This paper presents a comprehensive framework for wide-area modeling and harmonic resonance assessment in the AC single-phase Swedish electric railway power system (ERPS). The methodology integrates the modeling of key elements of the catenary system, such as synchronous generators, transmission lines, transformers, and filters, while addressing the dynamic behavior of rolling stocks and inherent system uncertainties. Study cases, including Monte Carlo simulations, are developed to evaluate probabilistic scenarios and impedance variations across the network using nodal admittance modeling and frequency scanning. Key contributions include a method to model moving loads, a comprehensive approach to harmonic resonance analysis based on meshed grid characteristics of the ERPS, and an uncertainty assessment framework that highlights insights for system planning and mitigation actions. Discussion outlines future research directions for improved ERPS harmonic resonance studies. 

The waveform distortion interactions and time-varying behavior in electric railway power systems (ERPS) are explored in this paper by investigating measurements from a traction converter station. The paper proposes a methodology aimed at contributing to three aspects: screening detailed measurements with high resolution in time and frequency, comprehensively assessing waveform distortion parameters of the system, and developing a time-varying framework to assess waveform distortion interactions and sub-1-min variations in the railway grid. Specific focus is given to identifying disturbance sources and patterns during operation, including limitations of traditional methodologies based on aggregated values and addressing the challenges posed by the differences between the two electromagnetic environments (railway grid and public grid). The results propose new indices ( z-WDSV,z-WDSV_w ) for evaluating waveform distortion in ERPS, highlighting the suitability of the methodology for assessing time-varying interactions and probabilistic aspects. The proposed framework can determine and quantify the frequency-domain components impacted by the operation of vehicles in the traction sections. Additionally, the limitation of longer measurement intervals is confirmed by the relationship between the aggregated value and variance due to the rapid variation caused by rolling stock operations. Other aspects of mechanisms involving waveform distortion on both sides of the traction converter station are discussed.

Railway electrified systems are one of the most popular and essential forms of transportation globally, and the performance of those systems impacts society. The electric railway power systems (ERPS) comprehend the infrastructure and apparatus that aims to deliver power for the rolling stocks in different types of railway transportation. Due to the broad application of static power electronics, ERPS is characterized by several sources of waveform distortion. Waveform distortion is a critical power quality (PQ) issue and a challenge to managing electromagnetic compatibility (EMC) in railway systems. It englobes harmonics (disturbances synchronous with the fundamental power frequency up to 2 kHz), interharmonics (disturbances asynchronous with the fundamental power frequency up to 2 kHz), and supraharmonics (synchronous and asynchronous disturbances between 2 and 150 kHz).

The ERPS has several system complexities that should be taken into consideration when assessing waveform distortion related to the characteristics of the phenomena: extensive distribution system with intricate circuit arrangements and moving single-phase loads; multiple voltage levels and electromagnetic environments, including railway grid and subsystems, as well as public grid; waveform distortion has time-varying behavior dependent on operating states of rolling stock, traffic plan, grid balancing, and spatial position of the vehicles; a mix between traditional equipment or infrastructure and population of new power electronic conversion stages with a lack of guidelines and standardization; and variety of waveform distortion sources and signatures.

The objective of this research is to gain knowledge and a better understanding of waveform distortion, including not only harmonics but also interharmonics and supraharmonics in railways systems, to characterize emission sources, propagation, the impact of the operation on time-varying behaviors in several scales, interaction among systems and subsystems, and adverse effects. The focus of the work is alternating current (AC) electrified railways, with a deeper assessment of, but not limited to, the railway system solution of Sweden (15 kV 16 ⅔ Hz). The development and scope of this work provide a comprehensive literature review of waveform distortion assessment for electrical railway power systems and build up a framework for future contributions, characterization of waveform distortion for electrical railway power systems using measurements, conduct detailed measurements on waveform distortion in a traction converter station, modeling waveform distortion propagation for ERPS considering complexities of the system, application of unsupervised deep learning (DL) methods to find patterns in waveform distortion data and investigation of the impacts related with those issues. The research contributions from those defined scopes are summarized below.

·         Identification of the challenges of waveform distortion assessment in ERPS and categorizing the available literature to address some of those challenges.

·         Characterization and screening of the waveform distortion time-varying dependencies in different time scales.

·         Providing a methodology for assessing time-varying waveform distortion in railway systems, adapting traditional methodologies, advanced statistical analysis, and machine learning approaches.

·         Modeling waveform distortion interaction within the ERPS in Sweden, incorporating challenges such as moving loads, meshed grid analyses, and a wide range of disturbances propagation in ERPS.

·         Addressing the different mechanisms affecting waveform distortion at the catenary and public grid sides.

·         Investigation of the impact of waveform distortion performance on associated equipment.

The work provides crucial steps for better establishing a PQ framework and future standardization for waveform distortion in ERPS by exploring multiple aspects and directions on the assessment side.

This paper aims to characterize the long-term variations of the Low Voltage (LV) distribution grid impedance in the MHz band, as well as the impedance variations between the electrical phases in three-phase installations, based on extensive field trials in real scenarios. These measurements were carried out in different scenarios and over different periods. The results provide valuable insights into the temporal evolution and variability of the grid access impedance at Broadband Power Line Communications (BB-PLC) frequencies. Comprehensive knowledge of these variations is essential for improving the design, reliability, and robustness of BB-PLC systems, as well as for developing more adaptive communication strategies and grid monitoring tools that can effectively cope with impedance variations.

Electric railway systems (ERS) are characterized by several particularities regarding the return current circuits, moving loads, multiple sources of waveform distortion, and extensive deployment of static converters from various manufacturers, topologies, and solutions. This work presents a methodology for application of load monitoring to classify rolling stock (RS) waveform distortion signatures. The proposed methodology combines the benefits and advantages of unsupervised deep learning and reconstruction error performance classification for performing non-intrusive load monitoring (NILM) in ERS. It consists of adapting autoencoder-based novelty detection for load classification problems. The method is applied to pantograph measurements from four rolling stock items using two types of data input (harmonic spectra up to kHz and VI diagram images), which are compared in binary classifications of the same kind of railway electrification. The methodology shows suitable classification performance with high accuracy, scoring an average of 98.81 % for spectrum input and 97.77 % for VI diagram input. It has also been validated with a NILM dataset (LIT) for multi-class applications showing 99.13 % for spectrum input and 94.28 % for VI diagram input. The proposed method has suitable computational times and scalability, allowing application to a wide range of NILM and classification problems using distortion signatures.

The specific frequency range of 9 to 150 kHz was omitted from the main part of the IEC 62236 (2018), which is equivalent to EN 50121, and is presented as an informative part due to the poor reproducibility of the measurement results of the radiated emission of trains. In this paper, the merits of time domain measurements and time-frequency analysis of the radiated emission of trains have been utilized in order to propose some prerequisites to lessen the uncertainties to obtain repeatable and reproducible measurement results in the frequency range of 9 to 150 kHz. To this end, 23 measurements from trains are presented, the performance of the trains have been investigated considering the previous IEC/EN limits, and comparisons have been made between some of them. Furthermore, based on the results of time-frequency analysis of the radiated emission, it has been revealed that the maximum amplitude of the radiated emission for some frequency components occurs before train arrival to (or after train passage from) the measurement location. Moreover, two indices have been introduced to compare the performance of different trains from radiated emission perspective. Finally, calculation of the rms radiated emission spectrum has been proposed to alleviate the influence of train operation (e.g., acceleration, cruising, coasting, and braking) on radiated emission measurement results; and some constraints have been proposed to minimize the uncertainties resulted from operation modes so that repeatable and reproducible results could be achieved to find more accurate curve of maximum radiated emission spectrum of a train.

This article evaluates the thermal impact of low-order harmonics on transformer loading capabilities in the Swedish electric railway power system (ERPS). Using real power quality (PQ) measurements and standard methodologies from IEC and IEEE, it estimates the hot-spot temperature (HST), top-oil temperature, and ageing parameters to assess harmonic contributions to transformer loss of life. Results indicate that harmonic distortion can increase HST by up to 25 °C and that over 50% of total ageing is attributed to harmonics. The findings align with the general view and values of the existing literature. While severe insulation degradation limits were not reached within the study period, future expansions in railway traffic may significantly elevate thermal stress, necessitating transformer derating. The article underscores the importance of harmonics in ERPS transformer health management and PQ performance.

Assessing harmonic distortion measurements in the electric railway power systems (ERPS) requires evaluating the time-varying behavior, interactions, and performance in different time scales. This paper aims to map and assess harmonic voltage levels in 13 traction converter stations for the Swedish railway power supply system, with findings that have direct practical implications. For that, measurements from the public and railway grid sides for 69 weeks are analyzed. Statistical values are explored for the harmonic voltage spectra and total harmonic distortion (THD) variation. The public grid side measurements are investigated using 95th percentile weekly values, and performance is evaluated by comparing the recommended planning levels of IEC 61,000–3–6. The intraweek variation complements the information about the time-varying behavior of the THD. The 95th percentile, minimum daily values, and intraday variation are explored to understand the time-based behavior since there are no reference limits from standards for comparison, looking to the railway grid side. Extended analysis is placed on the railway grid side to highlight some aspects of measurement time-aggregation based on 10-min values, and time-series trend analysis is used to confirm traffic planning impact. Discussion and findings regarding railway operation, the technology deployed at the traction converter station, time-varying behavior, traffic planning impact, measurement time-aggregation, and spectra patterns were presented.

This work addresses the imbalance in the literature regarding the modeling of waveform distortion resonance and propagation in low-frequency railway electrification systems, focusing on the Swedish Electric Railway Power Supply (ERPS). A framework is proposed for modeling synchronous components of waveform distortion up to 25 kHz, incorporating local interactions between traction converter stations (TCSs) and rolling stock. The nodal admittance matrix is developed for an autotransformer-fed circuit with three railway sections and four TCSs. Rolling stock is represented through a measurement-based Norton model capturing high-order components and probabilistic harmonic emissions. Monte Carlo (MC) simulations assess resonance and propagation uncertainties under variable operating conditions. Results reveal key influences of railway section lengths, filters, and stochastic emission models on impedance characteristics, offering ERPS tools for future assessment.