A V-Constrained Maximum Power Relationship for the Stability of Radial Lines

This paper presents results of a new circuit approach to the voltage stability of radial power lines as determined by the maximum deliverable powers in the lead/ lag power factor modes. The theory is based on the identification of maximum power boundaries for a line with constant sending voltage E; where these boundaries will necessarily include all possible maximum powers from zero up to a maximum of these maximums while the load power factor is defined according to terminal V_o. This uses an auxiliary reactive voltage source circuit at the receiving-end with variables that will establish a dynamic angle stability reference for the voltage-constrained maximum powers. As a result, a no-load voltage state VO has emerged as a variable that will set conditions for (a) the generation of V-dependent load impedance function constituents, (b) the classification of the state of equal sending and receiving voltages as a unique singularity condition, (c) the evolution of lower-bound cut-off voltages for the transfer of maximum power, and (d) the identification of the reactive power demand for any given power within the voltage stability range. The analytical solution results will allow depiction in graphical terms of stability information within this voltage range.