Our society takes the supply of electricity and energy sources for granted, so much so that we only notice it when it is not working perfectly. But there are a lot of things that have to come together for a smooth supply. And then electricity and gas should not be too expensive either. Gas in particular will play a crucial role in the energy transition. After all, natural gas is the fossil fuel with the lowest greenhouse gas emissions. Not only is it suitable for heating, but it can also help balance the intermittency of solar and wind power with fast-response gas-fired power plants.
In addition, green hydrogen is expected to gradually replace fossil natural gas in the coming years and decades. “Gas networks will therefore play a central role in the energy transition,” remarked René Henrion of the Weierstrass Institute for Applied Analysis and Stochastics in Berlin. The mathematician is involved in several projects to optimize gas and electricity networks, some of them with international partners.
The focus is on developing new mathematical methods – and this has certainly led to some surprising new insights. “As is often the case in mathematics, the methods developed can also be applied to other fields,” Henrion explained. “For example, we have found that our optimization methods are not only suitable for gas networks, but also for smaller electricity networks.” Although Germany’s power grid is integrated into the European grid and therefore too large for such an approach, “in many places in Africa there are smaller, local power grids, also known as mini-grids, for which our optimization methods can also be used.”
The Weierstrass Institute’s research activities in gas network optimization are bundled in the Transregio 154 Collaborative Research Center and include a large number of projects involving different problems and approaches. “The research area goes back to an old collaboration with industrial partners to study a specific problem,” stated Henrion. “However, some mathematical questions remained unanswered at the end of the project more than a decade ago, so we at the Weierstrass Institute, together with the other participating institutions, then concentrated on developing this research area, not least because of its importance for society as a whole.”
The scientists’ goal is to model, simulate, and optimize gas transport in the network. Regional gas networks have a large number of pipelines, plus a number of entry points from supra-regional networks and hundreds of distribution stations – for example, in towns and villages – from which gas is taken. In addition, pumps and compressor stations are needed to maintain the necessary pressure in the gas pipelines.
“When optimizing all these points, it is also important to note that many model parameters are inherently uncertain. Supply and consumption can change continuously, for example, because a cold day causes an increase in demand,” Henrion explained. This also changes prices, which in turn affects demand. External parameters, such as the weather, or technical parameters, such as the roughness of pipelines, some of which are decades old, cannot be accurately determined in mathematical models. For this reason, such research projects are also referred to as “optimization under uncertainty.
“An important goal of the research is to demonstrate that our mathematical methods can improve energy security,” Henrion said. “To do this, we use methods from stochastic optimization, where optimization and probability meet. Personally, I work with probability constraints in particular. These are designed to ensure that a given objective, in this case a secure gas supply, is achieved with a high probability, even under uncertain conditions”.
Interestingly, these methods are not only being used to optimize gas networks. “A former doctoral student and a colleague are in contact with researchers in Africa to help optimize small power grids there,” the researcher reported. In the Sahel region in particular, the challenge is that the large interconnected grid can only supply electricity intermittently, and power outages occur regularly. Instead, so-called mini-grids, i.e. local and small regional power grids, are supposed to ensure a power supply with minimal disruptions.
These mini-grids often rely on solar panels that provide electricity only during the day, battery storage, and diesel generators. The latter require expensive diesel fuel and should only be used when no other form of electricity is available. “A key question in optimizing such grids is how much electricity should be imported from the main grid in addition to solar power to charge the batteries while the grid is stable,” stated Henrion.
Whether the energy storage system is a battery, a hydroelectric plant, or a gas reservoir, similar mathematical models can be used for operational planning. Contacts have already been established with scientists in Tanzania and Ethiopia, among other places, which will hopefully lead to exciting projects in the future. “We always try to focus our research on the benefits to society as a whole,” Henrion concluded. “And of course it’s all the better if our work can also be used in developing countries.”
Dirk Eidemüller
