Circadian rhythms and microgrids might not seem to have much in common, but in the world of theoretical mathematics, they do.
New research published Friday in Science Advances suggests that the same mathematical models that help scientists better understand and explain biological phenomena could also be applied to making small, islanded power grids run more efficiently.
Microgrids come in various flavors, but usually they are localized grids that can disconnect from the larger power grid and operate independently. More recently, microgrids have combined clean energy generation and more traditional generation (such as diesel or natural gas turbines) to deliver both heat and electric power. They manage current with energy storage and controls.
Because the grids are small, they’re prone to more severe fluctuations in voltage and frequency than are larger grids, which can more easily smooth fluctuations across their wider systems.
This is where a well known mathematical model for synchronization, the Kuramoto model, can help, says Per Sebastian Skardal, assistant professor of mathematics at Trinity College and lead author of the paper.
The Kuramoto model is a phase oscillator model that defines each oscillator as just a phase angle. The behavior of each phase depends on its interaction with the other phases, explains Skardal.
The model has helped to explain the synchronization of various processes, including the rhythmic flashing of fireflies and neurons firing in the brain. “With the power grid, on the other hand, we are going one step further and using what we know about networks and synchronization to make deliberate choices to improve the functionality of a given system,” says Skardal.
Skardal and his collaborators found that in islanded microgrids that are disconnected from the large power grid, there are essentially a few problematic oscillators. They tend to prefer a frequency that is either much higher or lower than the other oscillators in the network, or they’re loosely coupled to the network. These problematic oscillators could be a set of solar panels that have widely variable output, or a large power draw that turns on and off suddenly.
Skardal says the model should apply regardless of the microgrid configuration. Although the work is firmly theoretical at this point, Skardal and his collaborator Alex Arenas, professor of physics at Rovira i Virgili University in Spain, are interested in applied mathematics, which would take further studies and engineering work.
The model would ultimately inform control systems for microgrids, giving the ability to identify the problem oscillators and adjust them in real time. Preventing or minimizing the grid fluctuations within a microgrid could potentially reduce costs because fewer inverters would be needed or a more simplified and standardized control scheme could be implemented.
Whether this research would apply to a microgrid when it is connected to the main power grid, or help to limit fluctuations in larger power grids whose stability is affected by the variability of inputs from renewable energy sources, is yet to be seen.
Skardal says he believes both may be future applications of the current research, but it is too early to say for sure. In the case of a microgrid that is not islanded, “I believe that the intuition behind the idea will hold,” says Skardal. But the Kuramoto network model would have to be adjusted to take some external forcing, which would be the influence of the larger grid, into account.
For large power grids with high levels of renewable energy generation, the complexity of the system would make the model more complicated, but the same math could potentially apply.
But power grids aren’t the only things that could benefit from this line of research, the authors argue. “We hypothesize that our findings here may potentially shed some light on the control of synchronization in other contexts,” they conclude in the paper, “such as cardiac physiology and neuroscience.”