Quantities of a multiterminal circuit determined on the basis of Kirchhoff's laws

Abstract

Abstract For multiterminal electrical networks the interdependency between voltages and currents of the branches of different equivalent circuits and the corresponding terminal quantities are determined using only Kirchhoff's laws. It is shown, that the only set of voltages appertaining to the set ofn currents passing the n terminals consists of the n voltages between the terminals and their common virtual star point, the potential of which is defined to be the mean value of the potentials of all n terminals. In the general case power quantities can be reasonably determined only using pairs which consist either of a terminal current and the appertaining terminal‐to‐virtual star point voltage or of a terminal‐to‐terminal voltage and its appertaining current, the definition of which is less well known. Apparent power is defined to be equal to the physically defined active power, assuming that all terminal currents would be proportional to their appertaining voltages and would have the same collective rms value as the set of actual terminal currents. All definitions can always be applied, including single‐phase and multiphase energy supply systems with or without neutral conductor.