EEAC theory reveals the mechanism of how the time-varying factor affects the stability of image systems. Based on this theory, the strong time-varying of image systems caused by the inner-cluster incoherency and the phenomenon of ill-conditioned FEP(IFEP) are analyzed. Moreover, their effects on the accuracy of the transient stability analysis are studied. With this knowledge, the identification method of IFEP and the correction method of transient stability margin of stable swings are proposed for enhancing the accuracy of stability assessments in strong time-varying systems. The effectiveness and robustness of the above methods are thoroughly verified in the New England system. This research also contributes to the study on stability mechanisms of nonlinear non-autonomous systems.