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It is well known that a power network can be represented as a multinode, multibranch Thevenin circuit connecting loads to generators. This paper shows that eigen-decomposition can be performed on the Thevenin impedance matrix, creating a set of decoupled single-node, single-branch equivalent circuits. The decoupled circuits can reveal important characteristics of a power system. By applying the transform to calculated or measured voltage phasor data, a technique for tracking the modes of voltage collapse and for identifying areas vulnerable to voltage collapse has been developed. Case studies conducted on multiple power systems have confirmed the effectiveness of the proposed method. In addition to voltage stability applications, the proposed transform presents a new approach for processing and interpreting multilocation phasor data.