Dual Transformer Model based on Standard Circuit Elements for the Study of Low- and Mid-frequency Transients

This thesis is a step forward toward achieving the final objective of creating a fully dual model for transformers including eddy currents and nonlinearities of the iron core using the fundamental electrical components already available in the EMTP-type programs. The model is effective for the study of the performance of transformers during power system transients. This is very important for transformer designers, because the insulation of transformers is determined with the overvoltages caused by lightning or switching operations. There are also internally induced transients that occur when a switch is actuated. For example switching actions for reconfiguration of distribution systems that offers economic advantages, or protective actions to clear faults and large short-circuit currents. Many of the smart grid concepts currently under development by many utilities rely heavily on switching to optimize resources that produce transients in the system. On the other hand, inrush currents produce mechanical forces which deform transformer windings and cause malfunction of the differential protection. Also, transformer performance under ferroresonance and geomagnetic induced currents are necessary to study. In this thesis, a physically consistent dual model applicable to single-phase two-winding transformers is proposed. First, the topology of a dual electrical equivalent circuit is obtained from the direct application of the principle of duality. Then, the model parameters are computed considering the variations of the transformer electromagnetic behavior under various operating conditions. Current modeling techniques use different topological models to represent diverse transient situations. The reversible model proposed in this thesis unifies the terminal and topological equivalent circuits. The model remains invariable for all low-frequency transients including deep saturation conditions driven from any of the two windings. The very high saturation region of the iron core magnetizing characteristic is modified with the accurate measurement of the air-core inductance. The air-core inductance is measured using a non-ideal low-power rectifier. Its dc output serves to drive the transformer into deep saturation, and its ripple provides low-amplitude variable excitation. The principal advantage of this method is its simplicity. To model the eddy current effects in the windings, a novel equivalent circuit is proposed. The circuit is derived from the principle of duality and therefore, matches the electromagnetic physical behavior of the transformer windings. It properly models the flux paths and current distribution from dc to MHz. The model is synthesized from a non-uniform concentric discretization of the windings. Concise guidelines are given to optimally calculate the width of the sub-divisions for various transient simulations. To compute the circuit parameters only information about the geometry of the windings and about their material properties is needed. The calculation of the circuit parameters does not require an iterative process. Therefore, the parameters are always real, positive, and free from convergence problems. The proposed model is tested with single-phase transformers for the calculation of magnetizing inrush currents, series ferroresonance, and Geomagnetic Induced Currents (GIC). The electromagnetic transient response of the model is compared to laboratory measurements for validation. Also, 3D finite element simulations are used to validate the electromagnetic behavior of the transformer model. Large manufacturer of transformers, power system designers, and electrical utility companies can benefit from the new model. It simplifies the design and optimization of the transformers' insulation, thereby reducing cost, and enhancing reliability of the system. The model could also be used for inrush current and differential protection studies, geomagnetic induced current studies, harmonic penetration studies, and switching transient studies.