Resilience Indices for Power/Cyberphysical Systems

An engineered system is designed to deliver certain performance related to its quality-of-service, and while doing so, it must also maintain stable operation. Resilience of a system is its ability to continue to offer system performance stably, while withstanding any adverse events. Motivated by this concept, we propose to measure the resilience level of a power system by quantifying its stability level as measured by: transient stability margin (TSM), critical clearance time (CCT), relay margin (RM), and load security margin (LSM), as well as its performance level as measured by: load loss (LL) and recovery/repair time (RT) while being exposed to adverse events. For comparability, we also propose a normalization for each of the 6 measures to a number in the unit interval [0, 1], which is scale-invariant, and further probabilistically average each of those across all possible sequences of faults (of a specified length) against their occurrence probabilities to arrive at a set of 6 unit-interval valued indices. New polynomial complexity algorithms (in the number of generators) are proposed for estimating TSM (in form of volume of region of stability) and CCT; new quadratic program formulation for precise computation of RM is developed and implemented; also, new security and stability informed notions of LSM and LL are introduced and implemented by extending continuation power flow. Such quantification of resilience levels provides a numerical measure to compare the relative abilities of different power grids to withstand the impact of sequences of adverse events. The proposed approach is illustrated by computing and comparing the resilience of three similar power system topologies differing only in the location of generators. The framework is further validated by implementing it on the IEEE 30-bus test system.

I. Introduction

Resilience is a key system property of its ability to continue to provide quality-of-service/ performance withstanding disruptive faults/attacks [1], which in turn requires its continued stable operation. Given the frequency of recent outages [2] in power systems, a class of critical infrastructures, understanding and quantifying its resilience are of paramount importance. Since the occurrence of disturbances and faults can affect both the stability and the performance levels, one way to quantify the resilience level is by quantifying the post-fault-clearance stability level as well as performance level. In our work, the stability levels are measured using: transient stability margin (TSM), critical clearance time (CCT), relay margin (RM), and load security margin (LSM), while the performance levels are measured using: load loss (LL) and recovery time (RT).