Solving the Overhead Transmission Conductor Heat Balance Equation Using the Newton Raphson Algorithm

Abstract

This paper utilizes the Newton Raphson (NR) iterative algorithm to solve a detailed heat balance equation for overhead transmission conductors, for the purpose of calculating a Dynamic Line Rating or temperature-dependent impedance using real-time or forecasted weather data. Provided ambient weather conditions, conductor parameters and electrical current passing through the conductor, a starting guess is formed and the iterative solution method arrives upon a solution within a preset solution tolerance. A simple method to approximate the Rayleigh Number / Nusselt Number and Reynolds Number / Nusselt Number relationships is proposed to ensure successful convergence. The paper performs a thorough, numeric electrothermal conductor simulation to demonstrate proper solution convergence. This exercise identifies a minimum conductor temperature rise necessary for the solution method to converge successfully. Error related to the minimum starting conductor temperature rise, and error introduced by the approximated air property functions is illustrated. The temperature solution method is compared with several well-known thermal models.