Simulation of Electric Networks Modes Using Steady-State and Heat Balance Equations

In the traditional calculations of the steady-state mode of the electrical network, the dependences of the active resistances of the overhead line wire on the ambient temperature and currents in the branches are not taken into account. However, the temperature is a function of the active power losses, the power losses are a function of the resistance and current, and the resistance is temperature dependent. Therefore, these relations should be related to the traditional equations for stationary regimes. In order to increase the accuracy of steady-state calculations, a temperature correction of the resistance of the branches is required. In this paper, we present a method based on the joint solution of nonlinear equations of the steady-state electric network regime and the thermal balance of the wires of overhead lines. The algorithm and the program of calculation of the steady-state mode of an electric network taking into account dependence of active resistances of a wire of an overhead line on ambient temperature and currents in branches have been developed. The quantitative influence of the load current, wire temperature, wind speed, solar radiation on the active resistance of the wires has been estimated, and the errors in calculating annual variable energy losses have been determined. Numerical experiments were carried out for a 6-node modified version of the IEEE test system and equivalent circuit of 110 kV. The results of the calculations of the steady-state regime on various test circuits showed that the non-account of the temperature dependence of the active resistances might cause errors in power loss for individual loaded lines up to 10 %, and for total losses of the system – up to 30 %. This is unacceptable in simulating the modes of the electric network. The results of simulation of steady-state regimes taking into account the temperature dependence of the resistance of the wires are presented on the example of 6-node and 7-node circuits.