{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:02:31Z","timestamp":1774353751397,"version":"3.50.1"},"reference-count":42,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We propose a two-stage stochastic version of the classical economic dispatch problem with alternating-current power flow constraints, a nonconvex optimization formulation that is central to power transmission and distribution over an electricity grid. Certain generation decisions made in the first stage cannot further be changed in the second stage, where the uncertainty due to various factors such as renewable generation is realized. Any supply-demand mismatch in the second stage must be alleviated using high marginal cost power sources that can be tapped in short order. We solve a Sample-Average Approximation (SAA) of this formulation by capturing the uncertainty using a finite number of scenario samples. We propose two outer approximation algorithms to solve this nonconvex program to global optimality. We use recently discovered structural properties for the classical deterministic problem to show that when these properties hold the sequence of approximate solutions obtained under both alternatives has a limit point that is a globally optimal solution to the two-stage nonconvex SAA program. We also present an alternate local optimization approach to solving the SAA problem based on the Alternating Direction Method of Multipliers (ADMM). Numerical experiments for a variety of parameter settings were carried out to demonstrate the efficiency and usability of our method over ADMM for large practical instances.<\/jats:p>","DOI":"10.1145\/2553084","type":"journal-article","created":{"date-parts":[[2014,2,11]],"date-time":"2014-02-11T14:39:42Z","timestamp":1392129582000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":32,"title":["Two-stage stochastic optimization for optimal power flow under renewable generation uncertainty"],"prefix":"10.1145","volume":"24","author":[{"given":"Dzung","family":"Phan","sequence":"first","affiliation":[{"name":"IBM T.J. Watson Research Center, Yorktown Heights, New York"}]},{"given":"Soumyadip","family":"Ghosh","sequence":"additional","affiliation":[{"name":"IBM T.J. Watson Research Center, Yorktown Heights, New York"}]}],"member":"320","published-online":{"date-parts":[[2014,1]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2047910"},{"key":"e_1_2_1_2_1","unstructured":"H. Bevrani and T. Hiyama. 2011. Intelligent Automatic Generation Control. CRC Press.  H. Bevrani and T. Hiyama. 2011. Intelligent Automatic Generation Control. CRC Press."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2006.10.011"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"S. Boyd and L. Vandenberghe. 2004. Convex optimization. Cambridge University Press.   S. Boyd and L. Vandenberghe. 2004. Convex optimization. Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"e_1_2_1_6_1","first-page":"3","article-title":"Contribution to the economic dispatch problem","volume":"8","author":"Carpentier J.","year":"1962","unstructured":"J. Carpentier . 1962 . Contribution to the economic dispatch problem . Bulletin Society Francaise Electriciens 8 , 3 (August 1962), 431--447. J. Carpentier. 1962. Contribution to the economic dispatch problem. Bulletin Society Francaise Electriciens 8, 3 (August 1962), 431--447.","journal-title":"Bulletin Society Francaise Electriciens"},{"key":"e_1_2_1_7_1","unstructured":"J. H. Chow D. K. Frederick and N. W. Chbat. 2003. Discrete-Time Control Problems Using MATLAB and the Control System Toolbox. Thomson-Brooks\/Cole Pacific Grove CA.   J. H. Chow D. K. Frederick and N. W. Chbat. 2003. Discrete-Time Control Problems Using MATLAB and the Control System Toolbox. Thomson-Brooks\/Cole Pacific Grove CA."},{"key":"e_1_2_1_8_1","volume-title":"Windpower","author":"Dragoon K.","year":"2003","unstructured":"K. Dragoon and M. Milligan . 2003. Assessing wind integration costs with dispatch models: a case study of PacifiCorp . In Windpower , 2003 , Austin, TX. K. Dragoon and M. Milligan. 2003. Assessing wind integration costs with dispatch models: a case study of PacifiCorp. In Windpower, 2003, Austin, TX."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592064"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581204"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581153"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12667-012-0056-y"},{"key":"e_1_2_1_14_1","volume-title":"2001 IEEE Porto Power Tech Conference.","author":"Fu W.","unstructured":"W. Fu and J. D. McCalley . 2001. Risk based optimal power flow . In 2001 IEEE Porto Power Tech Conference. W. Fu and J. D. McCalley. 2001. Risk based optimal power flow. In 2001 IEEE Porto Power Tech Conference."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(76)90003-1"},{"key":"e_1_2_1_16_1","doi-asserted-by":"crossref","unstructured":"L. Gan U. Topcu N. Li and S. Low. 2012. Exact Convex Relaxation for Optimal Power Flow in Tree Networks. (Aug. 2012). http:\/\/arxiv.org\/pdf\/1208.4076.pdf.  L. Gan U. Topcu N. Li and S. Low. 2012. Exact Convex Relaxation for Optimal Power Flow in Tree Networks. (Aug. 2012). http:\/\/arxiv.org\/pdf\/1208.4076.pdf.","DOI":"10.1109\/CDC.2012.6426045"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934810"},{"key":"e_1_2_1_18_1","volume-title":"Proceedings of the 1st IEEE International Conference on Smart Grid Communications. 519--524","author":"Ghosh S.","unstructured":"S. Ghosh , J. R. Kalagnanam , D. Katz , M. S. Squillante , and X. Zhang . 2010. Incentive design for lowest cost aggregate energy demand reduction . In Proceedings of the 1st IEEE International Conference on Smart Grid Communications. 519--524 . S. Ghosh, J. R. Kalagnanam, D. Katz, M. S. Squillante, and X. Zhang. 2010. Incentive design for lowest cost aggregate energy demand reduction. In Proceedings of the 1st IEEE International Conference on Smart Grid Communications. 519--524."},{"key":"e_1_2_1_19_1","volume-title":"Proceedings of the 1st IEEE Power Power Engineering Society ISGT Meeting.","author":"Ghosh S.","unstructured":"S. Ghosh , J. R. Kalagnanam , D. Katz , M. S. Squillante , and X. Zhang . 2011. Integration of demand response and renewable resources for power generation management . In Proceedings of the 1st IEEE Power Power Engineering Society ISGT Meeting. S. Ghosh, J. R. Kalagnanam, D. Katz, M. S. Squillante, and X. Zhang. 2011. Integration of demand response and renewable resources for power generation management. In Proceedings of the 1st IEEE Power Power Engineering Society ISGT Meeting."},{"key":"e_1_2_1_20_1","volume-title":"Analysis and Control System Techniques for Electric Power Systems","volume":"41","author":"Glavitsch H.","unstructured":"H. Glavitsch and R. Bacher . 1991. Optimal power flow algorithms . In Analysis and Control System Techniques for Electric Power Systems , vol. 41 . ACADEMIC Press Inc. H. Glavitsch and R. Bacher. 1991. Optimal power flow algorithms. In Analysis and Control System Techniques for Electric Power Systems, vol. 41. ACADEMIC Press Inc."},{"key":"e_1_2_1_21_1","first-page":"41","article-title":"Sur l\u2019approximation par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9, d\u2019une classe de probl\u00e8mes de Dirichlet non lineaires","volume":"2","author":"Glowinski R.","year":"1975","unstructured":"R. Glowinski and A. Marrocco . 1975 . Sur l\u2019approximation par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9, d\u2019une classe de probl\u00e8mes de Dirichlet non lineaires . RAIRO Anal. Num\u00e9r. 2 (1975), 41 -- 76 . R. Glowinski and A. Marrocco. 1975. Sur l\u2019approximation par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9, d\u2019une classe de probl\u00e8mes de Dirichlet non lineaires. RAIRO Anal. Num\u00e9r. 2 (1975), 41--76.","journal-title":"RAIRO Anal. Num\u00e9r."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2009.07.007"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00927673"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1049\/iet-gtd:20080273"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/59.589777"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/59.867147"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2011.2160974"},{"key":"e_1_2_1_29_1","unstructured":"North American Electric Reliability Corporation (NERC) Standard. 2005. Standard BAL-002-0: Disturbance Control Performance. (2005).  North American Electric Reliability Corporation (NERC) Standard. 2005. Standard BAL-002-0: Disturbance Control Performance. (2005)."},{"key":"e_1_2_1_30_1","volume-title":"Energy Function Analysis for Power System Stability","author":"Pai M. A.","unstructured":"M. A. Pai . 1989. Energy Function Analysis for Power System Stability . Kluwer Academic Publishers , Boston, MA . M. A. Pai. 1989. Energy Function Analysis for Power System Stability. Kluwer Academic Publishers, Boston, MA."},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1110.1036"},{"key":"e_1_2_1_32_1","volume-title":"A method for nonlinear constraints in minimization problems. Optimization","author":"Powell M. J. D.","year":"1969","unstructured":"M. J. D. Powell . 1969. A method for nonlinear constraints in minimization problems. Optimization ( 1969 ), 283--298. M. J. D. Powell. 1969. A method for nonlinear constraints in minimization problems. Optimization (1969), 283--298."},{"key":"e_1_2_1_33_1","volume-title":"Handbook in Operations Research and Management Science","author":"Ruszcz\u00fdnski A.","unstructured":"A. Ruszcz\u00fdnski . 2003. Decomposition methods . In Handbook in Operations Research and Management Science , Volume on Stochastic Programming, A. Ruszcz\u00fdnski and A. Shapiro (Eds.). Elsevier, Amsterdam, 141-- 211 . A. Ruszcz\u00fdnski. 2003. Decomposition methods. In Handbook in Operations Research and Management Science, Volume on Stochastic Programming, A. Ruszcz\u00fdnski and A. Shapiro (Eds.). Elsevier, Amsterdam, 141--211."},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(91)85027-R"},{"key":"e_1_2_1_35_1","volume-title":"New York: IEEE\/Wiley-Interscience.","author":"Shahidehpour M.","year":"2002","unstructured":"M. Shahidehpour , H. Yamin , and Z. Li . 2002 . Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management . New York: IEEE\/Wiley-Interscience. M. Shahidehpour, H. Yamin, and Z. Li. 2002. Market Operations in Electric Power Systems: Forecasting, Scheduling, and Risk Management. New York: IEEE\/Wiley-Interscience."},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.5555\/2678054"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-005-0581-8"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1137\/080724265"},{"key":"e_1_2_1_39_1","doi-asserted-by":"crossref","unstructured":"A. J. Wood and B. F. Wollenberg. 1996. Power Generation Operation and Control. John Wiley & Sons New York.  A. J. Wood and B. F. Wollenberg. 1996. Power Generation Operation and Control. John Wiley & Sons New York.","DOI":"10.1016\/0140-6701(96)88715-7"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1080\/073135600449116"},{"key":"e_1_2_1_41_1","volume-title":"Power Engineering Society General Meeting","author":"Xue Y.","year":"2007","unstructured":"Y. Xue , L. Chang , and J. Meng . 2007. Dispatchable distributed generation network - a new concept to advance DG technologies . In Power Engineering Society General Meeting , 2007 . IEEE. 1--5. Y. Xue, L. Chang, and J. Meng. 2007. Dispatchable distributed generation network - a new concept to advance DG technologies. In Power Engineering Society General Meeting, 2007. IEEE. 1--5."},{"key":"e_1_2_1_42_1","volume-title":"Power Energy Society General Meeting","author":"Yong T.","year":"2009","unstructured":"T. Yong , R. Entriken , and P. Zhang . 2009a. Reserve determination for system with large wind generation . In Power Energy Society General Meeting , 2009 (PES\u201909). IEEE. 1--7. T. Yong, R. Entriken, and P. Zhang. 2009a. Reserve determination for system with large wind generation. In Power Energy Society General Meeting, 2009 (PES\u201909). IEEE. 1--7."},{"key":"e_1_2_1_43_1","volume-title":"IEEE PES Power Energy Society General Meeting. 1--7.","author":"Yong T.","unstructured":"T. Yong , R. Entriken , and P. Zhang . 2009b. Reserve determination for system with large wind generation . In IEEE PES Power Energy Society General Meeting. 1--7. T. Yong, R. Entriken, and P. Zhang. 2009b. Reserve determination for system with large wind generation. In IEEE PES Power Energy Society General Meeting. 1--7."},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2010.2051168"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2553084","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T20:57:40Z","timestamp":1672433860000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2553084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1145\/2553084"],"URL":"https:\/\/doi.org\/10.1145\/2553084","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"value":"1049-3301","type":"print"},{"value":"1558-1195","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]},"assertion":[{"value":"2011-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-08-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-01-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}