Probabilistic characterization of current harmonics of electrical traction power supply system by analytic method

Current harmonics of an urban railway traction system in Hong Kong are investigated by an analytical approach. With the statistic knowledge of speed and notch number of the trains in the system, the mean and variance of harmonic current of individual trains are computed based on a behavior oriented model of the traction electrical unit. According to the large number law and central limit theorem, current harmonics at substations, which is a vectorial summation of harmonics of random number of trains electrically connected to it, are normally distributed provided that the number of trains is large enough. A set of equations are established by which probability density functions (PDFs) of current harmonics at a substation are calculated and found to be in good accordance with results obtained by Monte Carlo simulation. This approach of harmonics evaluation for traction system with random loading has evident advantages of cheap, fast and convenience and with no compromise of accuracy.