Review of Waveform Distortion Interactions Assessment in Railway Power Systems

Abstract

This work aims to cover the measurement, modeling, and analysis of waveform distortions in railway power systems. It is focused on waveform distortion as a phenomenon that includes harmonic distortion, interharmonic distortion, and supraharmonics. A comprehensive view of the interactions of waveform distortions in railway systems is needed, together with a grid perspective of power quality incorporating all aspects, sources, propagation, requirements, and effects. It is understood that the communities interested or involved in the subject of railway power systems would benefit from an integrated overview of the literature on the complex problem of waveform distortion. The literature review is divided into four categories: characterization and measurements, modeling, the application of artificial intelligence, and specific issues. For each category of work, the contributions are highlighted, and a discussion on opportunities, gaps, and critical observations is provided. The work successfully builds a framework for the subject with two main characteristics; the review is informative and propositional, providing a road map of opportunities for future works. Some aspects and recommendations can be highlighted. Suggestions for future works and research practices on waveform distortion in electrical transportation are offered.

1. Introduction

Transportation electrification is a pillar of the power and energy sector movement toward a more modern, sustainable, reliable, and efficient society. Railway transportation plays an essential role in the transport of goods and people in the world. Electric railway power systems comprise the infrastructure and apparatuses that guarantee power delivery to rolling stocks and crucial equipment for running the systems safely and reliably. The overall description of a traction system includes several electric supply substations connected by traction line sections, with a main moving load with particular power requirements and dynamic behavior [1,2]. Other static loads are also connected to these systems to support the operation. However, depending on the type of electrification, the traction supply substation, traction section arrangement, and voltage levels differ within a few solutions. Further, power delivery systems and signaling and communication systems, for instance, are integrated as essential apparatuses for the operation of railway transportation.

As the power system, in general, has been in a transition for decades towards greater deployment of non-linear loads, the same is valid for railway power systems, where the spreading of power electronics for power conversion in several applications is crucial for better performance and compliance with the modern requirements of demand and efficiency. The number of electric conversion stages increases with the intensity of the operating current, and higher switching frequencies of power electronics are expected, following the need for power concentration and optimal functioning [3]. Over and above this, the widespread use of static power converters is the main reason for waveform distortion in electric railway power systems (ERPS) [4]. Waveform distortion is still a big challenge for power systems, especially because the disturbances’ behavior, such as time-varying distortions and non-linear behavior, still needs to be entirely explored by traditional and well-established assessment methods. The railway system’s present distortion interactions and characteristics that result intrinsically from this system are due to the complexities regarding the abovementioned infrastructure aspects.

Waveform distortion corresponds to current and voltage harmonics, distortion multiples of the fundamental frequency, interharmonics, distortion that is asynchronous with the fundamental frequency, and supraharmonics, or synchronous and asynchronous distortions in the range of 2 kHz to 150 kHz. These phenomena are responsible for distorted waveforms, compared with the ideal 50/60 Hz fundamental frequency waveshape, and this distortion should be managed to avoid power quality degradation and to comply with technical recommendations, standards, and grid codes. Because of this, waveform distortion assessment is essential in electric railway power systems, and it can be carried out through measurement data analysis, measurement performance, modeling and simulation, or the application of advanced processing methods. Standards are also used as a reference for assessing distortion phenomena. Still, there is not always a reference requirement that covers all management (compatibility, immunity, and planning levels) for all parts of railways.

The literature presents several contributions that cover the assessment of waveform distortions in railway systems, as well as many aspects involving the subject. Using some of the main literature databases in power and energy research, including SCOPUS, IEEE Xplore, Wiley, and Link Springer, it is possible to find a diversity of works covering these aspects. Searching for a combination of words makes it possible to filter the work related to electric railway power systems and waveform distortion. The following search was used in the platforms, adapted for each platform syntax: “((railway OR locomotive OR {rolling stock}) AND ({waveform distortion} OR harmonics OR interharmonics OR supraharmonics OR {current noise} OR {voltage noise} OR {psophometric current} OR {psophometric voltage} OR {conducted disturbances})) AND NOT (vibration OR steel OR acoustic OR laser)”. The non-inclusion of words like “train” or the exclusion of the words “vibration, steel, laser” is meant to avoid mixing with non-relevant subjects in the field of railways for waveform distortion assessment. Figure 1 illustrates the results found on the SCOPUS platform. The search takes the title, keywords, and abstract into consideration. The search delivered 1622 documents, including 794 journal papers, 819 conference papers, four book chapters, three letters, one book, and one data paper. After the year 2002, the number of publications increased significantly, reaching its peak in 2018 with 114 publications. Most publications are from China, followed by other countries like Italy, United Kingdom, Germany, India, Switzerland, Sweden, etc. that may have experience and traditions in railway infrastructure. Figure 1c illustrates a map of the main keywords used in the literature of this subject.

The goal of this paper is to provide a literature review and cover the subject of waveform distortion assessment in electric railway power systems. For this purpose, a categorization of works is planned to better describe the types of contributions, covering the following aspects for railway systems: works on the characterization of waveform distortions, works on measurement performance for waveform distortions, works on modeling waveform interactions, artificial intelligence applied to waveform distortion data, and specific issues. The work aims to highlight the contributions and spot the main gaps in the literature, building a road map and discussion around the theme. Also, the work covers standardization aspects involving distortion management in railway systems. The works explored are the relevant ones in the literature that offer clear contributions for the category presented by this paper. The filtered/advanced search option in the database platforms supports the search for relevant contributions, but also manual searches and exploration were used. With these measures, it is possible to establish a framework on assessment and references for documentation on waveform distortion in electric railway power systems.

Several reviews were conducted in the field of power quality or harmonics in railway systems. In [5], an inclusive evaluation and classification of harmonic phenomena in railway systems is conducted, approaching low-order harmonics, low-frequency oscillations, harmonic resonance, and harmonic instability. The authors provide a perspective on the influence of the type of system, effective factors, sources, consequences, and compensation methods. For reference, the same background content is explored in [6], including interharmonics, in which the authors expand upon the content for other power quality phenomena like system imbalances, low power factors, transients, RMS variations, flicker, etc. In [7], the authors propose a comprehensive review of high-order harmonic resonances based on operation data from Chinese railways, deriving patterns and effects from real incidents covering the lack of holistic analysis linking these incidents with the phenomena and mitigation. The work provides several aspects and methods for modeling, influential factors, and practical considerations, including a proposition for the pre-identification of resonances in real systems as a prevention method.

An overview of harmonic problems, including composition, modeling, resonance, suppression methods, and an assessment of influential factors, is approached by the authors in [8], and a new phenomenon of harmonics and resonance is also discussed from measurement and simulation perspectives. The authors also discuss future studies for modeling aspects of a four-quadrant converter (4QC) from locomotives, resonance instability, detailed system aspects regarding harmonics and resonance points, and online identification. Moreover, the authors of [9] present a review of different characterization methods for the impedance of catenary lines for resonance studies, offering an analysis on the influence of the methods used in calculations for a real 25 kV catenary scheme. Other review papers cover some power quality or electromagnetic compatibility aspects of railway systems that can correlate with waveform distortion issues like low-frequency oscillation [10], the impact of space and weather [11], human exposure to low-frequency electromagnetic fields [3], pantograph arcs [12], radiated electromagnetic emission measurements [13], etc.

These previous works have covered important aspects and built up a robust literature for the particularities of waveform distortions in railway systems. This work aims to furthermore give additional information on waveform distortions in railway power systems, focused on harmonics, interharmonics, and supraharmonics. An integrated view for the assessment of waveform distortion interactions in railway systems is needed, together with a grid perspective of power quality incorporating all aspects, sources, propagation, requirements, and effects.

The evaluation and estimation of waveform distortion parameters is a crucial step in identifying, quantifying, and explaining problems caused by disturbances from multiple sources, with different time behaviors, which affect issues within specific electromagnetic environments. Assessment parameters should consider these features to adopt different time aggregations and suitable methods for each type of investigation related to the final problem or for standardization. Approaches that address analysis, estimation by modeling, and investigation of specific victims should include these challenges of the railway system due to its operation and arrangement characteristics. As such, in this work, the focus is on identifying and discussing the main contributions to assessing waveform distortions in ERPSs, pointing out gaps and opportunities, to provide directions for future evaluations and research development.

It is understood that researchers, industrial professionals, and general readers who are interested or involved in the subject of railway power systems would benefit from an integrated overview of the literature on the complex problem of waveform distortion. Waveform distortion studies can be divided into the following steps: identification, assessment, decision making, and mitigation. This work focuses on the two first steps, which will support studies to address the issues that are faced and to develop better methodologies in the future. An integrated view of assessment challenges will also be a point of discussion for creating a better standardization framework, which is also discussed in the paper.

The remaining work is divided as follows. Section 2 provides an overview of electrified railway systems and waveform distortion aspects, Section 3 highlights the standardization covering waveform distortion aspects inherent to railway system interactions, and Section 4 covers the literature review and discussion about contributions and gaps. Lastly, Section 5 concludes the work.

2. Overview of Electrified Railway Systems and Waveform Distortion

Electrified railway systems consist of subsystems that aim to provide a power supply to trains with efficiency, reliability, and quality and to keep railway operations safe. The power supply comprises traction supply substations (TSS), transmission power sections, transformers, and moving loads, all integrated and characterized by the widespread application of power electronics for power conversion needs. Several kinds of system solutions can be found, but most are single-phase alternating (AC) or direct (DC) systems. Below is a summary of common solutions [14,15]:

• Single-phase AC at a special frequency of 16.7 or 16 2/3 Hz at 15 kV (e.g., Sweden, Switzerland, Germany, Norway, and Austria).
• Single-phase AC at a special frequency of 25 Hz at 11–12 kV (e.g., United States).
• Single-phase AC at the main frequency of 50 or 60 Hz at 25 kV, 2 × 25 kV, 25.7 kV (e.g., France, Russia, Japan, China, Finland, Hungary, etc.).
• DC at 600/750/1500/3000 V (e.g., South Africa, Brazil, Spain, Slovakia, etc.).

Single-phase AC systems are mainly divided into two classes, industrial frequency systems and low-frequency systems. In low-frequency systems, the power supply can be from a generation at 16.7 or 16 ⅔ Hz or converted at the TSS through rotary or static converters (cycloconverters, DC link converters, and modular multilevel converters). There are two arrangements in this traction grid, called centralized and decentralized solutions [15]. For the centralized solution, a traction converter station and dedicated traction power generation are connected to a high-voltage transmission line that feeds the catenary system through the traction substation. Meanwhile, in the decentralized solution, only the traction converter station is connected directly to the catenary system, supplying it locally [15,16].

On the other hand, the traction grid in industrial frequency systems (the same as the public grid) is connected directly to the transmission grid at 50/60 Hz. The phase conductors of the traction substations are alternatingly connected to individual AC three-phase conductors [2]. Utilizing these systems, the national operator saves a lot of costs and investment in the infrastructure of generation and frequency converter stations. Still, this results in multiple power quality problems (current imbalances, flicker, and harmonics) for electrical utility, requiring system isolation or a Point of Common Coupling (PCC) at very high voltages and large substation transformers [17]. In the case of a DC railway, the TSS system is a rectifier substation that converts the three-phase public grid voltage into DC at the nominal voltage of the catenary line, using six, twelve, or twenty-four pulse rectifiers [2]. This supply can present advantages and disadvantages, mainly for urban or regional mass transportation. One positive point is the relation between voltage drop and longitudinal resistance only. Still, there are negative points related to stray currents and challenges regarding large amounts of DC voltage [1].

Figure 2 illustrates a summary of arrangements for different kinds of power supply systems for railway electrification. The choice of system is highly dependent on the historical context of the infrastructure, the type of transportation meant for that system, and technology availability. Factors regarding the power system assets that are available also play a role. The kind of transportation can be separated into heavy-traction railways, light-traction railways, metros, and low-speed transportation [1]. Each type has its own characteristics and attends to a particular societal demand, like differences in cruising speed, voltage levels, distances, stop frequency of the rolling stock, etc. Figure 3 shows examples of each kind of train in operation.

Understanding the basic structure of power supply methods and the types of railway systems makes it possible to comprehend waveform distortion issues. In addition to the infrastructure that is discussed for delivering power for the moving loads’ propulsion, there are also auxiliary supply grids for loads that help the system and workers to run the operation of the railway system (such as signals, lighting, heating, station buildings, etc.). This power supply also can support other subsystems regarding communication and signaling. Usually, these systems are along the tracks and in traction stations. These are fed with dedicated transformers, which lower the mains voltage from medium to low voltage levels without transforming the frequency from the public network. Inside rolling stocks, the auxiliary load, usually supplied by the auxiliary converter in a tertiary winding of the traction onboard transformer, also interacts with the rest of the grid. These loads are for heating, air conditioning, ventilation, lighting, passenger facilities, operational controls, train control, door systems, and air supply [18].

All these systems and non-linear loads participate in waveform distortion interactions. According to EN 50388 [4], a significant contribution of waveform distortion in railway electrified systems is the broad utilization of static converters in fixed installations and onboard rolling stocks. Identifying the source of distortion as well as interaction aspects that should be assessed are essential for managing electromagnetic compatibility in railway systems. Characteristics regarding the presence of loads with time-varying operations and locations, multiple sources of disturbances, mixed manufacturers and solutions for interoperability, and exposure to environmental conditions are issues that comprise difficulties for management. These are the reasons why railway systems have always been subject to higher tolerance limits for disturbances compared to traditional industrial systems [14]. The interaction among subsystems, the public grid, and other nearby installations are also challenges regarding waveform distortion. Several classifications of waveform distortion sources and problems in railway systems are discussed below.

• Characteristic harmonics: originate from signature harmonic emissions from the power electronics application onboard the rolling stock or in traction converter stations, around the switching frequency of PWM converters, characteristic pulses, low-order odd harmonics, etc. [1,8,19]. Non-characteristic harmonics will occur under real operating conditions [1].
• Interharmonics: caused by back-to-back conversion stages in traction converter stations and variable-speed drive inverters [1,20]. Interharmonics can also originate from the switching frequency of PWM converters.
• Supraharmonics: originate from increased switching frequency, in the range from 2 kHz to 150 kHz, of control loops of static converter applications in railway systems [21,22,23]. Additional sources include other typical loads like uninterruptible power supplies, switching mode power supplies, etc. [24].
• Background distortions: predominantly due to the penetration of waveform distortions originating from the public grid upstream, or from other sources that are at a similar level as the power supply system [8,25].
• Distortion resonances: interaction between capacitive and inductive parameters of railway system equipment and components, causing amplification of the injected distortion. This is considerably dangerous for the operation, especially for components in the supraharmonic range [7,26].

From the point of view of emissions from the onboard converters of rolling stocks and multiple units or trains in the same power supply, different emission sources are described by variations in the distortion components’ amplitude, frequency, and phase rotation in [1,27].

Table 1. Classification of emission sources onboard the rolling stock [27] ¹.

Classification	Description	Examples
Unsynchronized emission source with fixed frequency	Emissions with fixed frequency and variable or fixed amplitude. Each vehicle has it owns controller operating in the same frequency; the emissions are identical or close, but random phase shifts are expected.	-Interference pattern produced by fixed-frequency chopper vehicles on DC-supplied lines.
Synchronized emission sources with fixed frequency	Converters can be synchronized through a common controller, and phase shifts are dependent on the quality of synchronization or interlacing.	-Multiphase choppers on the same vehicle. -Multiple units with synchronized and interlaced choppers. -Synchronized and interlaced 4QC of the same traction vehicle. -4QC converters of identical vehicles operating in the same AC supply track.
Uncoupled emission sources with variable frequency	Converters operating independently produce emissions at different frequencies.	-Traction inverters of two independent vehicles. -Auxiliary converters driving induction motors at variable speeds (cooling blowers, compressors, etc.).
Coupled emission sources with variable frequency	Mechanical coupled variable-frequency inverters or non-synchronized converters driving the same variable setpoint.	-Traction inverters of two bogies on the same vehicle, or of two vehicles in multiple unit operation. -Auxiliary inverters on the same vehicle, driving different induction motors, but with the same setpoint for the motor speed.
Modulation products between fixed and variable frequency sources	Modulation product between a fixed frequency chopper or 4QC and a variable frequency load on the DC link side, resulting in modulation sidebands on both sides of the characteristic harmonic components of the fixed-frequency converter.	-Low-frequency load variation caused by bad mechanical conditions. -Motor inverter harmonics of a 4QC vehicle.

¹ The content of this table is from reference [27]. A further and complete explanation are available in the source reference.

summarizes these classifications.

The adverse effects of waveform distortion are a concern for power system agents, including operators and customers. Traditionally, harmonic distortions are associated with interference from communication circuits and other equipment such as protection devices, losses, overheating of electromagnetic devices, and aging of components [28,29]. These issues also are extended to other phenomena, but specific concerns can be associated with interharmonics and supraharmonics. Interharmonics can create problems related to sub-synchronous oscillations, transformer saturation, light flicker, interference with PLL-based control loops, etc. [30]. In [31,32], the interferences and effects associated with supraharmonics are reviewed and emphasized: acoustic noise on low-voltage applications [33], interference with power line communications [34], the impact on energy meters [35], the impact on the material of MV cable terminations [36], telephone interference [37], and several equipment malfunctions [38,39,40].

For ERPS, some of these issues are more critical and characterize the problems with waveform distortions in these systems with normal or resonance conditions. Disturbances can interfere with signaling and communication and control devices and result in instability, overvoltage, motor failure, arrester damage, transformer breakdown, audible noise from inductive train radio systems, misactivation of protection systems, etc. [7,8,26,41,42,43].

Several voltage levels and subsystems are involved in ERPS, where different interactions between sources and electrical circuits should be considered. The compatibility, emissions, and immunity of equipment and the electromagnetic environment should be evaluated according to the interaction and its issues. For instance, one can determine several interactions between railway power supply systems and public grid power supply systems, railway power supply systems and rolling stocks, rolling stocks and track circuits, or railway power supply systems and auxiliary grids. The complexity of ERPS requires different assessments and aspects for each of these relations. One aspect that can be highlighted is the aggregation time for harmonics studies adopted by traditional standards. Ten-minute aggregated values are based on the thermal effect of harmonics in power system equipment, but the effects regarding interference in railway system apparatuses and subsystems might require a more suitable aggregation time.

3. Waveform Distortion Standardization for Railway Systems

The standards are documents that clarify and define the main conditions and management procedures for power quality and electromagnetic compatibility management in power systems. On electromagnetic compatibility and waveform distortion, these reference requirements guide the assessment of grid parameters to comply with expected levels, defining conditions of analysis, procedures for measurements and tests, description and classification of the electromagnetic environment, and limits for disturbances. The leading professional organizations with published frameworks on the subject are the International Electrotechnical Commission (IEC) and the Institute of Electrical and Electronics Engineers (IEEE). Other organizations on the company side or national institutions also attend to the necessity of requirements and support documentation for establishing suitable equipment and power system performance. The focus of this section is to comment on the standardization framework related to waveform distortion specific to ERPS interactions.

The limits of waveform distortions (voltage or current) of equipment of an electrical installation are based on the effect of the emissions on the voltage quality of the connected environment [44]. The standards work under the umbrella of concepts such as emission limits, compatibility levels, planning levels, and immunity levels [45]. These concepts are explained below [44,45,46,47].

• Emission levels: This is the disturbance level emitted from a particular device, piece of equipment, system, or installation. Usually, limits are applied for these sources to reduce negative effects on the performance of the power system where it is connected.
• Compatibility levels: This defines the expected performance of the power supply system and serves as a reference for equipment emission limits and for equipment immunity. These levels aim to coordinate between the emission disturbance levels and immunity levels.
• Planning levels: These are considered as internal power quality objectives to be detailed at a local level by those responsible for planning and operating the power supply system. The exceedance of these levels indicates issues in the system.
• Immunity levels: These indicate the maximum allowed level of disturbance on a piece of equipment or a system. Such a level, even if it is not desired, allows for operating activity with high enough performance.

For ERPS, there is a lack of standardization to address the issue of waveform distortions for specific concerns in the traction power supply. ERPS has been seen as a particular case in which the performance regarding waveform distortions is limited only for signaling system interference [48,49] and induced noise on trackside circuits [50,51], allowing for a higher tolerance to disturbances compared with traditional power systems [14,52]. However, the standards applied to industrial system classes and public grid power supply systems can be used and explored to evaluate distortions in ERPS subsystems, interactions, and points of common coupling with the public power supply. Table 2 describes the key points of evaluation in ERPS regarding waveform distortion and the standards that play a role in controlling the disturbances in these environments/systems. These standards function as references and recommendations, which the organizations and national operators apply according to their necessities. National standards are also responsible for defining the disturbance controls on ERPS. The summary in Table 2 aims to clarify the different electromagnetic environments related to railway systems to which the standards can be applied, or which are suitable as reference documents. Further information on the limits or compatibility levels applied to different frequency ranges of disturbances can be found in the referred documents.

Challenges remain, even for traditional power systems, regarding the standardization of interharmonics and supraharmonics. The initial recommendation for interharmonics was that a very low limit should be established to avoid adverse effects, for example, that interharmonic voltage cannot be higher than 0.2% according to IEC standards, in order to avoid bad performance of ripple control receivers and possibly cause flicker [44]. Discussions have been conducted with different options for establishing similar individual limits as those for harmonics, or for correlations between adopted limits with short-term flicker severity, or for creating a structured framework for limits considering the effects of equipment and systems [30]. In [30], the authors present an overview of the challenges and issues in the standardization of interharmonic distortions. The same concern applies to the supraharmonics approach, especially about the lack of consensus between emission test measurements and grid measurements for the supraharmonic range. In [32,53], a general standardization for supraharmonics is discussed regarding the compatibility levels in low-voltage distribution systems and emission limits for specific equipment such as power line communication, active in-fed converters, lighting equipment, induction stoves, and industrial or scientific or medical equipment.

For the assessment of waveform distortion parameters, the standards refer to IEC 61000-4-30 and IEC 61000-4-7 [54] procedures for disturbance measurements. However, these standards are specified for 50 Hz or 60 Hz power systems, and the proposed measurements apply digital Fourier transformer (DFT) based on an interval of 10 or 12 cycles (200 ms) for voltage and current. This limits the application of these standards for ERPS, as only 50 Hz railway systems would give the recommended frequency resolution (5 Hz) for calculations and grouping. The same approach is difficult to apply in traction power supply systems that use DC electrification or low-frequency (e.g., 16 ⅔ Hz, 16.7 Hz, or 25 Hz) AC power supply systems. Indeed, these standards do not take into consideration the specific necessities of railway applications, and there are no procedures that establish coordination metrics for measurements for electrified railway networks [55,56]. The aggregation time can also create a challenge in the application of standards for traction power supply systems. Due to the time-varying behavior of the waveform distortions in these systems, aggregated values (e.g., 10 min values) can lead to the wrong results or missing information on the impact of operating conditions. In [55,57], the authors propose some alternative methods adapting the standard procedures to apply them to DC and low-frequency ERPS for waveform distortion measurements. In [58], the authors propose a different time window (300 ms) and a new calculation of subgroups for harmonics and interharmonics for low-frequency AC electrification. These contributions are discussed in the following literature review.

Table 2. Application of standards in different points of evaluation in ERPS.

Point of Evaluation	Standard	Managed Parameter
Point of Common Coupling (PCC) between public power supply and traction power supply	-IEC 61000-3-6 [44]	-Indicative planning levels for harmonic voltage in MV and HV systems.
	-IEEE 519 [29]	-Recommended limits for harmonic voltage and current at PCC of several voltage levels.
	-IEC 61000-2-12 [59]	-Compatibility levels for harmonic voltage in MV systems.
Traction power supply	-EN 50388 [4]	-Waveform distortion should not cause overvoltage.
Auxiliary grid	-IEC 61000-2-4 [60]	-Compatibility levels for harmonic voltage in industrial installations.
	-IEC 61000-2-12 [59]	-Compatibility levels for harmonic voltage in MV systems.
	-IEC 61000-2-2 [46]	-Compatibility levels for harmonic and supraharmonic voltage in LV systems.
Trackside circuits	-CENELEC-CLC/TS 50238-2 [48]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-CENELEC-CLC/TS 50238-3 [49]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-CENELEC-CLC/TR 50507 [61]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-ITU-T K.68 [51]	-Recommends a limit of 1.5 A for psophometric current.
Power supply for costumer inside the train	-EN 50121-3-2 [62]	-Limits the AC power outlet port for public use for THD < 8%.

Table 2. Application of standards in different points of evaluation in ERPS.

Point of Evaluation	Standard	Managed Parameter
Point of Common Coupling (PCC) between public power supply and traction power supply	-IEC 61000-3-6 [44]	-Indicative planning levels for harmonic voltage in MV and HV systems.
	-IEEE 519 [29]	-Recommended limits for harmonic voltage and current at PCC of several voltage levels.
	-IEC 61000-2-12 [59]	-Compatibility levels for harmonic voltage in MV systems.
Traction power supply	-EN 50388 [4]	-Waveform distortion should not cause overvoltage.
Auxiliary grid	-IEC 61000-2-4 [60]	-Compatibility levels for harmonic voltage in industrial installations.
	-IEC 61000-2-12 [59]	-Compatibility levels for harmonic voltage in MV systems.
	-IEC 61000-2-2 [46]	-Compatibility levels for harmonic and supraharmonic voltage in LV systems.
Trackside circuits	-CENELEC-CLC/TS 50238-2 [48]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-CENELEC-CLC/TS 50238-3 [49]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-CENELEC-CLC/TR 50507 [61]	-Limits the waveform distortion currents produced from the rolling stock according to the track system.
	-ITU-T K.68 [51]	-Recommends a limit of 1.5 A for psophometric current.
Power supply for costumer inside the train	-EN 50121-3-2 [62]	-Limits the AC power outlet port for public use for THD < 8%.

4. Waveform Distortion Assessment in Railway Systems: Literature Review

This section describes the literature review performed by this work, discussing the contribution of works and gaps in the literature regarding the assessment of waveform distortions in ERPS. The works are divided into four categories: characterization and measurement performance, modeling, the application of artificial intelligence, and specific issues. A description of each classification is given below.

• Characterization and measurement performance: This includes works with methodologies that aim to describe, inform, evaluate, measure, quantify, explain, screen, or analyze the parameters of current or voltage waveform distortion in railway systems. Methods include the utilization of traditional power quality assessments and other alternative applications, presentations of the behavior of emission sources, the mapping of disturbance levels for different points of evaluation in ERPS, etc.
• Modeling: This includes works aiming to model ERPS for waveform distortion studies, focusing significantly on the frequency domain approach. Modeling aspects of the system consider the challenges of ERPS, including disturbance sources, propagation, network elements and components, and interaction studies. Methods and contributions propose the estimation of waveform distortion parameters through modeling approaches. Modeling and simulation studies aim to expand the sampling space of scenarios, investigate the parametrization of components, and assess conditions for planning and decision studies.
• Application of artificial intelligence: This includes works that use specific methods that apply artificial intelligence tools to support waveform distortion assessment in power quality data for finding patterns, forecasting behavior, the classification of issues, or anomaly detection.
• Specific issues: This includes works that aim to provide an assessment of waveform distortions, including methods with characteristics of the items above, but with a specific focus on the investigation of the subsystem interactions in ERPS, signaling systems, nearby communication, or adjacent systems (e.g., pipelines), as well as onboard apparatuses.

4.1. Characterization and Measurement Performance of Waveform Distortions in Railway Systems

Good practices for measuring waveform distortion problems in ERPS are found in the literature. The characterization of disturbances from rolling stocks has been explored regarding voltage and current spectra or power terms caused by these sources. Measurement methodologies and systems have been presented, and measurements have been performed in several electrified railways to assess the pantograph voltage and current [63,64]. The results in [65,66] show analyses on harmonic spectra, harmonic distortion, and displacement factors for several load conditions of 2 × 25 kV 50 Hz in France and Italy. The behaviors of spectra are correlated to the type of locomotive under consideration. The authors of [65,66] discuss particularities of the pantograph impedance impact and present a statistical distribution of the spectra and correlation between the variation in current and voltage components. This approach is also considered in [64] for measurements from a locomotive operating in a 16.7 Hz system in Switzerland.

Several works have explored the distortion of pantograph quantities for an evaluation of the impact on energy measurement using the quantification of harmonic power [52,67,68,69] and for the characterization of spectral power time-varying behavior [70,71,72]. For instance, the literature contains an evaluation of harmonic producer indexes using pantograph voltages and currents for AC and DC systems, showing that active power terms are more consistent and better describe the characteristic components under different operating conditions of the rolling stock, as well as the spectral behavior of those power term components. The analyses are carried through the power quantities defined in IEEE 1459 [73] to estimate energy consumption measurement performance uncertainty. This is assessed to discuss EN 50463-2 [74] aspects that do not consider harmonic power terms in measurement requirements, causing erroneous energy measurements containing fundamentals and harmonics. The power terms of harmonics seem suitable for showing the characteristic variations in harmonic patterns. In [75], the paper assesses the applicability of reference power quality measurement procedures for the evaluation of harmonics in a 25 kV 50 Hz traction power supply, showing that a reduction in aggregation time is suitable for assessing time-varying frequencies. Under this improvement in the measurement methodology, active harmonic power was evaluated to estimate the impact on the energy meter system on board locomotives for several train trajectories, providing valuable results and recommendations for future standards, as illustrated in Figure 4. The analysis supports measuring only the total energy to ensure the fair trade and accurate evaluation of energy consumption. These works also show that evaluating harmonic power helps to identify network and locomotive distortions, allowing for the measurement and understanding of harmonic disturbance stresses on railway systems.

In [76], the author provides a measurement dataset and information regarding pantograph quantities for four rolling stocks, one commercial and three under test conditions. The measurements from France, Germany, Italy, and Switzerland are voltage and current waveforms of five cycles’ duration for a certain period. The authors describe each rolling stock’s characteristics and show up to 5 kHz harmonics. The operating conditions of the locomotives are available for each snapshot, making evaluations over the waveform distortion up to 25 kHz possible, and emission time-varying behavior is linked to the operation. Such measurements can also be used to detect harmonic overvoltage and resonance in AC railways [26]. The author of [26] uses harmonic and current spectra to obtain impedance and power spectra, which are used in assessing resonances, discussing the influence of location and time, and pointing out key features of the system that influence the evaluation of resonance and anti-resonance.

Exploring pantograph current emission, the paper in [58] aims to characterize the rolling stock emission behavior for different operating conditions. The time-varying nature of harmonics, interharmonics, and supraharmonics are explored employing variations in spectra and total distortion indices, as illustrated in Figure 5. The results show a dependency between the distortion and the absorbed current by the locomotive, and the operating states play a role in the rolling stock emission. In the paper, the authors discuss the variations in distortion and emission patterns for different operating conditions varying in time. The authors also propose a grouping method based on IEC61000-4-7 using a 300 ms window for the DFT calculation that should be used in 16.7 Hz or 16 ⅔ Hz fundamental frequency systems—an alternative for processing and assessment for measurements that are different from a system with 50 Hz power frequency, which is an aspect that is also explored in [55]. Lastly, the importance the limitation of the time aggregation used in traditional power quality methods on the variation behavior of rolling stock emissions is highlighted. Among the power quality issues discussed in [55], the authors propose an assessment of waveform distortion, using a window of 180 ms for the DFT computation of harmonics subgroups and 600 ms for the inclusion of interharmonics for the 16.7 Hz system. They also propose a 200 ms window for DC system measurements, considering all spectrum frequencies to calculate a total index. An experimental case provides validation for the proposed methods.

The investigation of power quality regarding waveform distortion characterization also extends to grid measurement and analysis, both the traction power supply grid and the public grid. In [77], the authors analyze measurements from a 220 kV/25.7 kV traction substation for the Wuhan-Guangzhou high-speed electrified railway. Among the power quality parameters highlighted, the harmonic content is correlated with the traffic operation. The harmonic levels still comply with the regional requirements, because the substation is connected to a strong power supply system with a large short-circuit capacity. The daily characteristic distribution of harmonics for the different operating conditions in a Chinese high-speed railway is discussed in [78], illustrating the characteristic harmonics’ spectra for voltage and current, and showing a power function relationship between THD and RMS system currents. A consideration is made regarding the traction and regenerative braking conditions and admittance coupling among harmonic orders. In [79], a practical method considering IEC 61000-3-6 for evaluating harmonic levels in the PCC of a connected AC electrified railway is investigated using the standardized three-stage approach to assess the emissions level of traction loads.

The IEEE 519 is used in the investigation of an AC ERPS in India [80], using measurements at traction substations. The effect on the public grid is taken into consideration with several load conditions based on the RMS system’s current variation. A similar assessment is performed in [81] with measurements in a 132 kV public grid power supply and at a 25 kV railway level, showing the compliance of voltage harmonics to IEEE 519 limits, but there is a lack of compliance in low-order harmonic currents up to the 27th order. This work also presents an evaluation of interharmonics showing high levels of current distortion for the phenomena, highlighting the time-varying behavior and the need for standardization. The voltage quality level of the Croatian transmission grid is evaluated to measure the impact of railway systems in the country in [82]. The authors screen the measurements of THD, and imbalance at the 110 kV levels shows compliance with the national grid code. In [83], the authors show the results of a measurement campaign in the AC railway line (28.8 kV 60 Hz) used for commuter trains out of New York, where monitoring of the current and voltage were performed at the 28.8 kV side of the traction substation and at the 115 kV PCC connection. The results showed high levels of emissions on the third harmonic from the railway line in the system, and limits were violated for that specific order and the total demand distortion regarding IEEE 519. In a comprehensive evaluation of harmonic distortion in [84], written in 1989, the authors summarize practical measurements made by the New Zealand Railway for the North Island main trunk railway, based on the 2020/55 kV substation.

Investigating waveform distortions in traction converter stations in low-frequency railway systems is also essential due to the application of static frequency converters on these systems’ power supply. Still, there is a need for more scientific papers exploring these aspects. In [22], the authors present measurements in the supraharmonic range at a 70 kV busbar supplying a frequency converter used in Swedish traction power supply systems. The paper explores arrangements of the feeding busbar, showing variations in the supraharmonic voltage levels up to 5 kHz and the impact of the number of static converters in operations on supraharmonic levels up to 150 kHz. Considering the same system as in [22], the authors in [20] extend the assessment for interharmonic spectra and the total waveform distortion indexes. The results provide a relation between the interharmonic levels, and the static frequency converter is connected to the busbar. Some interharmonic components are on the high-level side if compared with the recommended values for interharmonic distortion at the PCC. Interharmonics correlates to a random switching strategy of the power electronic control loops, common in multilevel converters.

The impact of DC traction power supply systems in the public network is also explored in the literature. The measurement of the harmonic voltage and current at the 33 kV AC side of a rectifier substation (12-pulse) from the Dubai Metro (750 V DC system) are shown in [85], and characteristic and non-characteristic harmonics are observed. The authors show compliance with the requirements of IEEE 519, but considerations are stated for the non-characteristic harmonics compared with previous measurements. In [86], the authors highlight the importance of methodologies based on measurements, field monitoring of the Taipei Mass Rapid Transit System (750 V DC system) is performed and screened, and characteristics of the harmonics on the DC side of the power supply are presented. The measurement methodology is based on magnetic field measurements, showing suitability for assessing harmonics on the DC side. The harmonics were explored for different conditions of the locomotive: standing by, at low speed, and at high speed. The paper in [87] provides a survey of measurements on the traction power supply system for the metro-transit in Rome; the system uses 1500 V DC with a traction rectifier substation taking the supply from a 20 kV public grid. The campaign made it possible to observe patterns in daily harmonic variations at the PCC and measured background distortions during the ERPS contingency, allowing for better inference of the results. The impact of ultra-fast charging for onboard energy storage in light rail transit on power quality is evaluated in [88]. Measurements were performed at the 22.8 kV AC side of a rectifier substation in Taiwan. Abnormal harmonic content is observed when the fast charging is activated. Lastly, an assessment of the effects of DC railway electrification in the public grid in Poland is performed in [89], together with other power quality problems, showing that a disturbance in the rectifier traction station distorts the voltage in the medium-voltage point of connection, and power quality issues can affect non-traction lines and auxiliary circuits of the DC railway system.

All the contributions above support the literature in different applications and regarding the level of complexity that is evaluated. Still, aspects like methods of assessing waveform distortion, the screening of measurements, and discussions of the factors influencing the impact of waveform distortions in both traction power supply systems and public grid power supply systems are missing. Considerations of these categories can be given in future evaluations on the subject:

• The majority of works focus only on harmonics or full spectra parameters. The characterization of interharmonics and supraharmonics as separate phenomena is lacking in the literature, and more investigations should be conducted in all aspects of ERPS.
• There is an imbalance in publications regarding types of electrification. The characterization of the impact of ERPS on the waveform distortion phenomenon at the public grid side is mainly for AC 50 Hz or DC ERPSs. The literature lacks an assessment of the effects of 16.7 Hz or 16 ⅔ Hz systems’ effects on the public power supply side. Publications that are not in English may be found, for instance, by German or Swedish authors, but these are not helpful for the general scientific community.
• A consensus on the waveform distortion assessment of the railway voltage and current at different points of interest in traction power supply systems should be addressed; the lack of standardization and the variety of possibilities in terms of analysis introduces difficulty in creating a framework for the assessment of these disturbances in ERPS. Frameworks are built to address specific problems (e.g., the standardization of energy meters), but there is no defined assessment for the big picture of conducted disturbances and electromagnetic compatibility in railways. Though the impact of the public grid is more straightforward due to its proximity to the traditional assessment of power systems, more considerations of operating conditions and time-varying behavior should be incorporated.
• Lastly, good research and engineering practices can be found in the literature, and the collected contributions are fair examples of how to assess waveform distortions in ERPS for characterization and measurement performance.

4.2. Modeling the Waveform Distortion Interactions in Railway Systems

Modeling and simulation are crucial in waveform distortion assessment. The literature is rich on the modeling aspects of the railway grid such as emissions, propagation, and resonance analysis. The study of ERPS should cover track section models, distortion source models, ERPS components (transformers, filters, loads, etc.), and interactions. Methods can vary among frequency-domain and time-domain models or a combination of the two.

Simplified mathematical models have been developed and explored in the literature on the assessment of the resonance and distortion propagation of track circuits in ERPS. In [90], a formulation of line voltage waves is presented, considering the variability in the line impedance due to the moving characteristics of the train load for a DC railway traction system, and a further investigation on the sensitivity of the railway track parameters is presented. The authors derive a mathematical model of the line impedance as simply as possible for supporting fast checks and probabilistic distortion analysis; based on the equivalent distributed model, line parameters are considered as the per-unit length of a two-conductor representation of the traction line. Frequency-independent models can lead to inaccurate impedance values as the frequency increases but give good enough results for the low-frequency range. Such an approach is explored in [91] to consider the effects of different locomotive filters, substation filters, and frequency-dependent traction lines, showing the positive impact of considering frequency-dependent parameters and the influence of filters in the analysis. In [92], the frequency-dependent parameters of an AC railway line are explored before using the same mathematical model, considering the interaction of more connected substations and two vehicles on the track. The authors also evaluate the electromagnetic interference with trackside communication lines, an assessment based on the psophometric current. In this sense, the authors in [93] derive a line expression for several assumptions and validate it against the reference system for a DC traction system, which can be extended for other traction systems with adequate line parameters. Frequency-dependent parameters are used in this paper. Sensitivity analysis is also conducted in the same paper to analyze the impact of different traction substation configurations based on international practices for other countries.

The modeling method explored in these works is based on transmission line theory for the estimation of rolling stock in loco or pantograph impedance Z, and the pantograph source of disturbances is supplied by two substations and between two track sections [1]. Figure 6 illustrates the concept of pantograph impedance. According to the listed works, the equivalent impedance for both sides of the locomotive loco, $Z_1$ and $Z_2$, can be estimated by Equation (1), and the equivalent $Z$ is shown in Equation (2):

$$Z_1=Z_C\frac{Z_{TPSS}cosh\left(\gamma x\right)+Z_{c}sinh\left(\gamma x\right)}{Z_{TPSS}sin\left(\gamma x\right)+Z_{c}cosh\left(\gamma x\right)}{ Z}_2=Z_C\frac{Z_{TPSS}cosh\left(\gamma (L-x)\right)+Z_{c}sinh\left(\gamma (L-x)\right)}{Z_{TPSS}sin\left(\gamma (L-x)\right)+Z_{c}cosh\left(\gamma (L-x)\right)}$$

(1)

$$Z=\frac{Z_1{Z}_2}{Z_1+Z_2}$$

(2)

where $Z_C$ is the complex characteristic impedance of the line, $Z_C=\sqrt{(r+j\omega l)/j\omega c}$, $\gamma$ is the propagation constant, $\gamma =\sqrt{(r+j\omega l)j\omega c}$, and $r$, $l$, and $c$ are the transmission line parameters per unit length, where these values should be frequency-dependent parameters. The distance between traction stations is given by $L$, and $x$ is the investigated distance from the locomotive location. In [26], the authors provide considerations on 25 kV 50 Hz systems. Due to the phase separation, the system will have a TPS at one end and a floating end to the neutral section. In this case, the authors describe the formula for ${ Z}_2$ in the case of a neutral section instead of a TPSS:

$${ Z}_2=Z_C\frac{1}{tanh\left(\gamma (L-x)\right)}$$

(3)

Such models can be used for several analyses in investigating voltage propagation, resonance, and interference caused by the rolling stock in the traction line. However, apart from its simplicity, the model cannot represent the entire arrangement of circuits and coupling effects of elements of the traction section that contain more than a pair of conductors, adjacent circuits, transformers (autotransformers or boost transformers), and complex return current paths. For a complete assessment of the interactions between emissions, background distortions, and propagation in the track section, multiconductor transmission line (MTL) modeling [95] is recommended. The development of MTL for the propagation of disturbances in transmission lines in power systems is well-established [96,97,98]. This is also true for the subject of ERPS. Several works exhaustively validate models and use them in studies for several applications in traction power supply systems.

In [99], the authors use the MTL model to estimate the reference impedance of up to 30 kHz to support the assessment of conducted emissions from rolling stocks. Sensitivity analysis incorporates varying parameters of filters from the locomotive and the substation, together with the position of the disturbance source. To investigate the distribution of the return current for both AC and DC single-track systems, the work in [100] applies the MTL model to assess the traction lines. The work shows a comprehensive analysis that includes an investigation of the influence of earth resistivity and rail-to-earth conductance parameters, computation of the results from the transfer functions between locomotive emissions and the rail parameters, and a discussion of the method utilization. Experimental data are compared with the MTL model and show good agreement in [101], highlighting the leading causes of uncertainty and covering the range up to 200 kHz. These works are followed by other analyses: a recommendation for the calculation of the total disturbing current from rolling stocks considering the superposition of conducted interference in the range up to 20 kHz [27]; MTL model simplification for large-scale studies considering a 2 × 25 kV system [102]; an investigation on the behavior of the return current for the validation of crucial electrical parameters in an autotransformer system (2 × 25 kV) [103]; etc.

Further models were developed for integrating all main elements of railway systems. The admittance matrix model is suitable and presents a wide possible range of applications in power systems. It consists of the calculation of the frequency response of the power system at different nodes, containing the information of all impedances of the system, for the assessment of node voltages based on the current injections [104]. In [105], the authors propose a modeling methodology based on a characteristic admittance matrix, providing methods for using the chain circuit model to describe the traction supply system for different feeding systems. The work details how to build up the admittance matrix considering series elements (MTL sections, boost transformers, series impedance, breakers) and shunt elements (trans-versal connection, autotransformers, shunt impedance). Also, the electric source is modeled as the Thevenin equivalent connected between the contact wire and rail. The rolling stock source impedance can be seen as a shunt element. With a focus on suppressing high-frequency resonances in high-speed railways, the work in [106] uses a similar modeling approach to identify the resonant frequencies to support filter design. Using this strategy, the work in [107] presents a comprehensive 2 × 27.5 kV AC railway system model, including a modern locomotive model for harmonic analysis. Modal sensitivity analysis and resonance mode assessment are explored to find the resonance impacted by the locomotive, and the results are validated through measurements. The authors in [108] previously investigated a complete model for the Korean high-speed train system. The model uses a similar approach as the other works in this group but proposes expanding the two-port network theory for eight-port representation, focusing on the current amplification to find characteristics of harmonic behavior.

The authors in [109] investigate the harmonic resonance characteristics of a hub traction power supply, which means that a traction substation supplies multiple railway lines. Exploring the chain matrix admittance modeling of the railway system together with the Norton model of a CRH380-type train, the authors perform a sensitivity analysis taking into consideration several parameters of all railway lines such as the number of lines, the power system capacity, centenary lengths, the length of supply lines, etc. In [110,111], the two papers address the necessity of a 24 h assessment of harmonic pollution from trains. A novel harmonic source model for locomotives based on measurements and parameters of the operating system is presented, generating an implementation of Norton-equivalent models based on the explored features. The model is incorporated into the complete model of the high-speed Chinese system to calculate the voltage using the proposed harmonic power flow calculation. The paper contributes a comprehensive perspective on a harmonics assessment for this kind of system, covering several aspects. At this point, the importance of modeling the complete design and adequate disturbance sources is clear. In [25], the authors approach the primary sources of harmonic pollution in traction power supply systems, addressing its characteristics based on measurements from a 50 Hz high-speed train system. The background distortion from the public power supply and harmonics from the locomotive are modeled with stochastic and statistical features. The interaction between the public power system and the traction power supply system is modeled as a simple Thevenin- and Norton-equivalent interaction, respectively, assuming the distortion of the trains as a source for the disturbances in the public grid. Other examples of ERPS modeling for resonance and distortion studies can be found for the analysis of the harmonic sources [112], impedance identification [113,114], harmonic penetration to the local power supply of the traction substation [115], filter design [116], improved propagation studies [114,115,116], etc.

Review papers [7,8] provide a good overview of modeling aspects for harmonics assessment in ERPS. The main elements for modeling ERPS in the frequency domain are covered in the literature, as well as the MTL model for the traction section, the chain admittance matrix for connecting all elements of ERPS, and the Norton/Thevenin equivalent for investigating the emissions from distortion sources and the background. Figure 7 illustrates the main model aspects to address in the assessment of ERPS waveform distortions. From this, investigations can be conducted considering emission behaviors, sensitivity and parametrization analysis, and the effects of different sources and interactions.

Frequency domain analysis presents several advantages such as good convergence, modeling the frequency-dependent behavior of power system elements, efficiency regarding time consumption, and good compatibility for the linear operating regions of devices [117]. Incorporating non-linearities in the frequency domain, such as a discretization of the time domain emission behavior of locomotives for several frequency domain instances, overcomes some limitations in the region of convergence for non-linear scenarios. Another advantage of frequency domain methods is the suitability to incorporate a probabilistic or stochastic approach, which is ideal for including uncertainties regarding waveform distortion emissions in ERPS. Frequency domain methods can be supported or implemented based on real measurement data. All these aspects have been included in the presented literature, and the contributions highlight the modeling aspects for waveform distortion studies in railway power systems.

The frequency domain model can be derived from analytical models, time domain simulations, or measurements to model the emissions from the static converter onboard the locomotive. In [118], the authors develop a frequency domain method to derive a model for an interlaced PWM converter drive system. They show a faster computation time than time domain models, and the results include the effects of parameter asymmetry and load imbalance. Validation is provided through measurements. A harmonic transfer function method for modeling a time-periodic system is described and used for deriving a diode converter for locomotive emissions in [119]. The model is validated in time domain simulations. In [19], the authors present a modeling approach for the harmonic current injected from PWM converters of high-speed railways in a steady operating state. The models are based on the double Fourier series theory, and the results are validated by comparing time domain representations. A similar analytical approach is explored for modeling the line current harmonics of a three-level neutral-clamped EMU in [120]. The works in [121,122] present a model based on modulation function theory and use iterative harmonic and interharmonic analysis for AC and DC locomotive converters. The method presents some advantages regarding accuracy and reductions in computational burden.

In [123], a modeling approach for an electric locomotive based on measurement data is presented, which incorporates the operating points’ relation to the harmonics of the locomotive and the probability of their distributions. It highlights the advantage of incorporating information regarding topology and control loops for the power electronics deployed in the rolling stock. A similar harmonic modeling method for high-speed trains is developed in [124] based on non-parametric estimation and prediction based on confidence intervals. EMU was used for a case study. Test data of a CRH6A EMU is used for calculating harmonic emissions considering the impact of active power and voltage on the grid side in [125]. Combining polynomial and probability models, a harmonic model is established. In [126], the authors review several electric locomotives’ modeling aspects and characterization. Some examples of time domain electromagnetic transient simulation models can be found for investigating the current distortion in 4QC converters in [127,128,129].

The works presented here provide a comprehensive review regarding waveform distortion modeling in ERPS. Some aspects can be highlighted from the discussed literature:

• The works on the subject should address how the assessment of waveform distortion using the presented models must be adapted for specific phenomena such as harmonics, interharmonics, and supraharmonics. The presented methods for modeling traction power supply systems are not limited to harmonics, and the frequency domain is suitable for incorporating interharmonics and supraharmonics. These phenomena have their own characteristics to take into consideration for modeling aspects. For instance, supraharmonics has been successfully investigated in low-voltage distribution systems, and several concerns and specific analyses are addressed for this problem [32,130].
• The theory of transmission line models is well-established and has been tested for waveform distortion analysis, covering the range up to 150 kHz. But other components and devices require better investigation. Transformers, for example, have non-linear behavior due to the stray capacitance for the supraharmonic range, which is usually neglected in models. A capacitive transfer impedance is expected for these elements and should be considered.
• Measurement-based models for sources are suitable for application in ERPS studies; these models can reproduce the non-linearity and complexity of the sources of waveform distortions, incorporating time-varying behavior into frequency-domain models.
• The works that are explored and discussed provide exhaustive references for modeling practices for the investigation of waveform distortion interactions in ERPS.

4.3. Artificial Intelligence Applied to Railway System Waveform Distoriton Data

Data analysis for the assessment of waveform distortions is vital for understanding and observing patterns in emissions, time-varying behavior of different timespans (e.g., sub-second, sub-10 min, hourly, weekly, seasonal periods, etc.), the identification of disturbance sources, anomaly detection, or physical explanations associated with the distortion. Assessing power quality measurement data for different periods can provide professionals, researchers, and ERPS stakeholders with knowledge for better management of harmonics, interharmonics, and supraharmonics. Artificial intelligence (AI) methods can support this task by providing automatic data processing and capturing the main features of the data. The contribution of strategies based on artificial intelligence such as machine learning is becoming more evident and more necessary for measurements with big data characteristics, which involve high volumes, high sampling, significant variety, and suitable accuracy, as explained in [131].

AI is defined as the attribution of machine knowledge to reproduce human mental capacities such as perception, understanding, learning, decision making, etc. [132]. Examples of methods in this category are decision-making algorithms, game theory, expert systems, and machine-learning methods [131]. Among all the possibilities, machine-learning algorithms are the most attractive techniques for power quality data analysis regarding waveform distortions. A distinguishing characteristic of machine learning is its iterative approach, enabling it to acquire knowledge from past computations and then to autonomously adjust [132]. Machine-learning algorithms learn a task based on training with a set of examples, and the training can be supervised, unsupervised, or through reinforcement. Figure 8 illustrates examples of machine-learning methods. A brief explanation of the training groups is as follows [131,133]: supervised means that the training includes pre-knowledge of the data through association with labels, allowing the algorithms to make decisions, predictions, or classifications; unsupervised means that the model does not have prior knowledge of the data, but rather deals with massive datasets to find patterns during the handling process in training; and training by reinforcement implies that the algorithm learns by itself through an empirical process in which the correct inferences are rewarded.

In [134], the authors detail a machine-learning method, an adaptative artificial neural network based on a group method of data handling (ANN-GMDH), for harmonic analysis in railway traction power supply stations. The current THD time series was explored in a prediction model for forecasting the distortion from time-delayed samples, and the results present excellent performance utilizing the indices’ regression coefficient, root mean square error, and mean absolute error. Similar methods using stacked autoencoders and backpropagation were applied to harmonic distortion time series from the public grid of ERPS in [135]. The authors applied short-term forecast methods in 3 min values of harmonic variations for several days and received satisfactory results. In [136], the authors used an artificial neural network combined with wavelet transform for monitoring waveform distortion interference in audio frequency track circuits. A new detection method is proposed, and the disturbance causing the interference, exceeding a permissible level, is assessed using a wavelet packet and Shannon entropy. Four classes of disturbances based on the current harmonics are classified using an artificial neural network, and the network’s performance is evaluated by the mean square error, showing its suitability for such an application.

An anomaly detection framework for electrical waveform quantities based on classification is explored in [137], including experimental tests to validate the method’s usability. The authors used Hilbert transform to acquire an instantaneous envelope and a convolutional neural network to learn deep features and perform pre-classification. The anomaly identification is conducted by processing the distances between features. Harmonic resonance is also identified among the power quality anomalies, and such a method can be used to identify waveform distortion phenomena. The applicability of non-intrusive load monitoring in AC railways using pantograph quantities is evaluated in [138], where both a voltage–current (VI) diagram and power harmonic spectra are explored in the extraction of features for classification and clustering. Methods such as principal component analysis (PCA) and partial least squares regression (PLSR) were used for extracting the main features, and the latter showed better performance in the classification of different locomotive emissions. Finally, the authors in [23] applied unsupervised deep learning based on a deep autoencoder (DAE) and clustering to find patterns in waveforms and harmonic and supraharmonic spectra of the pantograph current from a Swiss locomotive. The work contributes to the assessment of sub-10 min variations in waveform distortion, characterizing rolling stock emissions. The correlation between the clusters’ distributions and the dynamic operation parameter allows for better inferences about the locomotive’s patterns and operating states. Figure 9 illustrates the methodology in [23] and examples of results. The results shown in Figure 9b are the reconstructed spectral patterns of the Swiss rolling stock emissions assessed by the deep clustering technique, and the pattern distribution is linked with the operating condition of the locomotive expressed through the absorbed current. Figure 9c illustrates the waveform patterns from the time domain representation input case for an Italian locomotive, assessed by the methodology. Voltage segmentation of the current waveform during the operation was also performed based on the cluster distribution.

The number of works regarding the application of artificial intelligence for waveform distortion analysis in ERPS is still modest. Based on the described results, the potential of machine-learning methods for this purpose is promising. Some considerations and recommendations can be highlighted:

• Unsupervised deep learning has been explored in the literature for power quality analysis and for finding patterns in waveform distortion data in several applications for power systems: daily harmonic variations [139], multilocation daily harmonic variations [140], the identification of spectral patterns in photovoltaic power plant installations [141], supraharmonic measurements in low-voltage systems [142], harmonic distortion analysis in wind power plants considering active power [143], and third harmonics and their correlation with the solar elevation angle of solar tracking systems [144]. Following this trend for the analysis of disturbances in measurement data from ERPS, we can address the complexities of railway systems to cover aspects such as time-varying behavior, limitations in traditional power quality assessment methods, disaggregation of emission sources, and correlations between operation and waveform distortion.
• Deep-learning methods can also support the modeling aspects of waveform distortion in ERPS. Data-driven models are suitable for overcoming the complexity of modeling non-linear operations or systems. Waveform distortion sources are an essential aspect that would benefit from grey-box models that incorporate dependencies and actual behavior without the necessity to derive exhaustive mathematic models. Examples of such applications can be found in the literature in [145,146,147,148,149].
• More AI applications for ERPS measurements regarding power quality require more measurements and open datasets. Those involved with investigating harmonics, interharmonics, and supraharmonics in ERPS should promote more measurements to provide more validation and observe more samples/scenarios for AI models.

4.4. Specific Issues Associated with Railway Systems and Waveform Distoriton

This section addresses works regarding the specific problems in the assessment of waveform distortions for railway systems, focusing on the impact of the signaling system, nearby communication systems or trackside infrastructure, and railway system apparatuses. Such analysis opens a discussion on issues dealing with electromagnetic compatibility requirements for ERPS, taking into consideration characterization, measurements, or modeling aspects.

In [150], the authors discuss signaling system malfunctions and accidents due to the urgent braking of locomotives caused by unbalanced traction harmonic currents. A comprehensive investigation is conducted for mechanisms, modeling, and solutions. A mathematical analysis of the relationship between traction harmonic currents and the induced voltage in the signaling system is established, followed by a design of a filter based on a real case. A field test and an effectiveness analysis of the solution are presented. Based on the limits of CENELEC-CLC/TS 50238-2, the authors in [151] analyze the characteristic harmonics produced by an EMU that confirms a violation of these current emissions. A suppression method based on multiple control strategies is designed and verified by simulation and experimental operation tests, showing the suppression and compliance with the limits. In [152], the authors investigate a method based on wavelet transform to assess the interference harmonics for steady-state conditions and transient conditions of a tested EMU. Curve fitting based on the least squares fitting method is used for interpolating a harmonic frequency analysis of the measurements. A similar approach is used for an analysis using Zoom Fast Fourier transform in [153], improving the frequency resolution for harmonic signal identification. The authors consider acoustic track circuits. The authors in [154] propose a method for measuring and estimating harmonic currents on track circuits of the Rome-Naples track line for high-speed railways. Focused on audio frequency track circuits, in a range of disturbances from 2.1 kHz to 16.5 kHz, the measurement assessment consists of the injection of currents by a signal generator at different frequencies, and rail currents are also measured at the point of a short circuit. With the support of transducing rail current systems, an assessment of the current distribution is performed. The interference coupling mechanism of traction harmonics to signaling equipment is evaluated in [155], which proposes a harmonic mitigation solution based on a passive filter; four filter designs are explored and compared. The authors focus on the signal sensitivity of ZPW-2000 series equipment. And a practical approach to the measurement of current harmonics for track circuits is evaluated in [156], considering the requirements for a Korean railway system; the measurements show compliance with the investigated rolling stock. The exciting development in this work is that operating conditions and time-varying behavior are discussed, and waveform distortion is discussed in terms of limits.

Time-domain modeling of the traction power supply and its interaction with signaling systems for the evaluation of disturbances affecting track circuits is proposed in [157]. The results involve transfer functions between the pantograph current and the track-circuit-induced voltage. The assessment provides evidence about the characteristics of model parameters and the resultant interference. Considering the cab signaling problem of the ZPW-2000 track circuit, the authors in [158] calculated the volt–age–current correlation in the conductive and coupling process of disturbance sources and victim-induced voltage. For validation of the coupling relationship, the finite element method was performed. An indirect immunity test method applying the coupling relationship is proposed, and the voltage indexes for immunity limits are defined. The authors in [159] describe a complete modeling approach for track circuits with a validation of the results. A range of applications is recommended such as track circuit validation, interference estimation, and enhancement of on-site tuning. The model validation was achieved by a comparison with field measurements in an Italian railway system.

The paper in [160] evaluates the induced voltages in a 2 × 25 kV 50 Hz system using the simplified International Telegraph and Telephone Consultative Committee (CCITT) method. Using the MTL model to investigate the uncertainties of the parameters and screen factors stated by CCITT, the authors aim to consider factors such as electrification system topology, the quality of earthing, the type of victim, and the operating conditions. The authors also present a validation based on actual measurement data of the explored results. In the same vein, the work in [161] presents some real case studies to calculate the induced voltage in trackside cables. Induced voltage limits with their specific clearing time from EN 50122-1 [162] and ITU.T K.33 [163] are explored for fault conditions, and the standards aim to define parameters to guarantee good performance on electrical safety and earthing. The paper also details the different effects between phase-to-phase and phase-to-ground faults. The authors also identify vital aspects that influence the analysis. An overview of these aspects for coupling interference phenomena in electric transportation systems is presented in the magazine paper in [164]. The work in [165] investigates the effect of harmonic distortions on electromagnetic interference. Since the standardization disregards harmonic distortion management for the separation of the pipeline-railway system, even the induced voltage can cause adverse effects on buried pipelines. Using complete models based on the frequency domain characteristic of these systems and different total harmonic distortion conditions, the authors highlight the necessity of considering harmonics as the solution to the problem.

In [166], the authors analyze the harmonic pollution of railway locomotives on the train sound system. Measurement and simulation based on a time-domain model explore the interaction between propulsion power electronic emission and sound design. The paper indicates waveform distortion interactions between the rolling stock auxiliary converter power supply and the front-end converters, which can cause equipment and devices to malfunction, as well as common mode distortion circulating in the train or leaking disturbances. Such concerns are pointed out in [1,18,167].

The papers above provide a good visualization of the impact of waveform distortions in signaling systems, communication systems, and rolling stock apparatuses. More analysis should be taken in consideration:

• The impact of interharmonics should be explored more and should be well-defined for signaling and communication. Also, the supraharmonic range is a frequency region of interest for this evaluation and even has standardizations limiting the emissions from traction systems. As stated above, different frequency ranges have their own characteristics in power system interactions, and one should address these reflections on the assessment methods presented above. The limits that are cited and discussed can also be a reference for a more robust standardization for waveform distortion in ERPS.
• More measurements should be performed for waveform distortion in onboard auxiliary power systems. The characterization and evaluation of harmonics, interharmonics, and supraharmonics should be addressed due to the irregular earthing from these systems and the possible circulation of common mode disturbances. The customer power supply, for instance, is responsible for comfort appliances and power delivery for train passengers. Nowadays, such appliances are more common and are required. Still, the connection between non-linear devices such as switching mode power supply systems and other efficient-based power electronics can lead to intricate interactions and unknown problems.
• Also, further investigation and studies exploring signaling systems, communications, and other subsystems on the track side or special loads in ERPS will support the future management of waveform distortion regarding the aggregation time of the investigated current and voltage parameters. The traditional 10 min values can be limited to address several types of interferences, since the thermal effects of harmonics should be considered.

5. Conclusions

This paper has covered the state of art of waveform distortion assessment in ERPS. A comprehensive review on the topic is conducted, detailing the main concepts of railway electrification, aspects of harmonics, interharmonics, and supraharmonics distortions in these systems, waveform distortion standardization, and contributions to waveform distortion assessment. The literature review is divided into four categories: characterization and measurements, modeling, artificial intelligence applications, and specific issues. For each category of work, the contributions highlight a discussion on opportunities, gaps, and important observations. The work successfully builds a framework for the subject, which has two main characteristics. The review is informative and propositional, providing a road map of opportunities for future works. Some aspects and recommendation can be highlighted:

• Waveform distortion assessment in ERPS has particularities and challenges that differ from traditional power systems in some ways. Also, the frequency range differentiation up to 150 kHz and the associated phenomena should be better addressed as in other power systems. This will be beneficial from the perspective of future standardization and methods to assess the necessary inferences about disturbances.
• There is a clear imbalance among the investigations into different types of railway electrification systems. Aspects regarding assessment and research tendencies have been discussed, as these can explain and help with directions for future works. More comprehensive works should be conducted within the research community for ERPS with special power frequencies that are different from 50/60 Hz.
• Measurement-based methodologies for the modeling and assessment of waveform distortion using machine-learning techniques are promising due to the strong ability to reproduce or assess the complexities and non-linearities of ERPS. Their simplicity as a final solution is beneficial for understanding and the support of other investigations.
• Future research should cover aspects regarding the abovementioned categories of work to support ERPS stakeholders with better tools and assessment methods, as well as to integrate more frameworks for future standardization related to traction power supply systems and ERPS equipment.
• There are aspects that are not discussed in this literature review that might be of interest for future reviews or works in general: the link between electromagnetic interference risks and waveform distortion variations; the impact of power electronics control loops and topologies in waveform distortion emissions and propagation between systems; the impact of renewable integration into ERPS from the waveform distortion perspective; and multidisciplinary investigations for the assessment of the impact of waveform distortions (e.g., the relationship between waveform distortion variations and traffic planning, the shelf life of equipment, space and weather disturbances in power systems, transportation delays/accidents, user-related equipment malfunctions, and economic impacts).