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A necessary and sufficient condition for loss of transient stability is derived that describes a region of instability. A region of stability is also theoretically justified. A local potential energy boundary surface method is then developed based on a cutset energy function and the theoretically based descriptions of the region of stability and region of instability. The PEBS method is applied to a classical transient stability model and determines the critical clearing time extremely accurate. The PEBS method can also be appied to topological transient stability models.