{"id":186,"date":"2014-12-06T15:16:27","date_gmt":"2014-12-06T15:16:27","guid":{"rendered":"http:\/\/meyn.coron.us\/?page_id=186"},"modified":"2026-04-14T09:52:38","modified_gmt":"2026-04-14T14:52:38","slug":"convex-hull-pricing-in-energy-and-reserves-markets","status":"publish","type":"page","link":"https:\/\/faculty.eng.ufl.edu\/meyn\/publications\/convex-hull-pricing-in-energy-and-reserves-markets\/","title":{"rendered":"Convex Hull Pricing in Energy and Reserves Markets"},"content":{"rendered":"<p>This work concerns resource allocation in a power grid. \u00a0Scheduling of generation by a central authority takes place in two stages:<\/p>\n<ul>\n<li>Unit commitment: \u00a0Which generators are running and &#8220;plugged in&#8221;<\/li>\n<li>Level of generation for each generator.<\/li>\n<\/ul>\n<p>The first decision is cast as a combinatorial optimization problem, which is generally considered difficult by electrical engineer\/computer science\/computational academics<\/p>\n<p>The second step can be cast as a convex optimization problem, and most in these academic communities would declare that this problem is easy. \u00a0Whey then do the ISO\/RTOs in the U.S. find step 2 so difficult?<\/p>\n<p>One reason is that the objective function is not very sensitive to the precise allocation, but the <em>market<\/em> demands precise solutions to the optimization problem. \u00a0Slight errors in computation can mean great rewards to some participants in the energy market. \u00a0Consider the 2013 finding regarding Deutsche Bank&#8217;s alleged manipulation of energy markets, \u00a0 \u00a0<span style=\"font-family: Arial, Verdana, sans-serif;font-size: 12px\">(Reuters) &#8211; <\/span><a style=\"font-family: Arial, Verdana, sans-serif;font-size: 12px\" href=\"http:\/\/www.reuters.com\/article\/2013\/01\/22\/us-ferc-deutschebank-idUSBRE90L0SW20130122\">German bank Deutsche Bank AG will pay nearly $1.7 million to settle allegations it manipulated electricity markets in California in 2010<\/a><\/p>\n<p>These papers introduce more efficient and reliable computation tools for computation of allocations in energy markets to address these points.<\/p>\n<p><a href=\"\/meyn\/assets\/uploads\/2014\/12\/EPSD2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-136 size-full\" src=\"http:\/\/faculty.eng.ufl.edu\/meyn\/wp-content\/uploads\/sites\/671\/2014\/12\/EPSD2-1.png\" alt=\"EPSD(2)\" width=\"545\" height=\"178\" srcset=\"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-content\/uploads\/sites\/671\/2014\/12\/EPSD2-1.png 545w, https:\/\/faculty.eng.ufl.edu\/meyn\/wp-content\/uploads\/sites\/671\/2014\/12\/EPSD2-1-300x98.png 300w\" sizes=\"auto, (max-width: 545px) 100vw, 545px\" \/><\/a><\/p>\n<h3>References<\/h3>\n<p>@article{wanshazhelitmey13a,<br \/>\nTitle = {<a href=\"\/meyn\/assets\/uploads\/2014\/12\/EPSD_partI.pdf\" target=\"_blank\" rel=\"noopener\">An Extreme-Point Subdifferential Method for Convex Hull Pricing in Energy and Reserve Markets. {Part I:} Algorithm Structure<\/a>},<br \/>\nAuthor = {Wang, Gui and Shanbhag, U.V. and Zheng, Tongxin and Litvinov, E. and Meyn, S.},<br \/>\nJournal = {{<strong>IEEE Transactions on Power Systems<\/strong>}},<br \/>\nNumber = {3},<br \/>\nPages = {2111-2120},<br \/>\nVolume = {28},<br \/>\nYear = {2013}}<\/p>\n<p>@article{wanshazhelitmey13b,<br \/>\nTitle = {<a href=\"\/meyn\/assets\/uploads\/2014\/12\/EPSD_partII.pdf\" target=\"_blank\" rel=\"noopener\">An Extreme-Point Subdifferential Method for Convex Hull Pricing in Energy and Reserve Markets. {Part II:} Convergence Analysis and Numerical Performance<\/a>},<br \/>\nAuthor = {Wang, Gui and Shanbhag, U.V. and Zheng, Tongxin and Litvinov, E. and Meyn, S.},<br \/>\nJournal = {{<strong>IEEE Transactions on Power Systems<\/strong>}},<br \/>\nNumber = {3},<br \/>\nPages = {2121-2127},<br \/>\nVolume = {28},<br \/>\nYear = {2013}}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work concerns resource allocation in a power grid. \u00a0Scheduling of generation by a central authority takes place in two stages: Unit commitment: \u00a0Which generators are running and &#8220;plugged in&#8221; Level of generation for each generator. The first decision is cast as a combinatorial optimization problem, which is generally considered difficult by electrical engineer\/computer science\/computational [&hellip;]<\/p>\n","protected":false},"author":1347,"featured_media":0,"parent":27,"menu_order":9,"comment_status":"closed","ping_status":"closed","template":"page-templates\/page-section-nav.php","meta":{"_acf_changed":false,"inline_featured_image":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-186","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/pages\/186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/users\/1347"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/comments?post=186"}],"version-history":[{"count":1,"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/pages\/186\/revisions"}],"predecessor-version":[{"id":2907,"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/pages\/186\/revisions\/2907"}],"up":[{"embeddable":true,"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/pages\/27"}],"wp:attachment":[{"href":"https:\/\/faculty.eng.ufl.edu\/meyn\/wp-json\/wp\/v2\/media?parent=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}