A transformer is an electrical device that changes or converts the voltage level between two circuits. In the process, current levels are also converted. However the power transferred between the circuits remains unchanged except for the usually slight losses that occur in the process.

This transfer occurs only when alternating (a.c.) or transient electrical conditions are present. The operation of the transformer is based on the principle of induction as formulated by Faraday in 1831. He found that when a changing magnetic flux connects a circuit, a voltage or electromotive force (emf) is induced in the circuit.

The voltage induced is proportional to the number of turns connected by the changing magnetic flux. Thus, if two circuits are tied together by a common magnetic flux, the voltage induced will be different if the number of turns tied together in the two circuits is different. This situation is illustrated in Figure 1.1, which shows the iron core carrying the common magnetic flux. Since the coupling windings N1and N2 are different, the induced voltages V1and V2 are different.

**About the Book**

The third edition of this book expands and further develops some of the topics in the second edition. For example, the multi-terminal transformer model has been extended to include a second transformer for boosters and two-core phase shifters.

This second transformer can also be included in the impulse simulation program. The second edition addressed the linear impedance boundary method, but its deficiencies were pointed out in terms of calculating vortex losses in nonlinear magnetic materials such as tank steel. This new edition includes a section on modified methods for nonlinear materials.

The directed-flow disk thermal model calculations, which were more complex in the previous edition, have been replaced by more efficient calculations based on graph theory.

Transformer design typically begins with optimization calculations to create a least-cost design based on customer requirements. Therefore, Chapter19 on optimization methods, which was included in the first edition, has been added. This calculation produces a starter design that can be further modified when more detailed screening is performed by other design programs. Although a starting point for most designs, this chapter is near the end of this book.

The bulk of this document concerns detailed design methods. These are based on realistic transformer models that cover the specific characteristic satrans former must meet and the associated limitations. Because of the unique customer specifications, especially for large power transformers, a generic transformer design is usually not possible. Furthermore, new materials with different material constants are being developed and used, such as natural ester oil instead of mineral oil.