In railway traction, the definition of “electromagnetic field” is functionally connected to the concept of the reactive power consumed by the electric rolling stock, and characterized by the running and standing electromagnetic waves in the space of the inter-substation zones from the site of the AC traction system. Such a definition is established and theoretically justified by the theory of electromagnetic fields. This article uses the methodology of this theory, in particular, a method for power balance estimation in electromagnetic fields based on Maxwell’s equations, as well as methods for the analysis of running and standing electromagnetic waves based on the theory of reflection, propagation and transmission of plane harmonic waves. The research considers the regularities of standing electromagnetic waves in the space of inter-substation zones of electric traction systems, which occur due to the incomplete reflection of incident waves from the contact wire and metal parts of the roof surface and the frontal part of the body of the electric rolling stock. The flow of electricity to the roof surface and the frontal part of the body of an electric locomotive is considered. The possibility of using existing methods to reduce wave reflections and thereby to effectively compensate for reactive power in the space of inter-substation zones is discussed.

-The paper shows the methods of spectral analysis of stochastic traction voltages and currents. The results of analysis are shown for the voltage, which was recorded in the process of real operation of EPL2T electric multiple-unit train.

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The paper is dedicated to the estimation of instantaneous reactive power in a DC traction power system. Currently, the integral and frequency methods are mostly used to define reactive power and do not give high accuracy in the calculations of power balance or cannot describe the essence of physical processes. The problem is complicated in DC electric transport systems due to random impulse character of voltages and currents. As a comparison, the calculation of reactive power according to various approaches was performed for the DE1 electric locomotive. It is suggested that the instantaneous reactive power should be used for the analysis of electromagnetic exchange processes in DC power systems. The paper shows the definition and main formulas for defining the instantaneous reactive power taking into consideration the random character of voltage and current. Numerical calculations together with statistical analysis were performed for two variants of experimentally recorded voltages and currents: the first oneon the bus-bar of traction substation, which supplies the section with the Pendolino trains in Poland and the second oneon the current collector of the VL8 electric locomotive in Ukraine. They confirm the validity of the aforementioned method.

The regenerative braking is one of the most attractive ways for energy saving in electric transport. It has many advantages and its effectiveness is discussed in numerous researches, but there are no significant publications, which describe the power losses in the way of recovered current flowing. The paper describes an alternative method for estimating recovered energy losses in the elements of a DC electric transport system. In comparison with existing methods, it is based on the correlation theory of stochastic processes and takes into account the Fryze's concept for reactive power. The method is verified by the experimental researches, which are performed for the VL8, VL11M, VL11M6 locomotives, EPL2T multiple-unit train and T4D tram, which operate in DC sections, Ukraine. The losses are calculated for different elements of an electric transport system, and their theoretical and statistical distributions with basic probabilistic characteristics are shown. The results prove the validity and applicability of the method.