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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...
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