[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82285-en":3,"doc-seo-82285-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82285,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","A Multi-Frequency Input-Admittance Model of Locomotive Rectifier Considering PWM Sideband Harmonic Coupling in Electrical Railways","Electrical railway harmonic instability commonly emerges in the high-frequency range. Traditional converter small-signal averaging models neglect PWM sideband harmonic components, causing an effective frequency that falls below half the switching frequency. This work constructs perturbation-frequency propagation and PWM sideband generation, then derives a locomotive rectifier multi-frequency input-admittance model. A multi-frequency-to-SISO conversion retains sideband couplings while improving accuracy beyond half the switching frequency. Hardware-in-the-loop results further clarify the effects of switching frequency, control bandwidth, and traction network impedance on harmonic stability.","A Multi-Frequency Input-Admittance Model of Locomotive Rectifier Considering PWM Sideband Harmonic Coupling in Electrical Railways  \nXiangyu Meng, Zhigang Liu, Guorong Li, Xunjun Chen, Siqi Wu, Keting Hu  \narXiv :2607 .09275v1 [ ee ss . SY] 10 Jul 2026  \nAbstract—Electrical railway harmonic instability issues are common in the high-frequency range. The effective frequency of the traditional converter’s small-signal averaging model is below 1/2 switching frequency since the pulse width modulation (PWM) sideband harmonic components are ignored. In this article, the dynamic propagations of perturbation frequency and the generated PWM sideband components are constructed first. Then the locomotive rectifier’s multi-frequency input-admittance model is derived appropriately. Afterward, an admittance conversion approach is used to convert the multi-frequency model into the single-input-single-output (SISO) model whereas retaining the sideband frequency couplings. The proposed SISO model is more accurate than the traditional small-signal averaging model in the frequency range higher than 1/2 switching frequency. It is found that PWM sideband harmonics dominate the locomotive rectifier’s input-admittance characteristic higher than 1/2 switching frequency. Finally, based on the proposed model, the influence of different switching frequencies, control bandwidths, and traction network impedance on system harmonic stability is revealed by the hardware-in-the-loop (HIL) results.  \nIndex Terms-Electrical railway, harmonic instability, inputadmittance model, locomotive rectifier, StarSim.  \nI. INTRODUCTION WITH the rapid expansion of electrical railways in China, many new types of trains with ac-dc-ac traction drive systems, such as electric multiple units and high-power locomotives (collectively referred to as locomotives), have been put into service. Onboard converters, particularly rectifiers, are typical  \nnonlinear equipment, resulting in com  \nplicated interactions between the locomotives and traction network (L-N) system. As a result, interactions within the L-N system can lead to instability issues such as highorder harmonic resonance (HHR) [1] and harmonic instability phenomenon (HIS) [2] . These events will amplify the traction network voltage and current, endangering the safety and reliability of the L-N system. The HHR is mainly caused by the interaction between the intrinsic resonance sites of the traction network and the distinctive harmonics created by the locomotive rectifier switching process, which has been intensively investigated [2] . The magnitude of voltage and current in resonance frequency is constant when HHR occurs, indicating that the L-N system is critically stable. However, in comparison to HHR, the HIS is unstable, characterized by continuously oscillating on one or several frequencies [3] . The article examines the L-N system’s instability as a result of HIS. The impedance-based small-signal averaging approach is currently an effective tool for analyzing system stability issues [4] . The small-signal averaging model assumed that the  \npulse width modulation (PWM) process only contained a perturbation frequency because the averaging process in the low-frequency region allows the generated sideband harmonic components in the sampling and PWM processes to be ignored. As a result, the effective frequency range of the model is smaller than the 1/2 switching frequency. However, the model is no longer valid when the perturbation frequency exceeds 1/2 switching frequency [5] . Sampling and PWM processes will influence the impedance characteristics of the converter in the highfrequency range. Related studies that described the nonlinearity of these processes were mainly developed in the dc-dc system. In [6] and [7], the generated multi-frequency model that considered the PWM sideband harmonic components was used to analyze and construct the high-bandwidth dc − dc converters. However, unlike dc − dc converters, the ac-dc ","cbCaiiytygaikfE2","https://ap.wps.com/l/cbCaiiytygaikfE2","pdf",1941311,1,11,"English","en",105,"# Introduction\n## Harmonic resonance and instability in traction networks\n## Limits of small-signal averaging models\n## PWM and sampling sideband harmonic modeling\n## Motivation for switching-frequency impact","[{\"question\":\"Why do traditional small-signal averaging models fail above half the switching frequency?\",\"answer\":\"They ignore PWM sideband harmonic components, so the perturbation-frequency assumption no longer matches converter impedance behavior once the perturbation exceeds 1/2 of the switching frequency.\"},{\"question\":\"What is the key contribution of the proposed multi-frequency input-admittance model?\",\"answer\":\"It explicitly constructs perturbation-frequency propagation and PWM sideband components, derives a multi-frequency admittance model, and converts it to a SISO form while preserving sideband frequency couplings.\"},{\"question\":\"Which system factors are evaluated for their influence on harmonic stability?\",\"answer\":\"Switching frequencies, control bandwidths, and traction network impedance are studied using hardware-in-the-loop (HIL) results to reveal their effects on system harmonic stability.\"}]",1784179391,28,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"a-multi-frequency-input-admittance-model-of-locomotive-rectifier-considering-pwm-sideband-harmonic-coupling-in-electrical-railways","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/a-multi-frequency-input-admittance-model-of-locomotive-rectifier-considering-pwm-sideband-harmonic-coupling-in-electrical-railways/82285/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do traditional small-signal averaging models fail above half the switching frequency?","Question",{"text":75,"@type":76},"They ignore PWM sideband harmonic components, so the perturbation-frequency assumption no longer matches converter impedance behavior once the perturbation exceeds 1/2 of the switching frequency.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key contribution of the proposed multi-frequency input-admittance model?",{"text":80,"@type":76},"It explicitly constructs perturbation-frequency propagation and PWM sideband components, derives a multi-frequency admittance model, and converts it to a SISO form while preserving sideband frequency couplings.",{"name":82,"@type":73,"acceptedAnswer":83},"Which system factors are evaluated for their influence on harmonic stability?",{"text":84,"@type":76},"Switching frequencies, control bandwidths, and traction network impedance are studied using hardware-in-the-loop (HIL) results to reveal their effects on 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