The general treatment of non-symmetric, non-balanced star circuits: On the geometrization of problems in electrical metrology

Abstract

In the present note we provide the general solution of a question concerning non-symmetric AC star circuits that came up in a practical application: Given a non-symmetric AC star circuit, we need the quantities of the line voltages. For technical reasons these quantities cannot be measured directly but the phase-to-phase voltages can be. In this text we present a way to compute the needed quantities from the measured ones. We translate this problem in electrical metrology to a geometric one and present in detail a general solution that is well adapted to the practical problem. Furthermore, we solve the generalization of the problem that discusses the non-symmetric, non-balanced star circuit. In addition, we give some further remarks on the mathematical side of the initial problem.