Inherent Limitations on Transformations Possible by Stationary Apparatus

Expressions for electrostatic and electromagnetic energies, Joulian heat dissipation and power are given in complex quantities. The pure imaginary part of the expression for power in a static network is shown to be equal to 2 ω times the difference between the mean electromagnetic energy and mean electrostatic energy. Use is made of this new principle in considering the problems of power-factor correction and phase splitting. It is shown that in general for phase transforming by static apparatus both magnetic and electrostatic storage of energy are necessary, and it is shown how the minimum amounts of each are determined by the load. The symmetry of the coefficients in the general equations for the steady state in a static network is demonstrated, and it is shown that limitations upon voltage and current transformations follow. The voltage regulation of any phase-splitting arrangement is considered.