Renewable energy sources have a multifaceted impact on power grids, ranging from the reliability and quality of electricity to the selective impact on equipment. While renewables used to be distributed in distribution networks, now their capacity is commensurate with thermal power plants and their impact on the grid should not be underestimated. According to the statistics on the interruption of the bulk electric networks, one of the main reasons for emergency shutdowns of extra high-voltage power lines are single-phase short circuits. The problem of mathematical modeling of the limit modes in terms of static stability is very relevant to the design and operation of electric power systems (EPS). Calculations of limit modes have both an independent value and a component of other electrical engineering tasks related to ensuring the required level of reliability and cost-effectiveness of the operation of the united PS. Despite the great degree of development of issues of planning and control of electric modes, system accidents associated with unacceptable loads of network elements occur in the Ukrainian energy industry. Non-phase modes regularly occur in electric power systems, which can lead to an unacceptable load of intersystem network elements, which imposes significant restrictions on their throughput. Single-phase short circuits are more than 95% of other damage that occurs in the line. The use of single-phase auto reclose on the transmission lines allows disconnecting only the damaged phase for a short period of time and not the entire transmission line. This action preserves the transit of electricity along the line and prevents the violation of the stability of parallel operation. To achieve this, the current-free pause of the single-phase auto reclose should last as short as possible. On the other hand, an important task to be solved when using single-phase auto reclose is to choose the minimum duration of the current-free pause necessary for its success. The problem studied in this paper deals with the safety and correct operation of transmission lines (TS) of the Ukrainian bulk power system in special conditions (not predictable, changing due to frequent attacks). For a quickly changing configuration, the power grid uses switches, and in the case of ultra-high voltage, the TS needs to solve the problem of secondary arc currents and recovering stresses in the place of arc burning after its extinction. One of the methods of reducing secondary arc currents and recovering stresses in the place of arc burning after its extinction is the implementation of single-phase automatic reclosing (SPAR). The main theoretical result of the paper is a proposed mathematical model of a compensated power transmission line based on the use of matrix n-poles, which makes it possible to model in detail stationary power transmission modes, including the SPAR mode. The proposed mathematical model of three-phase power transmission has been created using phase coordinates and can be used for the analysis of complex asymmetric modes. The main practical result of the paper is physically interpreted simplified models of three-phase TS, which can be used for the study of resonant overvoltages and currents of the feeding arc in non-full-phase circuit SPAR. The conclusion that can be drawn from the obtained results points out which line lengths must take into account the influence of longitudinal asymmetry when choosing the inductive resistance, i.e., take into account the dependence of the mode parameters on the location of the damaged phase. The observed results show that the largest values of the multiplicity of overvoltages will take place in phase B. The novelty of the work is the developed technique that makes it possible to determine in advance, depending on the disconnected phase of the line, the values of the primary conductivities of the STC (static thyristor compensators) and the corresponding angles of control of the thyristor switches, which satisfy almost complete compensation of the secondary arc at any point of the line in the specific condition (hard) of the bulk power system operation.