| Summary: | The mathematical analysis of static electromagnetic devices such as transformers, voltage stabilisers, etc., is complicated by the nonlinear, multi-valued relationship between flux density and field strength in the ferromagnetic core. Initially, vdrious methods of analysis are discussed, with emphasis on the importance of incorporating a means of adequately representing the influence of the magnetisation characteristic, and the physical structure of the core. The single-valued exponential series representation of the flux density / field strength relationship which was developed in an earlier investigation into transient currents in transformers due to switching of the supply, is modified and extended to cater for the non-unique nature of the B/H relationship. This new representation is then incorporated into the mathematical models of single-phase and three-limb, three-phase transformers, which are utilised in the study of residual core conditions in these devices. The ways in which residual conditions are established, and the influence of such factors as load and primary circuit configuration are examined, both experimentally and theoretically, and the results used in devising a simple graphical technique for estimating the magnitude and polarity of remanent flux and m. m. f. A study is also made of the effect of residual conditions on the transient currents which occur on reapplication of the supply. An example of the extension of the range of application of the transformer model is demonstrated in a brief study of ferroresonance in single- and three-phase systems. The processes involved in the initiation of a stable resonant condition are considered, and a comparison of computed and recorded steady-state current, voltage and flax density waveforms is made. Finally, general conclusions are drawn, and some suggestions are made as to how the transformer model might be improved, together with examples of other areas of interest in which the analytical techniques developed for the transformer may be applied.
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