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This paper proposes a novel online real-time assessment method based on equilibrium solution region of branch power flow. This method demonstrates the use of line stability index in order to determine the voltage stability limits in a power system. Line voltage stability indices presented in the literatures are reviewed and discussed. The shortcomings of these methods are pointed out in the face of special operation mode. A new index is deduced based on the feasible solution region of branch equations. The equations of active power and reactive power via node voltage of the branch are listed to form the equilibrium solution region. The similarities and differences between the flow direction of active power and reactive power are analyzed to determine the incidence of them to equilibrium solution. The examples show that the new index has the advantage of low computation burden, and can supply an effective analysis tool for real time on-line assessment of voltage stability in power systems.