The “principled maximum likelihood” approach: The intensity of the colours quantifies the likelihood that a node is the source of the disturbance. The left and middle panels correspond to standard method (namely taking the Fourier transform of time series) and the right panel is the method employed in this study. Courtesy: R Delabays
A new algorithm can identify where an electric current surge occurred in a power grid, potentially making it easier to avoid outages and subsequent equipment failures along transmission lines. The algorithm was developed by researchers from the University of Applied Sciences of Western Switzerland (HES-SO) and Los Alamos National Laboratory in the US, and it requires no previous knowledge of the grid’s global structure to pinpoint the source of damaging phenomena.
When a component of an electrical grid malfunctions, it injects an unexpected signal into the system, causing persistent periodic disturbances known as forced oscillations to flow through the grid. These oscillations can show up as power swings along transmission lines and may have consequences thousands of kilometres from the source of the disturbance.
Such long-distance effects are possible because electric power grids are among the world’s largest human-made systems, observes Robin Delabays, an applied mathematician at HES-SO’s Institute of Sustainable Energy and the study’s leader. The European grid, for example, stretches from Portugal to Ukraine and operates as a single system. It is therefore impossible for anyone to monitor all its components all the time.
“Since power grids are complex structures, the sources of such disturbances are difficult to identify,” Delabays explains. “But with the method we propose, we are able to do just this solely based on voltage measurements. This means that we require no knowledge of the actual underlying power grid.”
Such “system agnosticism” is a big advantage, he adds, as the actual grid structure and parameters change constantly due to operational decisions and even weather conditions.
“Principled maximum likelihood” approach
The researchers’ model accounts for random power-flow fluctuations that are naturally present in transmission lines and uses them to determine the set of parameters needed to find the most likely origin of a forced oscillation. Using this “principled maximum likelihood” approach, Delabays and colleagues were able to identify the source of the oscillation in historical US transmission system data recorded during known forced-oscillation events.
“The algorithmic part per se is rather standard,” Delabays explains. “We solve a least square problem by an interior point method. Our main contribution was to be able to re-write the optimization problem in such a way that allows us to get rid of a lot of nonlinearities in the system.”
The work could help mitigate forced oscillations in future renewable-energy power grids, where such they could be a significant source of infrastructure failure and blackouts, he says. “The holy grail for us would be to be able to apply our method in real-time on measurement data and to identify a device (typically a transformer) that is currently malfunctioning,” he tells Physics World. “Our goal here would be to provide early warnings to grid operators and to be able to locate the source of these warnings.”
Delabays says the next step will be to get access to data for additional disturbance events for which the source has been identified, and use this to confirm the validity of the method. After that, he and his colleagues hope to apply the algorithm to historical measurement data for which the actual disturbance source is unknown. “The other improvement we envision is to leverage the knowledge we have of the power grid in general,” Delabays says. “We do not know everything about a grid, but there are many things that we do know and that we do not currently leverage. For instance, new power lines will not materialize from thin air, so even if we don’t know whether an existing line is active or not, we do know when two buses are not physically connected.”
The technique is described in PRX Energy.
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