The low fault current of high-impedance faults (HIFs) is one of the main challenges for the protection of distribution networks. The inability of conventional overcurrent relays in detecting these faults results in electric arc continuity that it causes the fire hazard and electric shock and poses a serious threat to human life and network equipment. Since about 1960, researchers have developed several methods to detect this fault. However, low accuracy, complexity, and high cost are thier most important challenges. One of the main parts of the protection system is to develop an appropriate fault detectin index and then to determine the appropriate threshold value for proper detection. After reviewing the high impedance fault models and existing detection methods, this thesis proposes two HIF detection algorithms based on quantifying the nonlinear and asymmetry features of HIF waveforms. In the first method, firstly, the substation current is sampled and then, the superimposed component of cross entropy signal calculated by comparing two subsequent half cycles of the current signal is determined as the HIF detection criterion. On the other hand, to overcome the challenge of the similar transient of equipement switching and HIF, the time duration of transient continuity is considered as the constraint of the proposed algorithm. The second method provides an algorithm based on the monitoring of the current waveform. Using the Kullback-Leibler divergence similarity measure, the nonlinearity and asymmetry features of two subsequent half cycles of the current waveform are quantified as the HIF detection criterion. A time duration based criterion is also used to distinguish HIFs from the load, capacitor, feeder, and distributed energy resource switchings and the voltage sag and swell events. The proposed schemes satisfactory work in the presence of nonlinear loads and does not need for training dataset, transformations, and calculations of harmonic and symmetrical components. The effectiveness of the proposed HIF detection algorithms is demonstrated using the time-domain simulation of IEEE 13 and 34 node test systems using MATLAB/Simulink.