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. >

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Complete transformer model for electromagnetic transients

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 >

A high frequency transformer model for the EMTP

One of the weakest components of modern transient simulation software is the transformer model. Many opportunities exist to improve the simulation of its complicated behaviors, which include magnetic saturation of the core, frequency-dependency, capacitive coupling, and topologically correctness of core and coil structure. This paper presents a review of transformer models for simulation of low- and mid-frequency transients. Salient points of key references are presented and discussed in order to give an accessible overview of development, implementation and limitations of the most useful models proposed to date. Techniques for representation of the most important behaviors are examined, with the intent of providing the needed foundation for continued development and improvement of transformer models.

Transformer modeling for low- and mid-frequency transients - a review

The ability to predict or confirm ferroresonance depends primarily on the correctness of the transformer model used by the computer simulation. Ferroresonance is introduced and a general modeling approach is given. An overview of available literature and contributors to this area is provided. A simple ease of ferroresonance in a single phase transformer is used to illustrate this "phenomenon". Three phase transformer core structures are discussed. Ferroresonance in three phase grounded-wye distribution systems is described and illustrated with waveform data obtained from laboratory simulations. Representation of the study zone is discussed, modeling techniques are presented, and implementation suggestions are made. Three case studies are presented. Transformer representation is critical to performing a valid simulation. The direction of ongoing research is discussed, and the reader is advised to monitor the literature for ongoing rapid improvements in transformer modeling techniques.

Modeling and analysis guidelines for slow transients. III. The study of ferroresonance

With the fast-paced changing technologies in the power industry, new references addressing new technologies are coming to the market. Based on this fact, there is an urgent need to keep track of international experiences and activities taking place in the field of modern transformer design. The complexity of transformer design demands reliable and rigorous solution methods. A survey of current research reveals the continued interest in application of advanced techniques for transformer design optimization. This paper conducts a literature survey and reveals general backgrounds of research and developments in the field of transformer design and optimization for the past 35 years, based on more than 420 published articles, 50 transformer books, and 65 standards.

Transformer Design and Optimization: A Literature Survey

Frequency dependent representations of eddy currents in laminated cores of power transformers are developed. One representation is based on a continued fraction expansion for the frequency dependent magnetizing impedance while the other is based on a discretization of flux distribution within the lamination. Both models are low order and reproduce the frequency characteristics of the transformer magnetizing branch up to 200 kHz with less than 5% error. The importance of modeling the frequency dependence of eddy currents for the calculation of the transient recovery voltage across a low voltage transformer breaker interrupting a nearby fault is demonstrated. >

Frequency dependent eddy current models for nonlinear iron cores

Existing matrix models for transformers reproduce specified short-circuit tests, portraying leakage flux in air, but do not explicitly model the core. Therefore, a precise relation between core flux and air flux is not clearly established. Core representation is defined simply on the basis of a specified excitation current (positive- and zero-sequence), permitting linear magnetizing branches to be incorporated in the matrix. Nonlinear inductances are connected separately at winding terminals to introduce core nonlinearities, however these are not identified physically with individual core limbs, making precise accommodation of hysteresis, saturation and eddy current effects difficult. Published models based on the duality existing between magnetic and electric circuits identify a means for correctly interfacing core flux with air flux, permitting core nonlinearities to be incorporated on a physical basis. However practical application of these models has been hampered by a difficulty in deriving the required model parameters. A formulation is presented here to build a topological model based on normally available test data. Results of short-circuit tests are presented demonstrating that existing matrix models can introduce errors. >

A. Narang

Papers

Frequency dependent eddy current models for nonlinear iron cores

Topology based magnetic model for steady-state and transient studies for three-phase core type transformers