[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83886-en":3,"doc-seo-83886-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83886,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Double Interior-Point Regularization for Large-Scale Capacity Expansion","Capacity expansion is central to planning future energy systems, but weather-dependent generation and long-duration storage create optimization problems far beyond the computational capability of conventional interior-point solvers, limiting cost-efficient and reliable renewable planning. The paper proposes double interior-point regularization (DIP-set) for Benders Decomposition, merging interior traversal benefits with proximity to a reference solution. Benchmarks on power-sector and energy-system cases show DIP-set outperforms competing regularizations across sizes and forecast levels, with 30–50% speed-ups on the largest, most critical instances, and improved convergence near the optimum.","Double interior-point regularization for large-scale capacity expansion  \nLeonard Gke, Giovanni Sansavini  \narXiv :2607 .05047v1 [ ee ss . SY] 6 Jul 2026  \nAbstract—Capacity expansion is a key tool for planning future energy systems. However, weather-dependent generation and long-duration storage result in problem sizes that exceed the computational limits of conventional interior-point solvers, making it impossible to plan renewable systems that are costefficient and reliable across a wide range of weather conditions. To tackle such large problems, this paper introduces the double interior-point regularization (DIP-set) for Benders Decomposition (BD), combining the advantages of traversing the interior of the solution space while remaining close to a reference solution. We benchmark the method on a power-sector problem and an energy-system problem, varying problem size and the level of foresight during operations. Results demonstrate that DIPset outperforms competing regularizations in all test cases. The speed-up increases with size, reaching 30-50% for the largest problems, which are the most critical for planning renewable systems and are too large for state-of-the-art methods. The key benefit of DIP-set is its ability to mitigate the sharp decrease in convergence as BD approaches the optimal solution.  \nIndex Terms—Power systems planning, capacity expansion models, decomposition methods, regularization  \nI. INTRODUCTION  \nMitigating climate change requires a fundamental transformation of power generation and consumption. Weatherdependent, and therefore variable and uncertain, generation from wind and solar energy replaces dispatchable thermal power plants. Consequently, the security of supply increasingly relies on both short-and long-duration energy storage [1] . Atthe same time, power consumption is shifting and rising, as direct or indirect electrification via e-fuels replaces fossil fuels in heating, transportation, and industry.  \nCapacity expansion models are essential tools for planning and guiding this transformation [2]; yet, modeling renewable and electrified systems is challenging. Capturing the weatherdependent variability of wind and solar generation requires high temporal and spatial resolution [3] . In addition, shortand long-duration storage introduce complex interdependencies over extended time frames. Moreover, integrating large shares of renewables depends on transnational power grids, which expands the spatial scope of the models [4] . Finally, the need for electrification closely couples the power sector with heating, transport, and industry, necessitating an extended sectoral scope [5] .  \nAdvancing capacity expansion models to address these challenges is difficult. State-of-the-art multi-sector models with a continental scope and hourly resolution yield large linear optimization problems that approach the practical limits of established interior-point solvers, as memory requirements and computation time scale polynomial to exponential with model  \nLeonard Gke and Giovanni Sansavini are with the Reliability and Risk Engineering Laboratory, Institute of Energy and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland.  \nsize. Increasing spatio-temporal detail, as suggested in the scientific literature, is not achievable with existing solution methods [6] . Moreover, current approaches hinder further methodological refinement, increasing the problem size; for instance, stochastic optimization to account for renewable uncertainty or robust optimization for planning a resilient transformation [7] .  \nTo tackle these limitations, an emerging research stream applies Benders Decomposition (BD) for large-scale power and energy planning. BD is a solution algorithm that decomposes the original problem into a top-problem (TP) and one or more mutually independent sub-problems (SP) connected to the TP via so-called complicating variables [8] . BD is particularly suited to two-stage stochastic problems, since ","cbCaikG7wcIRzglB","https://ap.wps.com/l/cbCaikG7wcIRzglB","pdf",1309772,4,1,10,"English","en",105,"# Introduction\n## Background and motivation\n## Limits of standard capacity expansion models\n## Benders Decomposition for large-scale planning\n## Prior regularization approaches\n## Interior-point methods and related work","[{\"question\":\"Why do conventional interior-point solvers struggle with large-scale renewable capacity expansion planning?\",\"answer\":\"Because weather-dependent generation and long-duration storage produce optimization problems whose size exceeds the computational limits of established interior-point methods, making reliable and cost-efficient planning across diverse weather conditions infeasible.\"},{\"question\":\"What is the main idea of DIP-set for Benders Decomposition?\",\"answer\":\"DIP-set introduces a double interior-point regularization mechanism for BD, combining the advantage of moving through the interior of the solution space with staying close to a reference solution.\"},{\"question\":\"What performance improvements does DIP-set achieve, especially near optimal solutions?\",\"answer\":\"Experiments show DIP-set outperforms competing regularizations in all tested cases, with speed-ups that grow with problem size (30–50% for the largest instances) and a key benefit of mitigating the sharp convergence decrease as BD approaches the optimum.\"}]",1784191232,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"double-interior-point-regularization-for-large-scale-capacity-expansion","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/double-interior-point-regularization-for-large-scale-capacity-expansion/83886/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","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 conventional interior-point solvers struggle with large-scale renewable capacity expansion planning?","Question",{"text":75,"@type":76},"Because weather-dependent generation and long-duration storage produce optimization problems whose size exceeds the computational limits of established interior-point methods, making reliable and cost-efficient planning across diverse weather conditions infeasible.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main idea of DIP-set for Benders Decomposition?",{"text":80,"@type":76},"DIP-set introduces a double interior-point regularization mechanism for BD, combining the advantage of moving through the interior of the solution space with staying close to a reference solution.",{"name":82,"@type":73,"acceptedAnswer":83},"What performance improvements does DIP-set achieve, especially near optimal solutions?",{"text":84,"@type":76},"Experiments show DIP-set outperforms competing regularizations in all tested cases, with speed-ups that grow with problem size (30–50% for the largest instances) and a key benefit of mitigating the sharp convergence decrease as BD approaches the optimum.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":22,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]