Roth, Maximilian ; Franke, Georg ; Rinderknecht, Stephan (2022)
A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models.
In: Mathematics, 10 (13)
doi: 10.3390/math10132226
Article, Bibliographie
This is the latest version of this item.
Abstract
As decentralized energy supply units, microgrids can make a decisive contribution to achieving climate targets. In this context, it is particularly important to determine the optimal size of the energy components contained in the microgrids and their optimal operating schedule. Hence, mathematical optimization methods are often used in association with such tasks. In particular, mixed-integer linear programming (MILP) has proven to be a useful tool. Due to the versatility of the different energetic components (e.g., storages, solar modules) and their special technical characteristics, linear relationships can often only inadequately describe the real processes. In order to take advantage of linear solution techniques but at the same time better represent these real-world processes, accurate and efficient approximation techniques need to be applied in system modeling. In particular, nonlinear-bivariate functions represent a major challenge, which is why this paper derives and implements a method that addresses this issue. The advantage of this method is that any bivariate mixed-integer nonlinear programming (MINLP) formulation can be transformed into a MILP formulation using this comprehensive method. For a performance comparison, a mixed-integer quadratic constrained programming (MIQCP) model—as an MINLP special case—is applied and transformed into a MILP, and the solution of the transformed problem is compared with the one of the MIQCP. Since there are good off-the-shelf solvers for MIQCP problems available, the comparison is conservative. The results for an exemplary microgrid sizing task show that the method delivers a strong performance, both in terms of approximation error (0.08%) and computation time. The method and its implementation can serve as a general user-tool but also as a basis for further methodological developments and research.
| Item Type: | Article |
|---|---|
| Erschienen: | 2022 |
| Creators: | Roth, Maximilian ; Franke, Georg ; Rinderknecht, Stephan |
| Type of entry: | Bibliographie |
| Title: | A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models |
| Language: | English |
| Date: | 25 June 2022 |
| Publisher: | MDPI |
| Journal or Publication Title: | Mathematics |
| Volume of the journal: | 10 |
| Issue Number: | 13 |
| DOI: | 10.3390/math10132226 |
| URL / URN: | https://www.mdpi.com/2227-7390/10/13/2226/htm |
| Corresponding Links: | |
| Abstract: | As decentralized energy supply units, microgrids can make a decisive contribution to achieving climate targets. In this context, it is particularly important to determine the optimal size of the energy components contained in the microgrids and their optimal operating schedule. Hence, mathematical optimization methods are often used in association with such tasks. In particular, mixed-integer linear programming (MILP) has proven to be a useful tool. Due to the versatility of the different energetic components (e.g., storages, solar modules) and their special technical characteristics, linear relationships can often only inadequately describe the real processes. In order to take advantage of linear solution techniques but at the same time better represent these real-world processes, accurate and efficient approximation techniques need to be applied in system modeling. In particular, nonlinear-bivariate functions represent a major challenge, which is why this paper derives and implements a method that addresses this issue. The advantage of this method is that any bivariate mixed-integer nonlinear programming (MINLP) formulation can be transformed into a MILP formulation using this comprehensive method. For a performance comparison, a mixed-integer quadratic constrained programming (MIQCP) model—as an MINLP special case—is applied and transformed into a MILP, and the solution of the transformed problem is compared with the one of the MIQCP. Since there are good off-the-shelf solvers for MIQCP problems available, the comparison is conservative. The results for an exemplary microgrid sizing task show that the method delivers a strong performance, both in terms of approximation error (0.08%) and computation time. The method and its implementation can serve as a general user-tool but also as a basis for further methodological developments and research. |
| Uncontrolled Keywords: | MILP, MINLP, MIQCP, big-M, sizing, scheduling, microgrids, linearization, nonlinear, bivariate |
| Divisions: | 16 Department of Mechanical Engineering 16 Department of Mechanical Engineering > Institute for Mechatronic Systems in Mechanical Engineering (IMS) |
| Date Deposited: | 06 Jul 2022 07:08 |
| Last Modified: | 03 Jul 2024 02:57 |
| PPN: | 496416626 |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Available Versions of this Item
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A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models. (deposited 26 Aug 2022 12:10)
- A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models. (deposited 06 Jul 2022 07:08) [Currently Displayed]
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