25 kV–50 Hz railway supply modelling for medium frequencies (0–5 kHz)

Abstract

In this paper, a modelling method of a 25 kV-50 Hz railway line, in a frequency range from 0 to 5 kHz, is presented. A model is proposed to quantify current and voltage harmonics generated by traction converters in different points of the network. An equivalent circuit, taking into account the skin effect for time-domain simulations, is also proposed. A new model, based on state space representation and transfer functions is developed to simplify the study of the interactions between several trains circulating on a line sector. As an example, the amplitudes of the harmonics generated by on-board active rectifiers are computed at several points of the network for a given topology of the overhead line and several positions of two trains on a sector with a junction.

Modelling of a 25 kV-50 Hz Railway Infrastructure for Harmonic Analysis

“…One can also see that the resonant frequencies depend on the sector on which the train runs. It has also been shown that these resonances depend on the train position [13,14].…”

“…Each iteration takes as initial parameters the result of the previous iteration. The algorithm of the optimisation is shown in Figure 8 and it is developed by Stackler et al [14].…”

25 kV–50 Hz railway power supply system emulation for power‐hardware‐in‐the‐loop testings

“…3 d . An optimisation, detailed in [12], has been made to calculate the values of the parameters. Finally, a three‐resistance‐two‐inductance‐ladder circuit has been obtained as an accurate model of a quadripole resistance with skin effect up to 5 kHz.…”

“…As on‐board power converters running on railway infrastructure reject harmonics into the overhead line, which can be amplified by the impedance of the overhead line [12], some overvoltages, possibly resulting in disturbances for other trains on the infrastructure or for rail signalling, can be observed. Both standards such as the standard EN 50388 [13] and railway companies limit the tolerated level of harmonics injected into the infrastructure by on‐board converters [14].…”

Hierarchical Robust Performance Analysis of Uncertain Large Scale Systems

“…These kind of systems are often modeled with cascaded blocks where each block models a short part of the line (this part should be of short length compared to the wave length). Usually blocks are modeled as quadripoles which are electrical circuits with two pairs of terminals to connect to external circuits, see [32] and the references within. Because of the modeling errors, the quadripole characteristic parameters are not precisely known and uncertainties should be considered to study the worst case stability scenario.…”