{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T09:19:51Z","timestamp":1778404791527,"version":"3.51.4"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T00:00:00Z","timestamp":1613088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EEA\/50014\/2019"],"award-info":[{"award-number":["UID\/EEA\/50014\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sustainability"],"abstract":"<jats:p>The increasing penetration of renewable electricity generation is complicating the bidding and estimating processes of electricity prices, partly due to the shift of the overall cost sensitivity from operation (fuel) costs to investment costs. However, cost minimization models for capacity expansion are frequently based on the principle that, for a perfectly adapted system allowing non-served energy, marginal remuneration allows overall operation and investments costs recovery. In addition, these models are usually formulated as finite-horizon problems when they should be theoretically solved for infinite horizons under the assumption of companies\u2019 infinite lifespan, but infinite horizon cannot be dealt with mathematical programming since it requires finite sets. Previous approaches have tried to overcome this drawback with finite horizon models that tend asymptotically to the original infinite ones and, in many cases, the investment costs are annualized based on the plants\u2019 lifespan, sometimes including a cost residual value. This paper proposes a novel approach with a finite horizon that guarantees the investment costs\u2019 recovery. It is also able to obtain the marginal electricity costs of the original infinite horizon model, without the need for residual values or non-served energy. This new approach is especially suited for long-term electricity pricing with investments in renewable assets when non-served demand is banned or when no explicit capacity remuneration mechanisms are considered.<\/jats:p>","DOI":"10.3390\/su13041993","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T18:46:31Z","timestamp":1613155591000},"page":"1993","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Annualization of Renewable Investment Costs for Finite Horizon Electricity Pricing and Cost Recovery"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0095-0543","authenticated-orcid":false,"given":"Fco. Alberto","family":"Campos","sequence":"first","affiliation":[{"name":"Institute for Research in Technology, Technical School of Engineering, Comillas Pontifical University, 28015 Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6954-9833","authenticated-orcid":false,"given":"Jos\u00e9","family":"Villar","sequence":"additional","affiliation":[{"name":"Institute for Systems and Computer Engineering, Technology and Science, 465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0578-1067","authenticated-orcid":false,"given":"Efraim","family":"Centeno","sequence":"additional","affiliation":[{"name":"Institute for Research in Technology, Technical School of Engineering, Comillas Pontifical University, 28015 Madrid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"P\u00e9rez-Arriaga, I.J. (2014). Regulation of the Power Sector, Springer Science & Business Media.","DOI":"10.1007\/978-1-4471-5034-3"},{"key":"ref_2","unstructured":"Genoese, F., Drabik, E., and Egenhofer, C. (2019, May 30). The EU Power Sector Needs Long-Term Price Signals. Social Science Research Network, SSRN Scholarly Paper ID 2782355. Available online: https:\/\/papers.ssrn.com\/abstract=2782355."},{"key":"ref_3","unstructured":"Mastropietro, P. (2016). Regulatory Design of Capacity Remuneration Mechanisms in Regional and Low-Carbon Electric Power Markets. [Ph.D. Thesis, KTH Royal Institute of Technology]."},{"key":"ref_4","unstructured":"Eckaus, R.S., and Parikh, K.S. (1968). Planning for Growth, MIT Press."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Conejo, A.J., Baringo, L., Kazempour, S.J., and Siddiqui, A.S. (2016). Investment in Electricity Generation and Transmission: Decision Making under Uncertainty, Springer.","DOI":"10.1007\/978-3-319-29501-5"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1109\/59.32610","article-title":"A nonlinear programming approach to optimal static generation expansion planning","volume":"4","author":"Ramos","year":"1989","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_7","unstructured":"Ventosa, M., Denis, R., and Redondo, C. (2002, January 24\u201328). Expansion planning in electricity markets. Two different approaches. Proceedings of the 14th Power Systems Computation Conference 2002 (PSCC 2002 SEVILLE), Sevilla, Spain."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1287\/opre.1050.0211","article-title":"Generation Capacity Expansion in Imperfectly Competitive Restructured Electricity Markets","volume":"53","author":"Murphy","year":"2005","journal-title":"Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1109\/TPWRS.2009.2017435","article-title":"Strategic Generation Capacity Expansion Planning With Incomplete Information","volume":"24","author":"Wang","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1109\/TPWRS.2010.2069573","article-title":"Strategic Generation Investment Using a Complementarity Approach","volume":"26","author":"Kazempour","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hinojosa-Mateus, V.H. (2016, January 20\u201324). Static generation capacity expansion planning using linear transmission distribution factors. Proceedings of the 2016 IEEE PES Transmission Distribution Conference and Exposition-Latin America (PES T&D-LA), Morelia, Mexico.","DOI":"10.1109\/TDC-LA.2016.7805678"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1109\/TPWRS.2016.2565058","article-title":"The Impact of Operating Reserves on Investment Planning of Renewable Power Systems","volume":"32","author":"Vos","year":"2017","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_13","first-page":"1002","article-title":"Stochastic Generation Capacity Expansion Planning Reducing Greenhouse Gas Emissions","volume":"30","author":"Park","year":"2019","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1838","DOI":"10.1109\/TPWRS.2014.2351374","article-title":"Generation Capacity Expansion Planning Under Hydro Uncertainty Using Stochastic Mixed Integer Programming and Scenario Reduction","volume":"30","author":"Gil","year":"2015","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shengyu, W., Lu, C., Xiaoqing, Y., and Bo, Y. (2015, January 11\u201313). Long-term generation expansion planning under uncertainties and fluctuations of multi-type renewables. Proceedings of the 2015 IEEE 5th International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), Riga, Latvia.","DOI":"10.1109\/PowerEng.2015.7266387"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/59.221258","article-title":"Power system expansion planning under uncertainty","volume":"8","author":"Gorenstin","year":"1993","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4784","DOI":"10.1109\/TPWRS.2016.2522505","article-title":"Investing in Generation Capacity: A Multi-Stage Linear-Decision-Rule Approach","volume":"31","author":"Conejo","year":"2016","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1109\/TPWRS.2012.2217510","article-title":"Capacity Expansion Equilibria in Liberalized Electricity Markets: An EPEC Approach","volume":"28","author":"Wogrin","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2526","DOI":"10.1109\/TPWRS.2011.2138728","article-title":"Generation Capacity Expansion in Liberalized Electricity Markets: A Stochastic MPEC Approach","volume":"26","author":"Wogrin","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, Q., Wang, J., Zhang, Y., Fan, Y., Bao, G., and Wang, X. (2020). Multi-Period Generation Expansion Planning for Sustainable Power Systems to Maximize the Utilization of Renewable Energy Sources. Sustainability, 12.","DOI":"10.3390\/su12031083"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.epsr.2013.12.013","article-title":"Joint energy and reserve markets: Current implementations and modeling trends","volume":"109","author":"Villar","year":"2014","journal-title":"Electr. Power Syst. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"18","DOI":"10.2307\/1909238","article-title":"Sufficient Conditions for Optimality in an Infinite Horizon Development Plan","volume":"38","author":"Manne","year":"1970","journal-title":"Econometrica"},{"key":"ref_23","unstructured":"Williams, J.B. (1997). The Theory of Investment Value, Fraser Publishing Co."},{"key":"ref_24","unstructured":"(2015, January 01). Renewable Power Generation Costs in 2014. Available online: https:\/\/irena.org\/-\/media\/Files\/IRENA\/Agency\/Publication\/2015\/IRENA_RE_Power_Costs_2014_report.pdf."},{"key":"ref_25","unstructured":"de Sisternes, M.V.F. (2013). Investment Model for Renewable Electricity Systems (IMRES): An Electricity Generation Capacity Expansion Formulation with Unit Commitment Constraints, MIT Press."}],"container-title":["Sustainability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2071-1050\/13\/4\/1993\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:23:19Z","timestamp":1760160199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2071-1050\/13\/4\/1993"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,12]]},"references-count":25,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["su13041993"],"URL":"https:\/\/doi.org\/10.3390\/su13041993","relation":{},"ISSN":["2071-1050"],"issn-type":[{"value":"2071-1050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,12]]}}}