High-Frequency Modeling and Simulation of a Single-Phase Three-Winding Transformer Including Taps in Regulating Winding

📝 Abstract

Transformer terminal equivalents obtained via admittance measurements are suitable for simulating high-frequency transient interaction between the transformer and the network. This paper augments the terminal equivalent approach with a measurement-based voltage transfer function model which permits calculation of voltages at internal points in the regulating winding. The approach is demonstrated for a single-phase three-winding transformer in tap position Nom+ with inclusion of three internal points in the regulating winding that represent the mid-point and the two extreme ends. The terminal equivalent modeling makes use of additional common-mode measurements to avoid error magnifications to result from the ungrounded tertiary winding. The final model is used in a time domain simulation where ground-fault initiation results in a resonant voltage build-up in the winding. It is shown that that the peak value of the resonant overvoltage can be higher than during the lightning impulse test, with unfavorable network conditions. Additional measurements show that the selected tap position affects the terminal behavior of the transformer, changing the frequency and peak value of the lower resonance point in the voltage transfer between windings.

💡 Analysis

Transformer terminal equivalents obtained via admittance measurements are suitable for simulating high-frequency transient interaction between the transformer and the network. This paper augments the terminal equivalent approach with a measurement-based voltage transfer function model which permits calculation of voltages at internal points in the regulating winding. The approach is demonstrated for a single-phase three-winding transformer in tap position Nom+ with inclusion of three internal points in the regulating winding that represent the mid-point and the two extreme ends. The terminal equivalent modeling makes use of additional common-mode measurements to avoid error magnifications to result from the ungrounded tertiary winding. The final model is used in a time domain simulation where ground-fault initiation results in a resonant voltage build-up in the winding. It is shown that that the peak value of the resonant overvoltage can be higher than during the lightning impulse test, with unfavorable network conditions. Additional measurements show that the selected tap position affects the terminal behavior of the transformer, changing the frequency and peak value of the lower resonance point in the voltage transfer between windings.

📄 Content

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Abstract—Transformer terminal equivalents obtained via admittance measurements are suitable for simulating high- frequency transient interaction between the transformer and the network. This paper augments the terminal equivalent approach with a measurement-based voltage transfer function model which permits calculation of voltages at internal points in the regulating winding. The approach is demonstrated for a single-phase three- winding transformer in tap position Nom+ with inclusion of three internal points in the regulating winding that represent the mid- point and the two extreme ends. The terminal equivalent modeling makes use of additional common-mode measurements to avoid error magnifications to result from the ungrounded tertiary winding. The final model is used in a time domain simulation where ground-fault initiation results in a resonant voltage build-up in the winding. It is shown that that the peak value of the resonant overvoltage can be higher than during the lightning impulse test, with unfavorable network conditions. Additional measurements show that the selected tap position affects the terminal behavior of the transformer, changing the frequency and peak value of the lower resonance point in the voltage transfer between windings.

Index Terms—Transformer, black-box model, electromagnetic transients, measurements, simulation, tap setting.
I. INTRODUCTION RANSIENT overvoltages are one of the root-causes of dielectric failures in transformers. The assessment of internal winding dielectric stresses is in the case of power transformers routinely performed by the manufacturers using in-house calculation programs. These programs make use of a detailed description of the transformer windings with circuit element parameters obtained using analytical expressions or Finite Element calculations, see [1] and references therein for an overview of methods. It has been shown [2] that when applied to a common geometry, the calculation programs by different manufacturers generally give similar results for the peak value of external and internal voltages when applying a lightning impulse voltage to the transformer. However, substantial differences were found for the resonance frequencies and damping. This fact raises concerns about the suitability of the manufacturer’s models when applied in simulations involving general overvoltages that result from the connected system. On the other hand, measurement-based black-box models can provide quite accurate results [3]-[7] for the voltage on external terminals, although the transformer must first be built before any measurements can be performed.
One of the dielectric weak parts of a transformer is the regulating winding which, depending on the selected tap position, can exhibit strong internal resonances. In the 1970s, American Electric Power experienced several failures in auto- transformer regulating windings [8], with resonant voltage build-up as root-cause. It is therefore of interest to extend the capability of the black-box model approach to also include points in the regulating winding.
CIGRE JWG A2/C4.52 has in 2016 performed a measurement campaign on a single-phase and a three-phase transformer in order to assess/improve the accuracy of currently applied white-box models, and to provide input for black-box and grey-box modeling. The measurements involve frequency domain and time domain measurements at the transformer external terminals and at some internal points.
This paper reports results obtained for black-box-modeling of the single-phase three-winding transformer. In addition to the four external terminals, the measurements include voltage transfer from external terminals to three points in the regulating winding. From the measurements, a wide-band model is extracted which can be applied in transient simulation in an EMTP-type environment. The various steps in the measurement and modeling procedure are described with emphasis on accuracy preservation. A few comparisons are made with white-box model simulation results to appreciate the fidelity of the proposed model. Also, the effect of the tap changer setting on transferred overvoltages between the windings is investigated. Finally, the model is applied in a transient simulation where a resonant voltage build-up takes place in the regulating winding. The resulting overvoltages are compared with those arising in the standard lightning impulse test.
II. TRANSFORMER UNIT AND MEASURED QUANTITIES The transformer is a 50 MVA single-phase three-winding transformer with rated voltages 230/69/13.8 kV at 60 Hz. The core has one mid-leg and two return legs. The internal connections are shown in Fig. 1. The regulating winding is a an interleaved disk winding with 10 circuits. The online tap changer (OLTC) has 11 tap positions and the polarity of this winding is reversible, giving a total of 21 tap positions.
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