Modeling of Power Line Operation Modes Based on Long Line Equations in Hyperbolic Functions Taking into Account Specific Corona Losses with Nonlinear Conductivity

An extra-high voltage (EHV) overhead power transmission line is represented in the form of equations of a line with distributed parameters in hyperbolic functions. These equations are obtained subject to assumption of a quadratic dependence of active power losses for corona on voltage. Active power losses for corona for EHV transmission lines depending on weather conditions along the line route are a function of voltage of the 4th to 8th power. An attempt to directly obtain analytical dependencies for a line with distributed parameters in hyperbolic functions taking into account the function of voltage of an arbitrary power by means of mathematical manipulations does not seem to be possible. At the same time, in solving some problems relating to EHV transmission lines, highly accurate modeling is required. The article proposes a technique and an algorithm for modeling active power losses for corona based on modeling long line equations taking into account active power losses for corona with nonlinear conductivity. The proposed technique can be used for improving the accuracy of modeling AC transmission line steady-state operation modes, for measuring active power losses and separating corona losses based on simultaneous measurements of current operation parameters at the ends of EHV transmission lines, and for performing a comparative analysis of the accuracy of simplified models. The adequacy and performance of the method, and the assessment of mathematical modeling methodological errors are analyzed taking as an example a 350-km long 500 kV transmission line.