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 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.

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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.

This article presents a new method for the estimation of active power losses based on a “field” approach, i.e., on the theory of the electromagnetic field and the theory of propagation of electromagnetic waves in a dielectric medium. Electromagnetic waves are assumed to transmit energy from the traction substation to electric rolling stock through the airspace of the inter-substation zone (i.e., not through the wires of the traction network) and meet electrically conductive surfaces on their way. The waves are partially reflected from the surfaces and partially penetrate them, thus creating thermal losses, the determination of which is the main task of this article. The analytical expressions for specific losses of active power are obtained by solving the system of Maxwell’s equations. Calculations of specific power losses in the catenary, rails, roofs, and bottoms of carriages and electric locomotives are performed. Power losses in carriages and electric locomotives are found to be at least 7%. A comparative assessment of the magnitude of total power losses of different types obtained by the “field” and “circuit” approaches is provided, which has established that “conditional” losses correspond to losses in rails, train carriages, and electric locomotives.

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Theoretical research of voltage emissions has been conducted for the collector of electric locomotive DE1. The comparative results of theoretical and experimental calculations have been provided.

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