A probabilistic model is developed for the characterisation of crosstalk sensitivity to random fluctuations of conductors in a bundle cross-section. A uniform and lossless three-conductor transmission line (TL) is used for the definition of generator and victim circuits, with general loading conditions. A novel circuit model for crosstalk is developed, in which the victim circuit embeds all the interference effects due to the presence of the generator circuit. Such effects are represented by a voltage and a current lumped noise-source and a distributed-parameter passive two-port. Under the weak-coupling assumption, and by assuming random fluctuations of the generator wire in the TL cross-section, closed-form expressions for the mean value and variance of crosstalk voltages are derived, valid both at low-frequencies and in the TL standing-wave region. These closed-form crosstalk estimators extend previous results, limited to electrically short TLs. All the theoretical developments are checked via a numerical repeated-run analysis.

This work deals with the use of the Clarke transformation for the theoretical derivation of circuit models for the analysis of asymmetrical transients in three-phase circuits. Asymmetrical transients occur when only one or two phases of a three-phase power system are involved in a switch operation. Such a condition is critical from a theoretical viewpoint since the Clarke transformation is based on the assumption of circuit symmetry between the three phases. If the symmetry assumption is not met, the equivalent circuits in the transformed variables α, β, and 0 are not uncoupled. The literature concerning numerical approaches for asymmetrical transient analysis is very rich, but a comprehensive and rigorous analytical investigation of circuit models within the framework of the Clarke transformation is still lacking. Contrary to numerical approaches, analytical solutions provide deeper insight into the phenomenon and allow for theoretical interpretation and better understanding of the transient behavior. The proposed circuit models show that the β variables are always uncoupled with α and 0 variables, whereas coupling between α and 0 variables can be properly represented by an ideal transformer. Moreover, in the case of single-line switching, the β variables have no transient, i.e., they keep the steady-state behavior. Transient properties can be readily and effectively observed by representing the trajectory of the space vector on the complex plane. All the analytical results have been checked numerically through the Simulink (Matlab R2020a, The MathWorks, Inc., Natick, MA, USA) implementation of a specific three-phase circuit introduced to illustrate the main theoretical issues.

This paper shows that in the radiated emission spectrum of high-speed railway systems, a low-frequency range exists in which the magnetic field space-frequency distribution is determined, to a large extent, by the railway infrastructure features. To prove this, electromagnetic modeling of a suitably long stretch of the railway infrastructure is developed, and an ad hoc experimental campaign is carried out for comparison. Modeling and experimental measurements refer to a 50 km stretch of the Italian 2 × 25 kV ac railway system. Infrastructure simulation is obtained by resorting to a simplified approach based on multiconductor transmission line. To this end, short segments of uniform lines are cascade-connected with lumped networks representing equipment and electrical devices placed along the line, and the radiated magnetic field is evaluated from the corresponding noise-current distributions. Since the emission source, i.e., the train, has unknown electrical properties, it is represented as a unit-current source. Thus, the proposed model provides a transfer ratio between the radiated magnetic field and the current source. As a result, the maximum values of train current corresponding to magnetic field limits provided by the International Standards can be readily derived. An optimized measurement procedure is used to show that in the frequency band 60-120 kHz, transient emissions due to random and unpredictable phenomena are negligible. In such a frequency range, where continuous and persistent emissions are present, the structure of time-frequency measurement data is readily explained, and the role of the railway infrastructure on the radiated magnetic field is unambiguously identified.

This paper deals with crosstalk estimation in a set of individually insulated wires laced together to form a bundle, and running above a ground plane. A simplified and numerically efficient multiconductor transmission line model is developed, involving a single reference cross section with pseudocircular shape and staircase approximation for the wire trajectories. The presence of lacing cords along the bundle is modeled as a sinusoidal modulation of the reference cross-section dimension. It is shown that crosstalk in wire bundles is mainly affected by the relative positions of the generator and receptor wires, whose paths are to be accurately represented as smooth curved trajectories, whereas it results to be substantially insensitive to rough modeling of the paths of the remaining wires. The weak random nonuniformity of the generator and receptor wires proves to be the fundamental property to be reproduced in order to obtain physically sound crosstalk predictions. This is enforced by deducing the staircase approximation of the generator and receptor wires from a preliminary representation of only that wire pair in terms of splines with a very small number of nodes. Differently, the staircase trajectories of the remaining wires are obtained by direct mapping onto the reference cross section. Model performance is assessed by comparing crosstalk predictions versus measurement data and theoretical results available in the technical literature. Predictions compare appreciably well with measurements, also in the most critical case of high-impedance loads. The coupling distribution shows nonsymmetrical structure and a long tail to the right, as several other crosstalk analyses have shown.

This work reports a modeling methodology for the prediction of conducted emissions (CE) in a wide frequency range (up to 100 MHz), which are generated by dc/dc converters and propagate along the power buses of satellites. In particular, the dc/dc converter seen as a source of CE is represented by a behavioral model, whose parameters can be identified by two unit-level experimental procedures performed in controlled test setups. A simplified multiconductor transmission-line (MTL) model is developed to account for the propagation of CE in shielded bundles of twisted-wire pairs used as power cables. The whole power system is represented by the interconnection of the circuit models of dc/dc converters, cables, and Power Conditioning and Distribution Unit (PCDU). By solving the obtained network, frequency spectra of CE can be predicted. Experimental results are reported to substantiate the accuracy of the proposed unit-level dc/dc converter model and the MTL model of cables. Finally, a system-level test setup composed of three dc/dc converters connected to a PCDU is considered, and predicted CE are compared versus experimental measurements.