Stability certification and identification of a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues need to be addressed for the systems with machine-learned components in the feedback loop. To develop a general theory for stability and stabilizability of neural network (NN)-controlled nonlinear systems subject to bounded parametric variations, a Lyapunov-based stability certificate is proposed and is further used to devise a maximal Lipschitz bound for a class of stabilizing NN controllers, and also a corresponding maximal Region of Attraction (RoA) within a user-specified safety set. To compute a robustly stabilizing NN controller that also maximizes the system’s long-run utility, a stability-guaranteed training (SGT) algorithm is proposed. The effectiveness of the proposed framework is validated through an illustrative example.

Prompt online detection of anomalies induced by malicious attacks enhances the efficacy of real-time operation and mitigation of attack, an indispensable part of any cyber-physical system (CPS) management. This article proposes a novel online rapid detection scheme that continuously monitors the data packet stream and infers the sequence of probability distributions, estimated as histograms, and alerts when a change in the histogram is detected, reporting both the attack as well as an estimate of its instant of commencement. A statistical data-driven attack model is proposed and employed that is general enough to represent two ubiquitous types of attacks on CPS: 1) replay and 2) bias-injection. The proposed detection framework relies on the fact that CPSs possess well-defined dynamics that are affected by quasistationary noise, which allows the histogram sequences of the system data packets to converge (to different distributions under the presence of the attack versus the absence of attack). The proposed online scheme detects an attack, and estimates the attack commencement time by relying on the computed distance between real-time estimated histogram versus apriori learned nominal histogram. Our formulation further sheds light on two different attack initiation-time-based subcases, “early” (attack starts before sufficient data of nominal behavior was collected to allow its histogram sequence to be closer to its nominal value) versus “late.” The designed algorithm of our scheme has linear time complexities in the dimension of data packets and algorithm parameters, which makes it suited for rapid detection. The proposed algorithm is implemented and validated on two real supervisory control and data acquisition system datasets, where a low detection delay demonstrates the effectiveness of the scheme.

Locating the source of low-frequency forced oscillation is an important aspect of bulk power system operation, and it facilitates operator’s intervention to the faulty component and timely implementation of mitigation measures. In this paper, a novel deep learning-based forced oscillation source locator is proposed to infer the oscillation-source using data from phasor measurement units (PMU). The locator is trained offline using the spectral information extracted from the sliding-window time-series data from simulated PMU measurements over a range of randomly chosen oscillatory events. The effectiveness of the proposed method has been validated on the Western Electricity Coordinating Council (WECC) 179-bus test system, comparing with an existing energy-based method. Noise-robustness of the method has also been evaluated.

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.