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The study of the digital simulation of electromagnetic transients has been an everlasting issue in power systems. Especially, after improvement by Dommel, the time-domain Bergeron model has been successfully applied in EMTP. But the pre-processing before simulating transients caused by various faults and operations are quite troublesome. This paper presents a new electromagnetic transients simulation method which can be generally used to calculate most of the electric faults in power systems. Unlike EMTP, the presented method doesn't need to calculate the initial values of the system again when the structure or parameter of the system changes. Meanwhile, this method can simulate faults on random locations in single- and double-circuit lines including series compensated lines, bus faults, operation of breakers and open-circuit faults. In addition, the fault-start-angle can be set in the method. Because the new method can conveniently simulate not only inrush currents, overvoltages and harmonics components at different fault locations, but also developing faults, it is significant in line protection simulation verification and overvoltage computation. Lots of tests show that the method is both accurate and fast.