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This article presents an algorithm and a method for calculating power flow of an open electric network with a voltage of 6-35 kV, taking into account the temperature dependence of active resistances. Calculation of the electric and thermal conditions of the electric network is carried out with a joint solution of the equations. The determination of stresses in the nodes is carried out using the inverse matrix of the nodal and intrinsic conductivities. The inverse matrix of nodal and intrinsic conductivities is determined based on the well-known direct Jordan-Gauss method. The equation of the heat balance of the wire used to calculate the actual temperature is solved numerically. Convective heat transfer is recorded only for forced convection, because wires of overhead power lines with a voltage of 6 kV and higher are located on various types of poles, at a height of at least 10 m. This fact allows us to abandon the use of formulas for natural convection and use expressions only for forced convection. Accounting for solar radiation in the presented algorithm is possible on the basis of two methods: simplified and considered in the standard of PJSC FGC UES, which allows you to take into account the actual location of the wire relative to the north. Using the test circuit as an example, the steady-state mode was calculated taking into account the temperature dependence of the active resistances. The results of a numerical experiment are presented, confirming the operability of the developed algorithm. The refinement in determining active power losses with and without taking into account the heating factor for the considered circuit is about 13%. Verification of the algorithm that implements the method of calculating the steady state (SS) of an open electrical network of a medium voltage class taking into account the temperature dependence of active resistances showed that in technically acceptable modes the developed algorithm has good accuracy in comparison with the RastrWin3 software package.

The use of new self-supporting insulated wires and high-temperature wires in the operation of power lines allows increasing the capacity of lines and, as a rule, reducing operational costs. An optimal utilization of the power line load capacity depends on the precise determination of the permissible current loads. The values of permissible currents and steady-state temperature are the main parameters of the line operating mode, affecting the strength and sag of the conductor. The temperature of the wire depends on weather conditions and current load. There are methods for determining the temperature and permissible currents for widely used traditional wires such as AC. They are partially outlined in the EIS (Electrical Installation Standard) and the standard of PJSC FGC UES (Federal Grid Company of Unified Energy System) of 2013. However, there is lack of studies in new types of wires. The paper considers the effect of weather conditions and load on the temperature and real-power losses in insulated and high-temperature wire, and solar radiation is under special consideration. For comparison, we present the results of calculations on traditional AC wires. The research shows that solar radiation, being taken into account, provides an increase of real-power losses of about 2 % with the given values of load and weather conditions. Calculations of permissible current values according to the developed technique for classical AC wires reveal a high coincidence with the values from PJSC FGC UES standard. The relative error is within two percent, and the proposed method is more generalized. It allows simultaneous analysis of both uninsulated and insulated wires. Due to the widespread use of self-supporting insulated wires, power industry experts can use the developed software in the design and operation of modern power lines to optimize capacity.