Theory of three-circuit transformers

The characteristics of three-circuit transformers, the literature of which is very meager, is discussed here in considerable detail. The features of the scheme of treatment are as follows: 1. The scope and general aspects of the problems of three-circuit transformers are reviewed. 2. Some peculiar phenomena of considerable theoretical interest are cited. 3. An electrical network equivalent to the magnetically interlinked circuits of a three-circuit transformer is developed, useful in visualizing the problem and in predicting by inspection a number of its characteristics. 4. Two physical interpretations of the equivalent network are given to assist the understanding of its principle and its applications. 5. The case of auto transformers interconnecting three circuits is interpreted so that the formulas developed for three-circuit transformers become universally applicable regardless of the presence or absence of metallic interconnection among the three circuits inside the case. 6. Formulas are developed for the calculation of regulation with various loads in the different windings. 7. Formulas are developed for the division of load between two primary circuits, or two secondary circuits in parallel. 8. Formulas are developed for the equivalent effective impedance for short circuits. 9. The behaviour of a three-circuit transformer operating in parallel with a two-circuit transformer is analyzed so as to determine the flow or distribution of load kv-a. in the network. 10. The problem of unsymmetrical loads, particularly that of single-phase line-to-neutral short circuits on a polyphase system are discussed in an appendix, with a simplified method of solution, deriving formulas for some representative cases. When the transformer is interconnecting two polyphase generating systems, the division of single-phase line-to-neutral loads and short circuits between the two systems is considered and solved by the same method and formulas. 11. The theory of three-circuit transformers is extended to four circuits in another appendix illustrated by an example, and is then generalized to n-circuit transformers. 12. For convenient reference, the more important formulas and symbols are collected in another appendix.