  To perform any meaningful optimization task, distribution grid operators need
to know the topology of their grids. Although power grid topology
identification and verification has been recently studied, discovering
instantaneous interplay among subsets of buses, also known as higher-order
interactions in recent literature, has not yet been addressed. The system
operator can benefit from having this knowledge when re-configuring the grid in
real time, to minimize power losses, balance loads, alleviate faults, or for
scheduled maintenance. Establishing a connection between the celebrated exact
distribution flow equations and the so-called self-driven graph Volterra model,
this paper puts forth a nonlinear topology identification algorithm, that is
able to reveal both the edge connections as well as their higher-order
interactions. Preliminary numerical tests using real data on a 47-bus
distribution grid showcase the merits of the proposed scheme relative to
existing alternatives.
