Voltage collapse proximity in case of a radial network

For cases of radial networks, an analytical approach to voltage collapse proximity determination is proposed. The method is based on a two-bus equivalent of a radial network. Following basic assumptions, the voltage phasors at the both ends of the radial network are transformed in order to form the voltage phasors of its two-bus equivalent. Exact voltage stability limit relations for the equivalent derived from Jacobian matrix are established via geometrical relationship between both voltage phasors. The procedure has been tested for practical examples of radial networks with various combinations of loads.