Development of a Spectral Theory for Analysis of Non-Stationary Pulse Stochastic Electromagnetic Processes in Devices of Electric Transport Systems

Abstract

A spectral analysis of traction voltages and currents is a basis for estimation of electromagnetic compatibility level and quality of consumed power in electric transport systems. However, such an analysis is usually performed for steady-state modes and only under the condition that the time realization of voltages and currents, being deterministic for continuous quantities, have infinite length. De facto, the electric transport devices operate in non-stationary dynamic modes (starting up, coasting, acceleration, regenerative braking, stopping, wheel spin, voltage surges, etc.). As a result, the voltage across the traction motors and the current flowing through them are noncontinuous pulsed stochastic processes. It is necessary to add that in emergency modes the voltage and current are short-term single pulses. The paper presents the spectral analysis of such random sequences of pulses as well as their fronts and decays, the concepts of actual and instantaneous spectra. The analytical expressions for amplitudes and the initial phases of k-th harmonics are obtained using the discrete Fourier transformation. The numerical calculations of the spectral composition of stochastic pulse processes of voltage and current were performed for the DE1 and VL8 electric locomotives (Ukraine) as well as for trams operating on the routes of the city of Dnipro. The actual and instantaneous spectra, as well as the spectra of the full correlation functions and their "tails", were determined for the electric traction voltages and currents.

Advances in Electric Traction System—Special Issue

“…Example calculations of active losses in all conductive elements, not only in the conducting circuits (rails, catenary), showed that the proposed "field" approach to active losses is more complex and takes into account losses in locomotives and wagons. Another approach to electromagnetic processes in electric transport systems is presented in paper [25].…”

Need of technical accounting at electric energy quality reduction under conditions of AC traction substation

“…The complexity of the formation of the load on the traction power supply system is caused by the simultaneous processes of electric locomotives movement and electric drives regulation. Researchers [4] note that the spectral analysis of traction volt ages and currents is the basis for assessing the level of electro magnetic compatibility and quality of power consumption in electric transport systems. Carrying out such an analysis is com plicated by the fact that electric locomotives operate in non stationary dynamic modes.…”