Harmonic Analysis of Rail Transportation Systems with Probabilistic Techniques

Harmonics in rail transportation systems are an important design aspect. The overall load in these systems consists of a few large traction motors, often supplied by thyristor controlled choppers or PWM converters. These converters produce high levels of harmonic currents, which may extend into the kHz range. Recognizing harmonic problems in an early stage of development is important in order to avoid high costs or bad performance at a later stage. To perform harmonic calculations with a high percentage of power electronics is not an easy task. For rail transportation systems, this task is even more difficult because the harmonic voltages in the traction system depend not only on the harmonic characteristics of the loads and the power supply system, but also on the type, position and state of the trains on the tracks. In a new approach, probabilities for the type of train, its position and its state were used. A Monte Carlo simulation was then performed on the basis of these probabilities to create a large number of operational conditions at random, in a non-chronological order. Each operational condition was analyzed by a detailed three-phase harmonic analysis. The results were stored as raw data in a database. After the Monte Carlo analysis had reached the chosen level of accuracy, the calculation stopped. The actual system analysis was performed in the statistical postprocessing of the raw data. This post-processing allowed for the calculation of min-max harmonic spectra, probability distributions of harmonic currents and voltages, risk calculations, sensitivity analyses, worst case detection and other data mining