A general method for determining resonances in transformer windings
TL;DR: In this article, the authors present a method for calculating terminal and internal impedance versus frequency for a lumped parameter model of a transformer, where the transformer's total frequency response can be accurately determined from this impedance data directly, i.e., the terminal resonance and anti-resonance and internal amplification factor characteristic can be calculated for a single or three-phase transformer model.
Abstract: 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
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TL;DR: In this article, a frequency response analysis (FRA) method was used to measure wind deformation in power transformers, and the results indicated that benchmark reference data was not always necessary to identify certain kinds of mechanical damage.
Abstract: Winding deformation in power transformers can be measured externally using a new frequency response analysis (FRA) method Field experience since 1975, on five separate transformers up to 550 MVA rating, 230kVclassindicatesthatthismethod hasadvantagesover the low voltage impulse (LVI) method as a practical maintenance tool. Results on suspect transformers indicate that benchmark reference data is not always necessary to identify certain kinds of mechanical damage.
314 citations
TL;DR: In this paper, a complete, three phase transformer model for the calculation of electromagnetic transients is presented, which consists of a set of state equations solved with the trapezoidal rule of integration in order to obtain an equivalent Norton circuit at the transformer terminals.
Abstract: A complete, three phase transformer model for the calculation of electromagnetic transients is presented. The model consists of a set of state equations solved with the trapezoidal rule of integration in order to obtain an equivalent Norton circuit at the transformer terminals. Thus the transformer model can be easily interfaced with an electromagnetic transients program. Its main features are: (a) the basic elements for the winding model are the turns; (b) the complete model includes the losses due to eddy currents in the windings and in the iron core; and (c) the solution of the state equations is obtained in decoupled iterations. For validation, the frequency response of the model is compared with tests on several transformers. Applications to the calculation of transients are given for illustration. >
279 citations
TL;DR: In this paper, the authors present a comprehensive procedure for calculating all contributions to the self-capacitance of high-voltage transformers and provide a detailed analysis of the problem, based on a physical approach.
Abstract: The calculation of a transformer's parasitics, such as its self capacitance, is fundamental for predicting the frequency behavior of the device, reducing this capacitance value and moreover for more advanced aims of capacitance integration and cancellation. This paper presents a comprehensive procedure for calculating all contributions to the self-capacitance of high-voltage transformers and provides a detailed analysis of the problem, based on a physical approach. The advantages of the analytical formulation of the problem rather than a finite element method analysis are discussed. The approach and formulas presented in this paper can also be used for other wound components rather than just step-up transformers. Finally, analytical and experimental results are presented for three different high-voltage transformer architectures.
255 citations
TL;DR: In this paper, a model to simulate the high-frequency behavior of a power transformer is presented based on the frequency characteristics of the transformer admittance matrix between its terminals over a given range of frequencies.
Abstract: A model to simulate the high-frequency behavior of a power transformer is presented This model is based on the frequency characteristics of the transformer admittance matrix between its terminals over a given range of frequencies The transformer admittance characteristics can be obtained from measurements or from detailed internal models based on the physical layout of the transformer The elements of the nodal admittance matrix are approximated with rational functions consisting of real as well as complex conjugate poles and zeroes These approximations are realized in the form of an RLC network in a format suitable for direct use with the ElectroMagnetics Transient Program (EMTP) The high-frequency transformer model can be used as a stand-alone linear model or as an add-on module of a more comprehensive model where iron core nonlinearities are represented in detail >
244 citations
TL;DR: In this article, a linear wide band frequency-dependent black box model of a two-winding power transformer was obtained for the purpose of calculation of electromagnetic transients in power systems.
Abstract: This paper describes the measurement setup and modeling technique used for obtaining a linear wide band frequency-dependent black box model of a two-winding power transformer, for the purpose of calculation of electromagnetic transients in power systems. The measurement setup is based on a network analyzer, shielded cables, and a connection board. The setup is demonstrated to give a consistent data set where the effect of the measurement cables can be eliminated. The accuracy of the data set is increased by using a combination of current measurements and voltage transfer measurements. A rational approximation of the admittance matrix is calculated in the frequency domain in the range of 50 Hz to 1 MHz and subjected to passivity enforcement, giving a stable model which can be included in electromagnetic transients program (EMTP)-type simulation programs. The accuracy is validated both in the frequency domain and in the time domain.
206 citations
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TL;DR: Electromagnetic transients in arbitrary single- or multiphase networks are solved by a nodal admittance matrix method based on the method of characteristics for distributed parameters and the trapezoidal rule of integration for lumped parameters.
Abstract: Electromagnetic transients in arbitrary single- or multiphase networks are solved by a nodal admittance matrix method. The formulation is based on the method of characteristics for distributed parameters and the trapezoidal rule of integration for lumped parameters. Optimally ordered triangular factorization with sparsity techniques is used in the solution. Examples and programming details illustrate the practicality of the method.
1,578 citations
TL;DR: In this paper, the relationship between the resonance phenomenon and pulse response is explained and illustrated with practical examples for the standard test waveforms, and a proposed alternative switching surge waveform is examined for its effect on the internal response of transformer windings.
Abstract: 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.
133 citations
01 Jan 1953-Transactions of The American Institute of Electrical Engineers. Part Iii: Power Apparatus and Systems
TL;DR: In this article, an equivalent circuit method is derived for the computation of all the natural frequencies of interest of both air-core and iron-core coils, which takes into account all mutual inductance linkages, which usually have been neglected in the literature.
Abstract: Knowledge of the natural frequencies of air-core and iron-core coils and of transformer and generator windings is of essential theoretical and practical importance. In this paper an equivalent circuit method is derived for the computation of all the natural frequencies of interest of both air-core and iron-core coils. This method takes into account all mutual inductance linkages, which usually have been neglected in the literature. Neglect of mutual inductance linkages leads to computed frequencies which do not agree with the measured frequencies. It is therefore necessary to consider the mutual inductance linkages in the computation of the natural frequencies of coils and windings. The equivalent circuit with all mutual inductance linkages may be solved by punch-card equipment, or by setting up an appropriate circuit on the a-c network analyzer. Both methods of solution are accurate; either one may be preferable in practice, depending upon the circumstances. The natural frequencies of a coil with air and iron core and different capacitive parameters, computed in this manner, are compared with the measured frequencies. Agreement between computed and measured values is excellent for the first seven harmonics of the air-core coil, and for the first three harmonics of the iron-core coil.
70 citations
TL;DR: In this paper, four failures of large EHV auto-transformers on the AEP system were described, initiated by flashovers in the no-load tap changer during system faults.
Abstract: 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.
41 citations