Chapter 5. Rabins&acirc;€™ Method for Calculating Leakage Fields, Forces, and Inductances in Transfo

# Chapter 5. Rabinsâ€™ Method for Calculating Leakage Fields, Forces, and Inductances in Transfo

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149 5. RABINS’ METHOD FOR CALCULATING LEAKAGE FIELDS, FORCES, AND INDUCTANCES IN TRANSFORMERS Summary Rabin’s method utilizes a simplified transformer geometry, consisting of a core, coils, and yokes of infinite extent, to solve Maxwell’s equations. This method works well for calculating the magnetic field near the coils so that quantities such as inductances and forces which depend on this near field are accurately calculated. Since the tank wall, clamping structure, and other details are omitted, this method does not allow one to calculate stray losses in these structures. We use this method to find forces, the two winding leakage inductance, as well as self and mutual inductances between coil sections. 5.1 INTRODUCTION Modern general purpose computer programs are available for calculating the magnetic field inside the complex geometry of a transformer. These numerical methods generally employ finite elements or boundary elements. Geometric details such as the tank wall and clamping structure can be included. While 3D programs are available, 2D programs using an axisymmetric geometry are adequate for most purposes. Although inputting the geometiy, the Ampere-turns in the winding sections, and the boundary conditions can be tedious, parametric procedures are often available for simplifying this task. Along with the magnetic field, associated quantities such as inductances and forces can be calculated by these methods. In addition, eddy currents in structural parts and their accompanying losses can be obtained with the appropriate a.c. solver. In spite of these modern advances in computational methods, older procedures can often be profitably employed to obtain quantities of interest very quickly and with a minimum of input. One of these is Rabins’ method, which assumes an idealized transformer geometiy [Rab56]. This simplified geometry permits analytic formulas to be © 2002 by CRC Press

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RABINS’ METHOD 150 developed for the magnetic field and other useful quantities. The geometry consists of a single leg of a single or possibly 3 phase transformer. The leg consists of a core and surrounding coils which are assumed to be axisymmetric, along with yokes which are assumed to be of infinite extent at the top and bottom of the leg. The entire axisymmetric geometry is of infinite extent radially. Thus there are no tank walls or clamping structures in the geometry. In addition, the core and yokes are assumed to be infinitely permeable. In spite of these simplifications, Rabins’ method does a good job of calculating the magnetic field in the immediate vicinity of the windings. Thus forces and inductances, which depend largely on the field-near the windings, are also accurately obtained. This can be shown by direct comparison with a finite element solution applied to a more complex geometry, including tank wall and clamps. Although the finite element procedure can obtain losses in structural parts, Rabins’ method is not suited for this. However, because the magnetic field near
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