The paper presents a hybrid model of disc-type power transformer winding for frequency response analysis (FRA) based on traveling wave and multiconductor transmission line (MTL) theories. Each disc of a winding is described by traveling wave equations, which are connected to each other in a form of MTL matrix model. This significantly reduces the order of the model with respect to previously established MTL models of transformer winding. The model is applied to frequency response simulation of two single-phase transformers. The simulations are compared with the experimental data and calculated results using lumped parameter and MTL models reported in other publications. It is shown that the model can be used for FRA result interpretation in an extended range of frequencies up to several mega Hertz and resonance analysis under very fast transient overvoltages (VFTOs).

A Hybrid Winding Model of Disc-Type Power Transformers for Frequency Response Analysis

When a transformer is subjected to very fast front transients, the penetration of the magnetic flux into the core becomes, in general, negligible. To represent this phenomenon, it is common practice to compute the winding inductance matrix (turn-to-turn) at very high frequencies using the expressions for air-core inductors. However, since the core becomes a magnetic insulating wall at very high frequencies (MHz), the distribution of the magnetic field is altered because the field cannot enter the region occupied by the core. Therefore, the air-core approximation formulae overestimate the inductance at high frequencies. This is especially true in the region inside the core window. Large errors are found when the inductances are computed with the air-core approximation. This paper presents a technique, based on the application of a multilayer method of images, to take the presence of the core into consideration. The final expressions are very simple, yet they give remarkably accurate results. Comparisons with finite-element analyses prove the excellent accuracy of the technique.

Accurate and Efficient Computation of the Inductance Matrix of Transformer Windings for the Simulation of Very Fast Transients

In this paper, a new equivalent circuit for the leakage inductance of multiwinding (or multisection) transformers is presented. The methods proposed in this paper unify terminal models with models derived from the principle of duality between electric and magnetic equivalent circuits. The new model is identified as the terminal-duality model (TDM). The elements of the circuit in addition to properly representing the transformer behavior at the terminals are physically related to flux paths in the transformer window. The circuit of the TDM consists of a set of mutually coupled inductors available in any circuit simulation program and, in particular, available in all Electromagnetic Transients Program-type programs. The circuit elements of the TDM can be computed in two ways: 1) from the observation of the behavior of the magnetic field in the transformer window (applying the principle of duality) and 2) from measurements on short-circuit tests performed at the transformer terminals. Both methods yield identical results. The 2-D finite-element simulations are used to compute the terminal behavior of a wide variety of winding configurations. Several examples are presented for the illustration of the model capabilities and validation.

Equivalent Circuit for the Leakage Inductance of Multiwinding Transformers: Unification of Terminal and Duality Models

The high frequency model of transformer winding is indispensable in analyzing the transients particularly caused by the very fast transients which occur at the time of disconnecting switch operations The transients in transformer have been analyzed using a circuit of interlinked inductances and capacitances whose values have to be properly determined The circuit constants have been hitherto calculated in a model taking each coil section pair as a building block The present paper proposes the method that enables further subdividing the unit The circuit transients are computed utilizing the FFT technique The voltage oscillations of the winding subjected to an impulse voltage are calculated The correspondence with the experimental results is satisfactory The response to a chopped impulse shows this method's applicability to high frequency analyses Since the constants are calculated directly from the design parameters of transformer winding, this technique is particularly useful in developing and designing transformers

High frequency model and transient response of transformer windings

In this paper, the prestrike and the restrike effects during switching a vacuum circuit breaker (VCB) connected to a dry-type foil-winding transformer are theoretically and experimentally analyzed. The analysis is conducted by performing a wide range of experimental three-phase switching on/off tests for a 3.75-MVA prototype test transformer connected to a VCB by a cable with different lengths and for different loading conditions. A refined transformer model is successfully applied for the computation of the voltage distribution along the transformer windings. In particular, the winding properties are separately investigated, for which the core influence for frequencies above some tens of kilohertz is studied, and the terminal impedance variation for a broad frequency range is accurately calculated. The simulated results are excellent. Based on these results, an analysis was performed to evaluate the severity of the switching operations by applying spectral analysis of the recorded signals. The statistical analysis of the overvoltages with respect to the cable length and the load value shows that long cables do not guarantee lower overvoltages because of the load and its interaction with the system that makes each case unique.

Analysis of Switching Effects of Vacuum Circuit Breaker on Dry-Type Foil-Winding Transformers Validated by Experiments

Very fast transient overvoltages generated in gas-insulated switchgear could cause a voltage oscillation inside the connected transformer. A practical method to calculate the high-frequency transients in the transformer winding is developed based on multiconductor transmission-line theory. Resonance characteristics of a transformer are assessed using the inductance matrix obtainable from its winding geometry. Applicability to transients of frequencies up to several megahertz is checked in a model transformer and an actual 500 kV transformer. The calculated interturn voltage waveforms are in particularly good agreement with experiment.

S. Fujita

Papers

Analysis of very fast transients in transformers