This repository contains a collection of mathematical optimisation models that have been developed for educational purposes for several lectures. They are collected here for easier maintenance and better visibility of what has been implemented already.
The common theme among these models is capacity expansion, power flow and plant scheduling for minimum total system cost (or - in the case of DHMNL - maximum revenue), each model stressing another aspect of common tasks in modelling of energy systems.
This linear programming model finds the minimum cost generation and network flow for a lossless network, while obeying linearised DC powerflow equations.
This mixed-integer linear programming (MILP) model finds the maximum revenue topology and size of a district heating network for a given set of source and demand vertices. The model can decide which demands to connect and consequently plans the location and size of the built network.
This LP model finds the maximum welfare solution for a given set of a) a discretised production cost curve (i.e. a merit order curve) and b) a discretised utility function of customers (i.e. a price-demand curve).
This LP model finds the minimum cost investment plan for for a set of two power plant technologies over multiple decades, allowing investment decisions every five years. Old investments phase out of the power plant fleet after the lifetime of each investment is over.
This model finds the minimum cost network within a graph to redundantly connect a set of source to a set of demand points. "Redundantly" means that the resulting network is resilient against the failure of any single edge in the network, i.e. satisfying the N-1 Criterion common in electric grid design.
Storage Optimisation for Smart Grid. This model optimises size and operation of a hypothetical lossless storage technology for electric energy. A given electricity demand must be satisfied from a) a cost-free (renewable) energy supply with intermittent characteristic or from b) purchase, i.e. buying of electricity from the grid for a time-dependent price. Find more explanation in a dedicated blog post that walks through the whole model.
This linear programming (LP) optimisation model finds a minimum-cost capacity expansion and unit commitment solution to a given demand timeseries for a combination of a fluctuating feed-in (renewables) and a controllable technology (power plant). This model focuses on correctly depicting the trade-off in sizing the power plant with respect to its operation point, which can exhibit less efficiency than when operating below its nominal size. These properties are approximated by a formulation that combines startup costs with a linearily increasing or decreasing conversion efficiency, depending on the operation point.
The standalone solver glpsol from the GNU Linear Programming Toolkit (GLPK).
For trying out these models, there is an in-browser WebApp for MathProg maintained by Jeffrey Kantor.
Binary builds for Windows are available through the WinGLPK. Just extract the contents of the ZIP file to a convenient location, e.g. C:\GLPK. You then can either call a model using
C:\GLPK\bin\glpsol.exe -m model.mod
or add the subdirectory w64, which contains the file glpsol.exe, to the system path (how), so that the command glpsol is available on the command prompt from any directory directly:
glpsol -m model.mod
Most distributions offer GLPK as a ready-made packages. If unsure, please consult your distribution's package index. On Debian or Debian-based (e.g. Ubuntu) distributions, executing the following command on the terminal (excluding the $ ):
$ sudo apt-get install glpk-utils
Note that package maintainers could potentially lag behind new versions up to several releases. To check which version you have installed, you can use:
$ glpsol --version
If you want the most recent version, you might consider downloading the source code from the project homepage and build the solver from source by following the instructions in the accompanying INSTALL file. Typically, this boils down to the following steps, where X-Y must be replaced by the version number, e.g. 4-60:
$ tar -xzvf glpk-X-Y.tar.gz
$ cd glpk-X-Y
$ ./configure
$ make
$ make check
$ sudo make install
To check whether (and where) the solver was installed, you can use:
$ which glpsol
/usr/bin/glpsol
Each model has its own author and license statement in the file header. Most models so far have the Creative Commons Public Domain Dedication, short CC0. In other words, you can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Some minor conditions still apply, most notably: When using or citing the work, you should not imply endorsement by the author or the affirmer. But that's about it. But when in doubt, read the read the full license text.