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A new fault detection/location technique with consideration of arcing fault discrimination based on phasor measurement units for extremely high voltage/ultra-high voltage transmission lines is presented in this two-paper set. Part I of this two-paper set is mainly aimed at theory and algorithm derivation. The proposed fault detection technique for both arcing and permanent faults is achieved by a combination of a fault detection index |M| and a fault location index |D|, which are obtained by processing synchronized fundamental phasors. One is to detect the occurrence of a fault and the other is to distinguish between in-zone and out-of-zone faults. Furthermore, for discriminating between arcing and permanent faults, the proposed technique estimates the amplitude of arc voltage by least error squares method through the measured synchronized harmonic phasors caused by the nonlinear arc behavior. Then, the discrimination will be achieved by comparing the estimated amplitude of arc voltage to a given threshold value. In addition, in order to eliminate the error caused by exponentially decaying dc offset on the computations of fundamental and harmonic phasors, an extended discrete Fourier transform algorithm is also presented.