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This paper proposes a security measure to indicate vulnerability to voltage collapse in electric power systems. The voltage-collapse phenomenon is modeled as a large deviation in the nonlinear dynamics of the system, driven by small magnitude, broad spectrum disturbances in load. This model relates the collapse to shrinking of the region of attraction for the operating point. The security measure indicating vulnerability to voltage collapse is based on expected exit time from the region of attraction for the stable operating point. It is shown that expected exit time can be related to a natural Lyapunov function for the power system, and that a security measure based on this expected exit time can be calculated simply by evaluating an exponential function of the Lyapunov "energy" at a neighboring load flow solution.