A General Steady-State Analysis of Power-Frequency Relations in Time-Varying Reactances

A time-varying reactance in an electrical network absorbs power at some frequencies and returns part of this power at other frequencies, the balance being delivered to the source of the reactance changes. This analysis is a study of these power transfers and establishes steady-stage energy relations which apply under very general conditions to varying reactances, including linear, nonlinear, static and electromechanical systems. These relations include the Manley-Rowe results as special cases and provide a useful description of the external characteristics of varying (and fixed) reactances. An "energy coefficient" is derived which specifies the behaviour of an individual frequency transformation. The modes in which an individual transformation can operate are described and the results related to the characteristics of a wide range of varying reactance devices. An example of the application of the theory is given in the Appendix. This theoretical analysis was undertaken as a basis for digital computer studies of varying reactance systems, since it provides both an over-all description of general characteristics and a means of numerical analysis of particular devices. A fuller account of the work will be available in a later paper by the author [l].