This paper presents a method for calculating terminal and internal impedance versus frequency for a lumped parameter model of a transformer The transformer's total frequency response can be accurately determined from this impedance data directly, ie, the terminal resonance and anti-resonance and internal amplification factor characteristic can be calculated for a single or three-phase transformer model Since most equipment associated with power system operation can be accurately modeled with lumped parameter networks, this method also provides an accurate, straightforward method for determining the resonance characteristic of those systems An additional significance of this method is that the accuracy of the calculation is limited only by the user's ability to represent the equipment or system Heretofore, the accuracy of this calculation was limited by the simplifying assumptions required of the network model by each solution method This paper presents the definitions and mathematical theory underlying the method Two examples are presented in which comparisons are made between measured and calculated values for a helical air core coil and a 200 MVA single-phase autotransformer The agreement is excellent

A general method for determining resonances in transformer windings

Some recent transformer failures have been attributed to part-winding resonances excited by a form of switching surge voltage pulse which produced internal overvoltages. This paper takes a tutorial approach to relate a transformer winding to an equivalent electrical network which can exhibit resonant effects both at its terminals and internally. The relationship between the resonance phenomenon and pulse response is explained and illustrated with practical examples for the standard test waveforms. A proposed alternative switching surge waveform is examined for its effect on the internal response of transformer windings. The material presented should promote the understanding required for consideration of changes in standard test waveforms.

Response of Transformer Windings to System Transient Voltages

A section of an actual power system was modelled on a Transient Network Analyzer for the purpose of defining high frequency transient voltages occuring during switching events. The variety of system switching events which were staged produced oscillatory voltages covering a broad band of frequencies. On a digital model of the system autotransformers it was demonstrated that such oscillatory voltages could excite internal natural frequencies, but none of the actual generated waves coincided closely with the particular transformer natural frequency. However, if the applied waveshapes were frequency-scaled to a closer match, internal response voltages of concern could be developed.

Transformer Response to System Switching Voltages

The recent failures of four EHV auto-transformer no load tap changers is interpreted. The failures were a direct and immediate consequence of transmission line faults as far as 340 miles away. The related system transient behavior is analyzed, and the transformer response to these transients is presented on a quantitative basis. It is demonstrated for these transformers that the ANSI standard dielectric surges offer an inadequate test of winding insulation remote from the line terminals where significant winding resonance is known to occur. The extent of these test limitations to other transformers is discussed.

On the significance of recent EHV transformer failures involving winding resonance

This paper investigates the internal voltages produced by various types of system overvoltages with special consideration to part winding resonance phenomena19297 which can result in very high voltage stress but may not be: adequately considered in design and test practice A case of oscillating voltage excitation is reported which caused the failure of a generator step-up transformer due to internal resonance According to theoretical considerations, internal oscillation and resonance voltages depend on the damping of the excitation voltage and of the windings For a 500 kV single phase generator step-up transformer, it is demonstrated that favorable damping characteristics of the windings can reduce to a large extent the risk of excessive internal voltages

Voltage Stresses Produced by Aperiodic and Oscillating System Overvoltages in Transformer Windings

Four failures of large EHV auto-transformers on the AEP system are described. The failures were initiated by flashovers in the no-load tap changer during system faults. Investigations and tests attribute the flashovers to part-winding resonance. Test data is presented for various terminal conditions and wave shapes corresponding to system transient conditions. The relationship of these tests to ANSI standard dielectric tests is discussed. Corrective measures for existing transformers include arresters tied to an internal crossover connection and capacitor banks connected to the delta tertiary windings.

H.B. Margolis

Papers

Experience with part-winding resonance in EHV auto-transformers: Diagnosis and corrective measures