A Branch and Bound algorithm to solve nonconvex MINLP problems via novel division strategy: An electric power system case study

Marcos Andre De Jesus Delgado, Mahdi Pourakbari-Kasmaei, Marcos Julio Rider

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

2 Citations (Scopus)

Abstract

This paper presents two Branch and Bound algorithms (B&B) for solving mixed-integer nonlinear programming (MINLP) problems with nonconvex search space. The main advantage of the proposed algorithms, comparing with the commonly used B&B algorithms, is using an innovative way of variables' separation and subproblems' division while, if necessary, one more variable is used in the separation process. This approach allows circumventing the probable difficulties caused by nonlinearity and nonconvexity. This paper aims at addressing the following issues of how to: 1) deal with nonlinear programming problems, 2) detect the infeasibility of the resulted NLP problems, and 3) deal with the nonconvexity of the problem. In order to show the applicability, the proposed algorithms are applied to one of the most complicated problems in power system, the long-term static transmission expansion planning, which is modeled as an MINLP problem. Several case studies such as Garver 6-bus, IEEE 24-bus, South Brazilian 46-bus, Bolivian 57-bus, and the Colombian 93-bus are conducted to reveal the effectiveness and shortcoming of the proposed algorithms. Results show that the proposed algorithms can find the best-known solutions for most of the aforementioned systems with a significant reduction in the number of subproblems.

Original languageEnglish
Title of host publicationConference Proceedings - 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2017
PublisherIEEE
Number of pages6
ISBN (Print)9781538639160
DOIs
Publication statusPublished - 12 Jul 2017
MoE publication typeA4 Article in a conference publication
EventIEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe - Milan, Italy
Duration: 6 Jun 20179 Jun 2017

Conference

ConferenceIEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe
Abbreviated titleEEEIC/I&CPS Europe
CountryItaly
CityMilan
Period06/06/201709/06/2017

Keywords

  • Branch and bound algorithm
  • Mixed-integer nonlinear programming
  • Transmission expansion planning

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