Abstract
We prove that the active power through a branch (referred to as branch active power) in a power system is a continuous function of the bifurcation parameter in the closed interval from an initial parameter value to the bifurcation-point value of a saddle-node bifurcation (SNB) or limit-induced bifurcation (LIB) of the power flow equation (PFE). Then we show that generally there is a sequence of branch active powers meeting maxima when the parameters are equal to intermediate values in the closed interval. These results can be used to qualitatively evaluate and classify the state of power system operation conditions in terms of voltage stability. Also, they well explain the limitation of the direct current (DC) power flow methods on stressed power systems. Numerical simulations of the IEEE 118-bus and 57-bus systems are used to illustrate the studies and their applications.
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