With the wide application of power electronized resources (PERs), the amplitude and frequency of voltages show significant time-varying characteristics under asymmetrical faults. As a result, the traditional phasor model, impedance model, and symmetrical components method based on the constant amplitude and frequency of voltages are facing great challenges. Hence, a novel asymmetrical fault analysis method based on conjugate vectors is proposed in this paper which can meet the modeling and analysis requirements of the network excited by voltages with time-varying amplitude/frequency. Furthermore, asymmetrical fault characteristics are extracted. As an application, a faulted phase identification (FPI) strategy is proposed based on the fault characteristics. The correctness and superiority of the asymmetrical fault analysis method and FPI strategy are verified in time-domain simulations and a real-time digital simulator.