Abstarct: Due to the low fault current, High Impedance Faults (HIF) are among those types of faults which could not being identified by conventional overcurrent relays. This type of fault occurs when the energized conductor is cut off and makes contact with a high impedance area, namely earth, asphalt, grass, sands, and trees. It is very possible that these faults result in unpleasant events like flashovers, conflagration, risk of life, and determination of power elements. Different approaches have been proposed in distribution system to identify HIF from capacitor bank switching and nonlinear loads which neither are easily implementable nor have an appropriate performance in all scenarios. Alongside the identification of HIFs, identification of low impedance faults is a significant task in power system. In this thesis, a novel method baxsed on Discrete-time Energy Separation Method is proposed to identify the high impedance faults. The proposed method has two major sections, the first section identifies the normal condition like normal load switching, capacitor bank and nonlinear loads outage from abnormal conditions. Second part must identify high and low impedance faults from abnormalities like applying capacitor bank and nonlinear loads. High identification speed (2-4 milliseconds), simple implementation, and low computation burden possible the real-time implementation of the proposed method. To assess the proposed method, different similar disturbances under noisy conditions and by considering the saturation of the current transformer in identification of low impedance faults have been simulated in EMTP-Rv and have been processed in MATLAB. Results show that the performance of the proposed method has a high efficiency in identification of high and low impedance faults from other disturbances even in noisy condition. This method can also identify the low impedance fault by consideration of saturation of the current transformer.