Analysis of model simplification for a system imposed by voltage unbalance generated by electric trains

The electrification of the Danish railway results in the connection of single-phase loads to the transmission grid, which consequently results in the need to estimate the effects of the introduced voltage unbalance. Many electrical grids are becoming more vulnerable to unbalanced loads, as the grids are being weakened by the tendency to have more power generated by units mechanically decoupled from the grid, which reduces the short circuit power in the system. In order to ensure secure operations, a certain level of accuracy is required when simulating the phenomenon, as a too high level of voltage unbalance can have adverse effects on the lifetime of rotating machines and malfunctioning of HVDC-LCCs and limits imposed by standards has to be followed. This paper aims to investigate the loss of precision when simplifying a fully detailed model used to estimate the level of voltage unbalance in Denmark. Three simplification factors have been investigated, namely the effect of the phase connections of the unbalanced loads, line transposition at the busbars and the line parameters. The importance of the line parameters has been tested in three different models: one including tower geometry, one including equivalent positive sequence impedance and one only including positive sequence reactance. Transposition has been tested with different unbalanced load connections and line parameters. It is seen that both unbalanced load connections and transposition at the busbars are of importance to the model, as the level of voltage unbalance greatly deviate when unbalanced load connections and transposition are simplified. Simplified models for line parameters are seen to have relative lower errors at higher voltage unbalance levels compared to lower voltage unbalance levels.