A Spectral Representation of Power Systems with Applications to Adaptive Grid Partitioning and Cascading Failure Localization

Abstract

Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a comprehensive framework based on spectral graph theory that fully and rigorously captures how multiple simultaneous line failures propagate, distinguishing between non-cut and cut set outages. Using this spectral representation of power systems, we identify the crucial graph sub-structure that ensures line failure localization -the network bridge-block decomposition. Leveraging this theory, we propose an adaptive network topology reconfiguration paradigm that uses a two-stage algorithm where the first stage aims to identify optimal clusters using the notion of network modularity and the second stage refines the clusters by means of optimal line switching actions. Our proposed methodology is illustrated using extensive numerical examples on standard IEEE networks and we discussed several extensions and variants of the proposed algorithm.

An MILP-based approach to tree partitioning with minimal power flow disruption and generator coherency constraints

“…The failure or the disconnection of a transmission line causes the power to be globally redistributed on the remaining lines, some of which can overload and also get disconnected -a phenomenon to which we refer to as failure propagation. It was shown in [8], [10], [11], [7] that line failures do not propagate across bridges, meaning that line failures in a tree-partitioned network only impact the flows on lines in the same cluster. Most power networks, however, have a very meshed structure and only have trivial bridges, making them very prone to non-local line failure propagation [8].…”

“…It was shown in [8], [10], [11], [7] that line failures do not propagate across bridges, meaning that line failures in a tree-partitioned network only impact the flows on lines in the same cluster. Most power networks, however, have a very meshed structure and only have trivial bridges, making them very prone to non-local line failure propagation [8].…”

“…The highlevel idea of tree partitioning is, instead of creating islands (i.e., disconnected components), to temporarily switch off lines to obtain "quasi-island" clusters that are interconnected in a tree-like manner (see Figure 1). As shown in [7] and [8], any line failure in a tree-partitioned network causes a power flow redistribution (and hence possible subsequent failures) only within the cluster where it occurred. This means that a tree-partitioned network has the same line failure localization properties as the corresponding islanding strategy, thus offering similar potential in mitigating cascading failures.…”

“…The first one is to minimize the network congestion, ensuring that tree partitioning does not lead to exceptionally high congestion levels on the surviving network. This is also the objective function at the core of the recursive approach for tree partitioning proposed by [8].…”

“…The corresponding optimization problem tries to minimize the sum of absolute flows on the switched off lines while ensuring specific generator coherency constraints. So far, the tree partitioning problem been solved with a heuristic two-stage approach in [7], [8]. The first stage identifies the best partition of the network into clusters using spectral clustering methods, while the second stage solves one of the two aforementioned optimization problems.…”