This article presents the results of comparative studies of existing methods to calculate the inductance of dynamic and static single-phase reactors of arc extinguishing by double-rod and armored magnetic circuits with non-magnetic gaps in terms of the geometric parameters of the device. There are proposed expressions to correct the determination of the effective area of the winding of reactors by the shunting magnetic flux. On the basis of numerical calculations, the significant influence of the correct calculation of the effective area of the reactor winding by the shunt magnetic flux on the result of calculating the inductance is shown, it undoubtedly affecting the accuracy of the operation of both many digital devices of existing substations in particular, and new digital substations being introduced in general. It was also found in the work, that carrying out the correct calculation will improve both electrical characteristics of the device, and technical economic indicators of capacitive current compensation systems as part of digital substations, when setting the inverse problem of determining the geometric dimensions of the electrical part of the reactor according to the known inductance value, which depends and is calculated on the parameters of the given network, including capacitive currents.

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Single-phase earth faults occur in 6–35 kV distribution networks. One of the devices designed to eliminate earth faults is the arc suppression reactor. The inductance of the reactor is set in resonance with the capacitance of the network, which results in the suppression of the capacitive component of the current. A method of determining the inductance of a reactor using instantaneous values of current and voltage is proposed. A differential equation linking the measured quantities is derived. The equation is written for two moments of time, and a system from which the expression for the reactor inductance is derived. Numerical approximation of the derivatives by means of the asymmetric difference derivative was carried out. The mathematical model of the reactor was composed. The influence of the asymmetry coefficient and the main parameters of the considered transients on the accuracy of determining the reactor inductance was analyzed. The influence of noise on the accuracy of determining the inductance of the reactor was considered. The influence of the main parameters of the considered transients on the stability of the method to noise is analyzed. The confidence intervals of the calculated inductance for different values of relative noise are constructed. An upgraded method for determining the detuning based on the solution of an overdetermined system of equations is proposed. The robustness of the upgraded method to the influence of noise was analyzed. The modernized method has shown to be more robust to the influence of noise in comparison with the method based on solving a system consisting of equations written for two moments of time. A test of the methods on a real oscillogram of current and voltage is described. Recommendations on the practical application of the developed methods are offered. The upgraded method is appropriate when there is a high influence of noise and no limitations on the computing power of devices, the method of calculating the inductance by two readings should be used in all other cases.