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Traditional distance relays based on phase comparison algorithm have two main disadvantages: severely affect by DC offset components and long time delay due to the fixed Fourier window length. In order to eliminate the effect of DC offsets, the line differential equation is integrated in a period (a sample period is selected) before it is converted into phasor domain by Fourier transforms, and once can get a new phasor equation, based on which the operating voltage phasor is newly defined at the assumption that the line is healthy before the setting point. It is proved that the relation between the new phasors is same as that of traditional phasors when the fault is internal or external. At the same time the variable window technique is utilized to construct a new principle for high speed tripping. The EMTP simulations show that the new relays have properties of high speed and simple calculations and are not influenced by DC decay component and high frequency components are effectively restrained.