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Definitions of angle radius and coordinates axis are presented to propose a new transient stability method that is simple and reliable for transient stability assessment. The concept of angle radius is further developed to introduce the novel concept of projection energy function (PEF), which in turn allow to the assessment of critical clearing time and generation limit of system in a new way. The advantage of the new method is that no concept of advanced generator group is required in the assessment contingency stability index. Case studies on the ten-generator New England test power system are reported to verify the validity of the PEF method.