High impedance faults (HIFs) that cause a relatively smaller current magnitude compared to the traditional low impedance faults are not easily detectable but can cause an extreme threat to electric apparatus and system operation. This paper introduces a new method of detecting and interrupting HIFs in DC power networks by specifying Z-source circuit breakers (ZCBs). The ZCB is a protective device for high power DC branches, with the capabilities of protecting bidirectional power flow and automatic/controllable turnoff function. In this new method, the operational mode of ZCB (i.e., either the detection mode or interruption mode) can be specified. Beyond previous research, the theoretical analysis has been performed on this method and the mathematical relationship between the maximum HIF resistance and required Z-source capacitance has been derived and verified. It has been found that the ZCB can respond to a HIF accordingly when its capacitances are properly adjusted in the ZCB circuit. With the adjustment of these Z-source capacitances, the ZCB can be specified to detect and report a HIF status to power system operators, or cut off the HIF branch and protect the rest of the DC system directly. The new method can detect/interrupt a HIF that is as small as 2 times of its nominal rated current and the effectiveness and general usage of the derived equation have been verified by both low power experiments in lab and high power simulation tests.