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Summary form only given. In the paper, the Tellegen's theorem and adjoint networks are used to derive a new, local voltage-stability index. The new approach makes it possible to determine the Thevenin's parameters in a different way than adaptive curve-fitting techniques, from two consecutive phasor measurements. The new index was rigorously tested on different test systems. The results were obtained on a static two-bus test system and on the dynamic Belgian- French 32-bus test system that includes full dynamic models of all power-system components crucial to the voltage instability analysis. The results show advantages of the proposed index: it is simple, computationally very fast, and easy to implement in the wide-area monitoring and control center or locally in a numerical relay.