Thévenin's Theorem Applied to the Analysis of Polyphase Transmission Circuits

The well-known and widely applied Thévenin theorem is applied to the operational analysis of ac transmission circuits. The approach is to model the transmission circuit AI as an n-port. The calculation of the Thévenin equivalent impedance is found by applying an n-vector of currents to AI and observing the behavior of the terminal voltages of AI. The Thévenin equivalent voltage is an n-vector and this is simply the open-circuit voltage of AI. The equivalent circuit is applied to conveniently study the transmission circuit performance for a range of different operating conditions. The treatment of controlled sources in the model is described. The application of Thévenin's theorem to a class of multiport circuits has been described before, and the application to three-phase circuits has been suggested; however, the contribution in this paper is the treatment of transformers and modeling mutual coupling between phases in transmission components, and the application to general polyphase circuits.