Current-transformer performance based on admittance-vector locus

In the past designers as well as users of current transformers have employed ratio error and phase-angle curves in which the abscissa represents primary or secondary current to a linear scale. Numerous curves were necessary both for obtaining a clear picture of the performance characteristics as well as for determining the errors for the multiplicity of possible secondary burdens. Part I of this paper shows that a more functional picture of current-transformer operation is obtained by replacing these commonly used curves by the admittance-vector locus of the secondary winding with the primary open circuited, the end point of the vector representing the independent variable in a curvilinear co-ordinate system. The numerous ratio and phase-angle curves resulting from various secondary burdens and, in case of multiratio transformers, from different numbers of turns, when referred to this new co-ordinate system revert to one single curve. Ratio error and phase angle for any burden at any power factor, turn ratio, and secondary current can be scaled or read directly from a chart using as a basis the admittance vector locus of the steel forming the magnetic circuit of the transformer. For designers as well as users it is often advantageous to be in possession of analytical expressions for ratio error and phase angle. In part II of the paper general formulas are set up which express the performance in terms of the various constants and variables of a transformer, making it unnecessary to refer to charts for the analysis of important design or performance factors.