{"id":149,"date":"2026-02-11T08:24:37","date_gmt":"2026-02-11T08:24:37","guid":{"rendered":"https:\/\/almoa.aau.at\/?page_id=65"},"modified":"2026-02-18T10:39:46","modified_gmt":"2026-02-18T09:39:46","slug":"dc-11-economic-nmpc-for-multi-stage-optimal-power-flow-problems-with-generator-up-downtime-constraints","status":"publish","type":"page","link":"https:\/\/almoa.aau.at\/?page_id=149","title":{"rendered":"DC 11 &#8211; Economic NMPC for Multi-Stage Optimal Power Flow Problems with Generator Up\/Downtime Constraints"},"content":{"rendered":"<div class=\"dc-project\">\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Project Title:<\/strong> Economic NMPC for Multi-Stage Optimal Power Flow Problems with Generator Up\/Downtime Constraints<br \/><strong>Doctoral Candidate:<\/strong> N.N.<br \/><strong>Host Institution:<\/strong>\u00a0Heidelberg University<br \/><strong>Supervisors:<\/strong> <a href=\"https:\/\/www.math.uni-heidelberg.de\/de\/abteilungen\/numerik-optimierung-und-scientific-machine-learning\">Ekaterina Kostina<\/a>, <a href=\"https:\/\/www.aau.at\/team\/wiegele-angelika\/\">Angelika Wiegele<\/a><\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Objectives:<\/strong> With the increasing availability of renewable energy sources and energy storage capabilities, the optimal economic operation of electrical microgrids is becoming an increasingly important task. In economic dispatch problems, the goal is to minimise the cost of active power generation while satisfying power flow equations and operational constraints. One way to account for generator ramp constraints and energy storage levels, as well as time-varying power requirements is to treat time-coupled multistage optimal power flow (OPF) problems by NMPC. As practically relevant models include thousands of nodes, the power flow equations present nonlinear equality constraints, and requirements such as minimum generator run times and generator start-up costs are considered, we get large MINO problems that are computationally prohibitive to solve, especially in NMPC context. This project aims to combine NMPC for OPF problems with the treatment of discrete generator requirements. Nonlinear power flow will be approximated by an SDP rel[[DC 12]]axation and an efficient numerical method to solve the resulting MI-SDP will be developed. The treatment of the discrete generator constraints will require careful design of the NMPC scheme to avoid recursive feasibility problems. The newly developed NMPC scheme based on multi-level iterations for inexact SQP methods will be implemented with regard to stability and real-time feasibility.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Expected Results:<\/strong> The central results of the project are efficient methods for MI-SDP together with multi-level iteration methods for NMPC scheme for OPF problems with discrete generator constraint.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Planned secondment:<\/strong> 3 months at Siemens (K. Majewski) at the end of the 1st year to gain experience with modelling of OPF problems; 6 months at UNI-KLU (A. Wiegele) to develop methods for MI-SDP problems during the 2nd year<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Degree awarding institution:<\/strong> Heidelberg University<\/p>\r\n\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Project Title: Economic NMPC for Multi-Stage Optimal Power Flow Problems with Generator Up\/Downtime ConstraintsDoctoral Candidate: N.N.Host Institution:\u00a0Heidelberg UniversitySupervisors: Ekaterina Kostina, Angelika Wiegele Objectives: With the increasing availability of renewable energy sources and energy storage capabilities, the optimal economic operation of electrical microgrids is becoming an increasingly important task. In economic [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_crdt_document":"","footnotes":""},"class_list":["post-149","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=149"}],"version-history":[{"count":2,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/149\/revisions"}],"predecessor-version":[{"id":507,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/149\/revisions\/507"}],"wp:attachment":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}