-type and U-type of the winding and the other between the three types of calculation. To apply 2D Rabin’s method of calculation, Kon ar Power Transformer software for force calculation SileKS was used, while 3D calculations were conducted with commercial finite element software Ansoft Maxwell. All calculations are conducted for peak short-circuit current. II. THEORY It is well known that axial force is the biggest at the top of the winding, and radial force in the middle. Both forces are calculated on the entire height of the winding with the special attention to the top wire of the top turn. Of course, the relevant value of the radial force is that from the middle of the winding. Once the magnetic field was calculated using the 3D finite element method, the following equations were used to calculate the force [3]: The vector force equation is F J B = × . (1) The scalar axial force equation is a z F Fa = ⋅ . (2) The scalar radial force equation is ( ) ( ) sin arctan cos arctan r x y x x F Fa Fa y y = ⋅ + ⋅ (3) The Rabin's method [4] allows analytical formulas to be used for magnetic field calculation on an idealized geometry of a power transformer. The power transformer is presented with a single core limb of an infinite magnetic permeability with a yoke that extends infinitely in the radial direction. Additionally, the sum of winding arrangement ampere-turns must be zero in order for the method to work. Although simplifications impair method’s accuracy for the field calculations far away from the winding, it works very well for the field calculations inside the windings or close to the windings. This, in turn makes the method a logic choice for the calculation of forces on the winding. The Kon ar Power Transformers software for force calculations SileKS calculates also the short-circuit voltage for a given transformer geometry. According to SileKS, the I-type winding has a bit higher short-circuit voltage than the U-type, 13,57 % versus 13,06 % respectively. Therefore, although the nominal current and flux are the same in both cases, the short-circuit current of 870 978-1-4244-1742-1/08/$25.00 c  2008 IEEE