Leakage reactance voltage represents the inductive component of a transformer’s short-circuit voltage. As it constitutes the predominant component, it is an important design parameter because it affects short-circuit currents as well as mechanical and thermal stresses. Its calculation is particularly demanding in transformers with a zig-zag connection, as conventional analytical models often fail to provide sufficiently accurate results. The aim of the first part of this master’s thesis is to compare different methods for calculating leakage reactance voltage and to determine which model most closely matches measurements obtained from actual transformers.
Both analytical and numerical approaches are considered. First, Rogowsky’s analytical method is presented, followed by several numerical models based on the finite element method and implemented in FEMM. The examined models include a single-limb two-dimensional axisymmetric model, a three-phase two-dimensional planar model, and several derived models with corrected volumes, in which the magnetic energy is recalculated using different representative radiuses.
The models are validated using several different transformer designs for which short-circuit voltage measurements from factory acceptance tests are available. The results show that the analytical model has limited applicability, while the basic planar model provides insufficient accuracy. The best agreement with the measurements is achieved by the corrected-volume planar model, in which the volume is determined using the radius where the center of magnetic energy is located. This approach provides a good compromise between accuracy and computational complexity and is suitable for practical application in designing transformers with zig-zag windings.
The second part of the thesis examines mechanical stresses during a three-phase short circuit. The study focuses on the cumulative axial force, calculated using the results of the axisymmetric and planar models. The maximum cumulative axial force, resultant cumulative axial force, and force acting on the flitch plates are considered, taking into account different observation instants and different axial displacements of individual windings. The planar model is divided into six submodels according to the position of the sampling grid. Among the planar submodels, the model with the grid positioned to the left of the middle limb most closely matches the axisymmetric model. Nevertheless, the results obtained using the planar models are widely dispersed and are frequently higher than those obtained using the axisymmetric model. It is concluded that the corrected-volume planar model is suitable for calculating leakage reactance voltage, whereas the axisymmetric model is more reliable for calculating axial mechanical stresses because it better represents the cylindrical geometry of transformer windings.
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