by Tim Varelmann
Energy is becoming more and more expensive, including electrical energy. Green electricity is now cheap electricity. However, its availability is not necessarily aligned with the demand for electricity because it largely depends on when the sun is shining and/or the wind is blowing. A fluctuating supply of renewable energy also leads to a fluctuating price for renewable energy, as the price describes the relationship between supply and demand. Large, industrial electricity users have access to "wholesale prices" on an electricity market called day-ahead market. There, the prices are hourly varying but they are usually fixed at mid-day of the previous day, so that electricity consumption can be planned in line with those prices. For such industrial customers, hourly variable electricity prices are business as usual; private households are often not yet familiar with this, although more and more electricity suppliers are already offering variable tariffs for them as well.
In the chemical process industry, there are many large electrical consumers. For a long time, chemical production processes have produced at exactly the same rate, often 24 hours a day, seven days a week. Such a production strategy simplifies process control, but actually many processes could also produce at temporally variable rates. As a scientist, I have researched how to use such flexibility to match the demand of industrial electricity users to the supply of renewable energy. This way, more renewable energy is consumed right when it is produced; the power grid needs less electrical energy storage capacity; and industry produces a lot when electricity is cheap and little when electricity becomes expensive, to reduce its energy costs.
In this series, I want to show in a simple way how numerical optimization can provide such production schedules. The production of aluminum will serve as an example. This process is physically relatively simple, and does not require an understanding of complicated science to illustrate the essence of numerical optimization. Of course, mathematical optimization can also be used in different production areas and with completely different goals - in particular where complicated decisions are made.
The raw material from which aluminum is produced is called bauxite. Bauxite is an aluminum ore that is mined in an open pit mine. An aluminum ore is a compound of aluminum molecules with other molecules, such as hydrogen and oxygen. For aluminum, bauxite is something like a sofa: when combined with other molecules, the aluminum molecules have made themselves comfortable, so bauxite has very little energy. Unlike people who lie on a sofa, aluminum molecules do not have to eat, go to the toilet, or leave their sofa for other reasons. Therefore, it is easy to imagine how low the energy of bauxite is: Think of bauxite as a sofa that was so comfortable that it was never left for possibly millions of years.
To produce aluminum requires to remove the aluminum molecules from the ore, i.e., to flush the molecules from the sofa – clearly, this requires a lot of energy. Nearly 15 MWh of electrical energy is needed for each ton of aluminum. That requires five large wind turbines to supply electricity for one hour! In electrolysis, electrical energy is used to separate the aluminum molecules from the bauxite in a container with a hot bauxite-aluminum mass. The pure aluminum is heavier than the bauxite-aluminum mass and therefore sinks to the bottom, where it can be easily collected.
Thus, the production of aluminum is an energy-intensive process, but with an optimal production schedule, it can increase the rate of renewable energy usage. Part 2 of this series develops a simplified model of the aluminum plant that describes the optimal production scheduling decisions in terms that a computer can understand. Part 3 describes important issues in selecting appropriate algorithms to solve the optimization problem and shows an optimal production schedule for the price profile depicted above.
If you also want to delegate complicated decisions to your computer, let me know; I'm happy to help!
Thanks to Simon Thiele for proofreading this article and providing valuable feedback.