OPTIMIZATION OF ANALYTICAL SOLUTIONS OF TRANSIENT PROCESS EQUATIONS FOR SINGLE-PHASE GROUND FAULTS IN MEDIUM VOLTAGE NETWORKS

Ю. О. Семененко, І. О. Рябенков

Abstract


The article discusses topical issues related to the transient process during single-phase ground faults in medium-voltage networks. The difficulty of obtaining an accurate analytical solution to the equations of the transient process during single-phase ground faults in medium-voltage networks is primarily due to the complexity of the calculation scheme for replacing the electrical network. The choice of the scheme depends on the purpose of the study and the need to take into account different stages of the development of the transient process. The process of a single-phase ground fault is accompanied by a redistribution of phase voltages relative to the ground: the potential of the damaged phase decreases to zero, and the potentials of the healthy phases increase. A single complex transient process is conventionally divided into four stages. The first and second stages belong to wave processes and are often combined into one discharge stage. The third stage - the exchange of energy between the source inductance and the capacitances of the network elements - is manifested by medium-frequency oscillations and is considered as a charging stage, which can be described by equations of electromagnetic transients in circuits with lumped parameters. The fourth stage corresponds to the establishment of the power frequency current.

The work has carried out analytical calculations and mathematical modeling, which indicate that the maximum overvoltages occur at the charging stage, therefore, in many calculations, the discharge stage is simplified, considering it instantaneous. However, when analyzing the impact of the transient process on the operation of protection against single-phase ground faults, estimating the amplitude-frequency spectrum of transient currents and determining the effective value of the current at the damage site, such simplification leads to significant errors. In these cases, the calculation scheme of the equivalent circuit must take into account both the charging and discharging stages of the transient process.

The article presents an optimization analysis of known approaches to the analytical solution of the equations of the transient process during a single-phase ground fault. It is shown that the most promising is the combination of analytical methods based on simplified schemes with simulation modeling in the MATLAB environment. At the same time, a comparative analysis of methods for obtaining analytical solutions is performed. It is established that a sufficiently accurate analytical solution, which considers the discharge and charge stages as a single process, is achieved on the basis of a two-frequency equivalent circuit of the electrical network. The proposed approach allows obtaining compact analytical expressions with an accuracy acceptable for engineering practice. It is recommended to use it for analyzing the impact of transients on the functioning of protection against single-phase ground faults, assessing the spectral characteristics of currents and in the design and adjustment of relay protection in medium-voltage networks.


Keywords


arc faults, overvoltage, capacitive currents, arc extinguishing reactor, isolated neutral, zero sequence, dual-frequency circuit

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DOI: https://doi.org/10.32620/oikit.2026.108.08

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