Stationary Networks and Transmission Lines Along Uniformly Rotating Reference Frames

This paper represents the first of a series of studies on the physical and mathematical analysis of the steady-state stability of conventional and long-distance transmission systems as influenced by the presence of voltage regulators and other control devices. As a first step attention is restricted to the transmission line as a component part of the over-all system and practical equivalent circuits are established for its representation, when the connected synchronous machines oscillate. For that purpose the basic equations of stationary networks are set up when viewed from uniformly rotating reference frames. An isolated inductor and capacitor, then a transformer, and finally a transmission line are used as examples. Their equations viewed from a simultaneously rotating and oscillating reference frame are given in reference 1.