Key Takeaways & Executive Findings
- •• • Filters installed at TCS nodes introduce resonances between the 10th and 25th harmonics, with amplification factors exceeding five times at specific locations, necessitating precise filter placement to avoid harmonic amplification and equipment damage. • • Monte Carlo simulations reveal that uncertainties in moving loads and rolling stock units cause variations in resonance frequency and magnitude, requiring probabilistic assessment for robust system planning. • • Wide-area modeling is essential as distant network sections influence harmonic impedance, with continuous power supply causing interactions beyond local TPSS, impacting overall system stability. • • Resonance amplification varies by location along the track, with some harmonic components showing amplification factors above five times, highlighting the need for location-specific mitigation strategies to prevent protection failures and thermal stress.
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Abstract
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. Results indicate that filters installed at traction converter stations (TCS) introduce resonances typically between the 10th and 25th harmonics, with amplification factors exceeding five times at certain locations. The wide-area modeling approach is essential due to continuous power supply and influence of distant network sections. Uncertainties related to moving loads, number of rolling stock units, and remote system areas cause variations in both frequency and magnitude of series and parallel resonances. Monte Carlo simulations effectively capture these variations, providing probabilistic information for resonance frequency location and impedance variation. The findings offer critical insights for system planning and mitigation actions in ERPS.
1. Introduction
Electric railway power systems (ERPS) are large infrastructures with particular power supply arrangement, usually single-phase systems that cope with high and variable demand, moving loads, irregular return current circuit, multiple harmonic sources, and overhead lines connecting traction power supply stations (TPSS). For AC single-phase systems, the most common configurations are railway low frequency or main grid frequency power supplies. Each kind of electrification solution will have inherent challenges, points of connection between multiple electromagnetic environments, and technologies deployed. Those aspects and complexities impact power quality and harmonic distortion performance on those systems. According to EN 50388, the primary source of harmonic distortion are static converters onboard rolling stocks and fixed installations. Those harmonic current components injected (e.g., around switching frequency, pulse components, or low-order harmonics) interact with the series and parallel resonances of the ERPS catenary grid, causing amplification also reflected on the voltage distortion. Harmonics components, with the contribution of resonances, can cause several problems in ERPS and adjacent circuits, like interference in signaling and communication, protection failure, thermal stress, damaging equipment, overvoltage, etc. The assessment and identification of harmonic resonances are critical for disturbance management within ERPS, not only for operational conditions but also for mitigation strategies and planning. The modeling investigation should include aspects like moving load, various scenarios, uncertainty, and multiple impedance interactions.
Comprehensive studies have been performed considering sections of the railway system for accessing harmonic propagation and resonance between trains and local connections within power supply networks. Simplified mathematical models exploring the wave propagation theory were used to identify resonances and assess distortion propagation, exploiting the frequency-dependent models of interaction between locomotives and one or more TPSS and its impact on trackside circuits, including influence of filters, defining and evaluating key parameters of line impedance expression, and suppression of harmonic resonances. More complete models for the catenary system were developed, but they often neglect the wide-area effects and uncertainties inherent in moving loads and multiple rolling stocks. This paper addresses these gaps by proposing a wide-area modeling approach that integrates detailed component models, moving load dynamics, and Monte Carlo simulations to assess harmonic resonance probabilistically. The methodology is applied to the Swedish ERPS, providing insights into resonance locations, amplification factors, and the impact of filters, thereby offering a robust framework for system planning and mitigation.
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Rafael S. Salles, Sarah K. Rönnberg (2026). Harmonic Impedance Studies of Swedish Railway Power System Using Wide-Area Modeling Approach. Railway Engineering Science (铁道工程科学). https://doi.org/10.1007/s40534-025-00408-1
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Frequently Asked Questions
What are the primary failure mechanisms induced by harmonic resonances in ERPS, and how does the proposed wide-area modeling approach mitigate them?
Harmonic resonances cause amplification of harmonic currents and voltages, leading to thermal stress, insulation degradation, protection maloperation, and interference with signaling. The wide-area modeling approach identifies resonance frequencies and amplification factors across the network, enabling targeted mitigation such as filter placement and operational adjustments. Results show amplification factors exceeding five times at certain locations, which without mitigation could cause equipment failure.
How does the cost of implementing wide-area harmonic impedance studies compare with the potential savings from avoiding equipment damage and downtime?
While specific cost figures are not provided, the paper implies that the wide-area modeling approach, though computationally intensive, can prevent costly failures. The Swedish Transport Administration's financial support suggests recognition of the economic benefits. Mitigation actions informed by such studies can avoid unplanned outages and extend equipment lifespan, yielding significant savings.
What are the scalability bottlenecks when applying this wide-area modeling approach to larger or more complex railway networks?
Scalability challenges include the need for detailed network data, computational resources for Monte Carlo simulations, and accurate modeling of moving loads and uncertainties. The meshed grid characteristics and continuous power supply require modeling of many nodes, which can increase simulation time. However, the modular nature of nodal admittance modeling allows for extension to larger networks with appropriate computational infrastructure.
How do the resonances introduced by filters at TCS nodes interact with the dynamic behavior of rolling stocks, and what are the implications for filter design?
Filters at TCS nodes introduce resonances between the 10th and 25th harmonics, which can interact with rolling stock harmonics, potentially exacerbating amplification. The dynamic behavior of rolling stocks, including moving loads and varying number of units, causes shifts in resonance frequencies. Filter design must account for these interactions, possibly using adaptive or wideband filters, to avoid adverse effects.
What are the key uncertainties in the model, and how sensitive are the resonance predictions to variations in parameters such as line impedance and train positions?
Key uncertainties include moving load positions, number of rolling stock units, and remote system area parameters. Monte Carlo simulations show that these cause variations in both frequency and magnitude of resonances. Sensitivity analysis indicates that line impedance variations can shift resonance frequencies by several harmonics, highlighting the need for probabilistic assessment rather than deterministic worst-case scenarios.
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