{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T20:42:03Z","timestamp":1777149723574,"version":"3.51.4"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,13]],"date-time":"2024-01-13T00:00:00Z","timestamp":1705104000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,13]],"date-time":"2024-01-13T00:00:00Z","timestamp":1705104000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1808169"],"award-info":[{"award-number":["1808169"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008047","name":"Carnegie Mellon University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008047","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Nested Benders\u2019s decomposition is an efficient means to solve large-scale optimization problems with a natural time sequence of decisions. This paper examines the use of the technique to decompose and solve efficiently capacity-expansion problems for electricity systems with hydroelectric and renewable generators. To this end we develop an archetypal planning model that captures key features of hydroelectric and renewable generators and apply it to a case study that is based on the Columbia River system in the northwestern United States of America. We apply standard network and within-year temporal simplifications to reduce the problem\u2019s size. Nevertheless, the remaining problem is large-scale and we demonstrate the use of nested Benders\u2019s decomposition to solve it. We explore refinements of the decomposition method which yield further performance improvements. Overall, we show that nested Benders\u2019s decomposition yields good computational performance with minimal loss of model fidelity.<\/jats:p>","DOI":"10.1007\/s10287-023-00469-9","type":"journal-article","created":{"date-parts":[[2024,1,13]],"date-time":"2024-01-13T14:01:43Z","timestamp":1705154503000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Nested Benders\u2019s decomposition of capacity-planning problems for electricity systems with hydroelectric and renewable generation"],"prefix":"10.1007","volume":"21","author":[{"given":"Kenjiro","family":"Yagi","sequence":"first","affiliation":[]},{"given":"Ramteen","family":"Sioshansi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,13]]},"reference":[{"key":"469_CR3","volume-title":"2013 4th IEEE\/PES innovative smart grid technologies Europe (ISGT EUROPE)","author":"P Ahlhaus","year":"2013","unstructured":"Ahlhaus P, Stursberg P (2013) Transmission capacity expansion: an improved transport model. In: Stursberg P (ed) 2013 4th IEEE\/PES innovative smart grid technologies Europe (ISGT EUROPE). Institute of Electrical and Electronics Engineers, Lyngby, Denmark"},{"key":"469_CR4","doi-asserted-by":"publisher","first-page":"112955","DOI":"10.1016\/j.rser.2022.112955","volume":"171","author":"J Barrera-Santana","year":"2023","unstructured":"Barrera-Santana J, Sioshansi R (2023) An optimization framework for capacity planning of Island electricity systems. Renew Sustain Energy Rev 171:112955","journal-title":"Renew Sustain Energy Rev"},{"key":"469_CR1","unstructured":"Black & Veatch (2012) Cost and performance data for power generation technologies. Technical report prepared for National Renewable Energy Laboratory"},{"key":"469_CR5","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"JF Benders","year":"1962","unstructured":"Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238\u2013252","journal-title":"Numer Math"},{"key":"469_CR6","first-page":"4561","volume-title":"Nonlinear programming","author":"DP Bertsekas","year":"1995","unstructured":"Bertsekas DP (1995) Nonlinear programming, 2nd edn. Optimization and Computation, Athena Scientific, Belmont, MA","edition":"2"},{"key":"469_CR7","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1198\/jasa.2011.tm10183","volume":"106","author":"J Bien","year":"2011","unstructured":"Bien J, Tibshirani R (2011) Hierarchical clustering with prototypes via minimax linkage. J Am Stat Assoc 106:1075\u20131084","journal-title":"J Am Stat Assoc"},{"key":"469_CR8","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1287\/opre.33.5.989","volume":"33","author":"JR Birge","year":"1985","unstructured":"Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33:989\u20131007","journal-title":"Oper Res"},{"key":"469_CR9","doi-asserted-by":"publisher","first-page":"104457","DOI":"10.1016\/j.eneco.2019.07.017","volume":"84","author":"L Boffino","year":"2019","unstructured":"Boffino L, Conejo AJ, Sioshansi R et al (2019) A two-stage stochastic optimization planning framework to deeply decarbonize electric power systems. Energy Econ 84:104457","journal-title":"Energy Econ"},{"key":"469_CR10","doi-asserted-by":"publisher","DOI":"10.2172\/1505935","volume-title":"Regional energy deployment system (ReEDS) model documentation: version 2018","author":"S Cohen","year":"2019","unstructured":"Cohen S, Becker J, Bielen D et al (2019) Regional energy deployment system (ReEDS) model documentation: version 2018. Tech. Rep. NREL\/TP-6A20-72023 National Renewable Energy Laboratory, Golden, CO"},{"key":"469_CR11","volume-title":"Decomposition techniques in mathematical programming","author":"AJ Conejo","year":"2006","unstructured":"Conejo AJ, Castillo E, M\u00ednguez R et al (2006) Decomposition techniques in mathematical programming, 1st edn. Springer, Berlin, Heidelberg","edition":"1"},{"key":"469_CR2","unstructured":"Energy and Environmental Economics, Inc. (2012) Cost and performance review of generation technologies: recommendations for WECC 10-and 20-year study process. Technical report prepared for Western Electric Coordinating Council"},{"key":"469_CR12","doi-asserted-by":"crossref","unstructured":"Falugi P, Konstantelos I, Strbac G (2016) Application of novel nested decomposition techniques to long-term planning problems. In: 2016 Power systems computation conference, Institute of Electrical and Electronics Engineers, Genoa, Italy","DOI":"10.1109\/PSCC.2016.7540872"},{"key":"469_CR13","doi-asserted-by":"publisher","DOI":"10.2172\/981991","volume-title":"Western wind and solar integration study","author":"GE Energy","year":"2010","unstructured":"GE Energy (2010) Western wind and solar integration study. Tech. Rep. NREL\/SR-550-47434 National Renewable Energy Laboratory, Golden, CO"},{"key":"469_CR14","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1061\/(ASCE)WR.1943-5452.0000258","volume":"140","author":"IG Hidalgo","year":"2014","unstructured":"Hidalgo IG, Fontane DG, Lopes JEG et al (2014) Efficiency curves for hydroelectric generating units. J Water Resour Plan Manag 140:86\u201391","journal-title":"J Water Resour Plan Manag"},{"key":"469_CR15","doi-asserted-by":"publisher","first-page":"189","DOI":"10.3390\/en12010189","volume":"12","author":"MN Hjelmeland","year":"2019","unstructured":"Hjelmeland MN, Helseth A, Korp\u00e5s M (2019) Medium-term hydropower scheduling with variable head under inflow, energy and reserve capacity price uncertainty. Energies 12:189","journal-title":"Energies"},{"key":"469_CR16","doi-asserted-by":"publisher","first-page":"e220","DOI":"10.1002\/wene.220","volume":"6","author":"D Huertas-Hernando","year":"2017","unstructured":"Huertas-Hernando D, Farahmand H, Holttinen H et al (2017) Hydro power flexibility for power systems with variable renewable energy sources: an IEA task 25 collaboration. WIREs Energy Environ 6:e220","journal-title":"WIREs Energy Environ"},{"key":"469_CR17","first-page":"199","volume":"8","author":"RG Hunter-Rinderle","year":"2021","unstructured":"Hunter-Rinderle RG, Sioshansi R (2021) Data-driven modeling of operating characteristics of hydroelectric generating units. Current Sustain Renew Energy Rep 8:199\u2013206","journal-title":"Current Sustain Renew Energy Rep"},{"key":"469_CR18","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1016\/j.energy.2014.07.017","volume":"74","author":"E Ibanez","year":"2014","unstructured":"Ibanez E, Magee T, Clement M et al (2014) Enhancing hydropower modeling in variable generation integration studies. Energy 74:518\u2013528","journal-title":"Energy"},{"key":"469_CR19","volume-title":"Decomposition algorithms for optimal manufacturing and power systems infrastructure planning","author":"CL Lara","year":"2019","unstructured":"Lara CL (2019) Decomposition algorithms for optimal manufacturing and power systems infrastructure planning. Carnegie Mellon University, Pittsburgh, PA"},{"key":"469_CR20","doi-asserted-by":"publisher","first-page":"3029","DOI":"10.1109\/TPWRS.2017.2746379","volume":"33","author":"Y Liu","year":"2018","unstructured":"Liu Y, Sioshansi R, Conejo AJ (2018a) Hierarchical clustering to find representative operating periods for capacity-expansion modeling. IEEE Trans Power Syst 33:3029\u20133039","journal-title":"IEEE Trans Power Syst"},{"key":"469_CR21","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1109\/TPWRS.2017.2694612","volume":"33","author":"Y Liu","year":"2018","unstructured":"Liu Y, Sioshansi R, Conejo AJ (2018b) Multistage stochastic investment planning with multiscale representation of uncertainties and decisions. IEEE Trans Power Syst 33:781\u2013791","journal-title":"IEEE Trans Power Syst"},{"key":"469_CR22","first-page":"17","volume":"8","author":"Y Liu","year":"2021","unstructured":"Liu Y, Hunter-Rinderle RG, Luo C et al (2021) How climate-related policy affects the economics of electricity generation. Current Sustain Renew Energy Rep 8:17\u201330","journal-title":"Current Sustain Renew Energy Rep"},{"key":"469_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-74503-9","volume-title":"Linear and nonlinear programming, international series in operations research & management science","author":"DG Luenberger","year":"2008","unstructured":"Luenberger DG, Ye Y (2008) Linear and nonlinear programming, international series in operations research & management science, vol 116, 3rd edn. Springer, New York","edition":"3"},{"key":"469_CR24","doi-asserted-by":"crossref","unstructured":"Maceiral MEP, Penna DDJ, Diniz AL, et\u00a0al (2018) Twenty years of application of stochastic dual dynamic programming in official and agent studies in Brazil-Main features and improvements on the NEWAVE model. In: 2018 Power systems computation conference, Institute of Electrical and Electronics Engineers, Dublin, Ireland","DOI":"10.23919\/PSCC.2018.8442754"},{"key":"469_CR25","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/j.ijepes.2018.06.008","volume":"103","author":"B Maluenda","year":"2018","unstructured":"Maluenda B, Negrete-Pincetic M, Olivares DE et al (2018) Expansion planning under uncertainty for hydrothermal systems with variable resources. Int J Electr Power Energy Syst 103:644\u2013651","journal-title":"Int J Electr Power Energy Syst"},{"key":"469_CR26","unstructured":"Mason T, Curry T (2012) Capital costs for transmission and substations: recommendations for WECC transmission expansion planning. B &V Project Number 176322, prepared for Western Electricity Coordination Council"},{"key":"469_CR27","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.eneco.2016.08.001","volume":"59","author":"JH Merrick","year":"2016","unstructured":"Merrick JH (2016) On representation of temporal variability in electricity capacity planning models. Energy Econ 59:261\u2013274","journal-title":"Energy Econ"},{"key":"469_CR28","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.energy.2016.06.081","volume":"112","author":"P Nahmmacher","year":"2016","unstructured":"Nahmmacher P, Schmid E, Hirth L et al (2016) Carpe diem: a novel approach to select representative days for long-term power system modeling. Energy 112:430\u2013442","journal-title":"Energy"},{"key":"469_CR29","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1029\/WR021i006p00779","volume":"21","author":"MVF Pereira","year":"1985","unstructured":"Pereira MVF, Pinto LMVG (1985) Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach. Water Resour Res 21:779\u2013792","journal-title":"Water Resour Res"},{"key":"469_CR30","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/BF01582895","volume":"52","author":"MVF Pereira","year":"1991","unstructured":"Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52:359\u2013375","journal-title":"Math Program"},{"key":"469_CR31","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.1109\/TPWRS.2016.2596803","volume":"32","author":"K Poncelet","year":"2017","unstructured":"Poncelet K, H\u00f6schle H, Delarue E et al (2017) Selecting representative days for capturing the implications of integrating intermittent renewables in generation expansion planning problems. IEEE Trans Power Syst 32:1936\u20131948","journal-title":"IEEE Trans Power Syst"},{"key":"469_CR32","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1016\/j.ejor.2016.12.005","volume":"259","author":"R Rahmaniani","year":"2017","unstructured":"Rahmaniani R, Crainic TG, Gendreau M et al (2017) The Benders decomposition algorithm: a literature review. Eur J Oper Res 259:801\u2013817","journal-title":"Eur J Oper Res"},{"key":"469_CR33","volume-title":"Electricity market reform: an international experience","author":"R Raineri","year":"2006","unstructured":"Raineri R (2006) Chile: where it all started. In: Sioshansi FP, Pfaffenberger W (eds) Electricity market reform: an international experience. Elsevier, Amsterdam"},{"key":"469_CR34","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.rser.2018.12.021","volume":"105","author":"G Ram\u00edrez-Sagner","year":"2019","unstructured":"Ram\u00edrez-Sagner G, Mu\u00f1oz FD (2019) The effect of head-sensitive hydropower approximations on investments and operations in planning models for policy analysis. Renew Sustain Energy Rev 105:38\u201347","journal-title":"Renew Sustain Energy Rev"},{"key":"469_CR35","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.enpol.2015.12.041","volume":"95","author":"R Sioshansi","year":"2016","unstructured":"Sioshansi R (2016) Retail electricity tariff and mechanism design to incentivize distributed renewable generation. Energy Policy 95:498\u2013508","journal-title":"Energy Policy"},{"key":"469_CR36","volume-title":"Springer optimization and its applications","author":"R Sioshansi","year":"2017","unstructured":"Sioshansi R, Conejo AJ (2017) Optimization in engineering: models and algorithms. Springer optimization and its applications. vol 120, Springer, Cham"},{"key":"469_CR37","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1109\/TPWRS.2021.3104768","volume":"37","author":"R Sioshansi","year":"2022","unstructured":"Sioshansi R, Denholm P, Arteaga J et al (2022) Energy-storage modeling: state-of-the-art and future research directions. IEEE Trans Power Syst 37:860\u2013875","journal-title":"IEEE Trans Power Syst"},{"key":"469_CR38","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545584","volume-title":"Power system economics: designing markets for electricity","author":"S Stoft","year":"2002","unstructured":"Stoft S (2002) Power system economics: designing markets for electricity. Wiley, New York"},{"key":"469_CR39","volume-title":"Analyses of issues arising in power systems and electricity markets with high renewable penetration","author":"K Yagi","year":"2020","unstructured":"Yagi K (2020) Analyses of issues arising in power systems and electricity markets with high renewable penetration. The Ohio State University, Columbus, OH"},{"key":"469_CR40","first-page":"222","volume":"8","author":"K Yagi","year":"2021","unstructured":"Yagi K, Sioshansi R (2021) Do renewables drive coal-fired generation out of electricity markets? Current Sustain Renew Energy Rep 8:222\u2013232","journal-title":"Current Sustain Renew Energy Rep"},{"key":"469_CR41","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/s10287-023-00451-5","volume":"20","author":"K Yagi","year":"2023","unstructured":"Yagi K, Sioshansi R (2023) Simplifying capacity planning for electricity systems with hydroelectric and renewable generation. Comput Manag Sci 20:26","journal-title":"Comput Manag Sci"},{"key":"469_CR42","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s10107-018-1249-5","volume":"175","author":"J Zou","year":"2019","unstructured":"Zou J, Ahmed S, Sun XA (2019) Stochastic dual dynamic integer programming. Math Program 175:461\u2013502","journal-title":"Math Program"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-023-00469-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-023-00469-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-023-00469-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T12:11:02Z","timestamp":1719058262000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-023-00469-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,13]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["469"],"URL":"https:\/\/doi.org\/10.1007\/s10287-023-00469-9","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,13]]},"assertion":[{"value":"31 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"16"}}