Background. For selective protection against single-phase earth faults in uncompensated 6–10 kV networks with isolated neutral or high-resistance resistive neutral grounding, maximum current and current directional zero-sequence protections are most widely used. Higher technical perfection (selectivity and stability of operation) is provided by current directional protection against single-phase earth faults. Almost all known modern digital designs of directional current zero-sequence protections of various manufacturers are based on monitoring the phase ratios of the components of the fundamental frequency of voltage and current of zero-sequence. It ensures an increase of their selectivity, but not always sufficient sensitivity in the most dangerous for the network and damaged connection arc intermittent earth faults. Therefore, the task to develop current directional zero-sequence protection with high technical perfection, both for stable and arc earth faults, is relevant. In our opinion, such designs of directional current zero-sequence protection can be obtained on the basis of a multi-frequency approach. It assumes the use of both the fundamental frequency components and the higher harmonic components of the steady-state and transient modes of single-phase earth faults in 6–10 kV networks.
Materials and methods. Considering the complexity of transient processes during arc earth faults in medium-voltage electric networks and the algorithms of the operation of relay protection devices based on the use of electrical quantities of transient processes in electric power facilities, the main research method is mathematical modeling using simulation models of 6–10 kV cable and overhead networks with an isolated neutral or with high-resistance resistive grounding of the neutral, and a model of the algorithm for the operation of multi-frequency directional protection against earth faults. They are implemented using the Simulink application program and the SimPowerSystems block library of the Matlab software package.
Results. The principles of implementation of multi-frequency directional protection against single-phase earth faults in cable and overhead networks with voltage of 6–10 kV are substantiated and an algorithm of its operation is developed. The results of the functional tests on simulation models of cable and overhead 6–10 kV networks, operating both with an isolated neutral and with neutral grounding through a high-ohm resistor, confirmed the efficiency of the developed principles of implementation and the algorithm of operation of multi-frequency directional protection for all considered types of single-phase earth faults.
Conclusions. The proposed technical solution implements a multi-frequency principle of directional protection against single-phase earth faults in 6–10 kV cable and overhead distribution networks with isolated neutral and high-resistance neutral grounding. It provides higher selectivity and sensitivity compared to traditional directional current protection based on the use of only fundamental frequency components, both for stable and for the most dangerous arc intermittent earth faults for the network.

