Topologically protected loop flows in high voltage AC power grids

Abstract

Geographical features such as mountain ranges or big lakes and inland seas often result in large closed loops in high voltage AC power grids. Sizable circulating power flows have been recorded around such loops, which take up transmission line capacity and dissipate but do not deliver electric power. Power flows in high voltage AC transmission grids are dominantly governed by voltage angle differences between connected buses, much in the same way as Josephson currents depend on phase differences between tunnel-coupled superconductors. From this previously overlooked similarity we argue here that circulating power flows in AC power grids are analogous to supercurrents flowing in superconducting rings and in rings of Josephson junctions. We investigate how circulating power flows can be created and how they behave in the presence of ohmic dissipation. We show how changing operating conditions may generate them, how significantly more power is ohmically dissipated in their presence and how they are topologically protected, even in the presence of dissipation, so that they persist when operating conditions are returned to their original values. We identify three mechanisms for creating circulating power flows, (i) by loss of stability of the equilibrium state carrying no circulating loop flow, (ii) by tripping of a line traversing a large loop in the network and (iii) by reclosing a loop that tripped or was open earlier. Because voltages are uniquely defined, circulating power flows can take on only discrete values, much in the same way as circulation around vortices is quantized in superfluids.

Flow and Elastic Networks on the $n$-torus: Geometry, Analysis, and Computation

“…[34] is the first paper to rigorously study multistability and establish that the active power flow equations have multistable solutions on a 6-node cycle network with balanced power injections. Several papers [10,14,32] have investigated mechanisms that create large loop flows and have shown that loop flows will persist even when the network returns to its normal operating condition. In [10], the basins of attraction for loop flows has been studied using Lyapunov theory.…”

“…In some cases, changes in the distribution of power injections (and withdrawals) across the network cause the stable operating point to change. In other cases, it result from changes in network topology-either when a line trips, destroying a cycle; or when a previously open line is closed, creating a new cycle [10].…”

Sample-Based Methods of Analysis for Multistable Dynamical Systems

“…It proves that voltage dynamics should be taken into account in model of synchronous machines. In mountain ranges, big lakes or inland seas we often observe large closed loops in high voltage AC power grids [17]. The basins stability method has been used to identify three mechanisms which create the circulating power flows.…”

Transient chaos enforces uncertainty in the British power grid

“…The latter explicitly takes into account that power grids -and thus reasonable parametrizations of the KM + -exhibit multistability. In fact, the phase space can be populated by multiple desired synchronized states [21,22] representing different operating modes as well as several undesired non-synchronized states representing power outages [18,23,24,25]. In a recent study [26], we contributed to the field of multistability-based stability analyses by determining the minimal fatal shock in a Kuramoto-like representation of the British power grid (figure 1(a)).…”