We expect power grids to reliably supply us with energy even when there are fluctuations and faults in the lines. Models of how to plan technical supply networks even better can be found in networks in nature. Based on these, Jülich researchers have developed a model with which they want to calculate optimal grids in the future.
A total power blackout would cripple a country’s infrastructure in no time. For this reason, power grids are usually constructed in such a way that they can compensate for fluctuations and damage to individual lines. This is achieved by having several pathways leading from the source to the consumer. If necessary, the power can thus bypass single interruptions in the grid. This so-called mesh architecture is therefore much less susceptible to disruption than a tree structure, which branches out increasingly, but in which only one pathway connects source and consumer at a time. However, the mesh architecture requires more lines in a power grid and incurs higher costs.
Larger regions, such as entire countries, are usually supplied by means of mesh power grids. For smaller areas, such as individual municipalities, the more economical tree structures are more likely to be used. Both types are also used in other technical networks, including water supply or telecommunications. Franz Kaiser and Prof. Dirk Witthaut from the Institute of Energy and Climate Research (IEK-STE) are using models to investigate how power grids should best be structured.
Nature as a model for power grids
When exchanging ideas with their colleague Dr. Henrik Ronellenfitsch (formerly of the Massachusetts Institute of Technology, now of Williams College in the USA), who does a lot of work on biological networks, they detected astonishing parallels. “We use the same mathematical equations for modelling our technical networks as he does for biological networks,” Franz Kaiser reports. Biological systems are also often made up of meshed networks, such as the fine vascular channels in plant leaves that are responsible for water transport, or our blood vessels. Today, a typical tree structure is only found in particular plant species that developed comparatively early in evolution, for example the ginkgo tree.
The similarities have inspired the researchers to design a mathematical model that can be used to predict how, in principle, a mesh structure develops from a tree structure and how additional meshes are created. “If we can better understand these relations, we can then draw conclusions about what we can improve in the construction of technical supply networks,” says Franz Kaiser.
Nature prefers mesh
Analyses by other researchers had already shown that in nature, fluctuations and disturbances in the networks lead to the formation of meshes. Apparently, the mesh structure has proven successful in compensating for interruptions in the system – for example, if insects nibble a leaf, the plant can use other pathways in the existing supply network to bypass the damaged area.
This network behaviour can be modelled. “With our simulations, we see that, for example, a network that is exposed to more damage develops differently from one that is largely ‘trouble-free’,” Kaiser explains. The scientists can also reconstruct when and at which location the first mesh in the network is created when certain parameters change. The surprising result: the change is saltatory. “You might think that the first mesh structure would form slowly when influences such as input fluctuations or the degree of the damage change slightly,” says Kaiser. However, that is not the case. From a mathematical point of view, even very small changes can lead to the model yielding a new ideal network in which there is suddenly a mesh where before there had been none – that is, a new pathway within the network.
Different network topologies
The researchers want to transfer their theoretical findings on the development of networks to concrete technical systems such as the power grid, using their model to calculate how to design such systems efficiently. At what points, for example, are meshes in a regional power grid expedient in order to compensate for possible disruptions, and what costs are incurred as a result? “If we then estimate the cost range of power outages, we can also estimate the savings that are possible with a mesh network,” Kaiser adds.
“The work is a good example of how interdisciplinary cooperation can advance research and how results that, at first glance, seem very theoretical can help answer everyday questions – in this case, the question of the optimal structure of power grids and other supply networks,” Dirk Witthaut says happily.
Photos: Forschungszentrum Jülich/Sascha Kreklau, Forschungszentrum Jülich/Ralf-Uwe Limbach, jopelka/shutterstock.com, Iryna Linnyk/shutterstock.com, Illustrations: SeitenPlan