In this brief, a novel tracking differentiator (TD) based on discrete time optimal control (DTOC) is presented. In particular, using the state back-stepping method, a DTOC law for a discrete-time, double-integral system is determined by linearized criterion, which equips the TD with a simple structure. The analysis of the proposed TD reveals its filtering mechanism. Simulation results show that it performs well in signal tracking and differentiation acquisition, and reduces the computational resources needed. Experiments conducted on the speed and position detection system for a maglev train demonstrate that the proposed TD group, with moving average algorithm, can filter noises, amend distortion signals effectively, and compensate for phase delays when the train is passing over track joints.

The online small-signal stability assessment of electrical power grids is typically a challenging problem due to uncertainties and parameter variations of power system dynamics as well as the incurred high computational complexity. This paper proposes a novel theoretical framework for dynamic small-signal stability assessment of power grids by estimating the region of attraction (ROA) for operating states in real time. By analyzing the latest sampling data of power grids in a fixed time window, an up-to-date training set is constructed with the aid of converse Lyapunov function, which enables us to develop an online learning approach based on Gaussian Process (GP) to assess the stability level of power grids. As a result, an iteration algorithm is designed to update the assessment parameters by learning the input-output pairs in the training set. Theoretical analysis is conducted to ensure the existence of converse Lyapunov function for differential-algebraic system that serves to describe power system dynamics, as well as to estimate the region of attraction for operating states with a given confidence level. In particular, a practical method is proposed to leverage time series of phasor measurement unit (PMU) measurements including voltage/current magnitude, phase and frequency (i.e., PMU data) of real power grids for validating the online GP approach. Moreover, validations are taken to substantiate the proposed approach by using PMU data of real smart-grid infrastructure and IEEE test cases. The proposed assessment approach contributes to situational awareness of human operators in the control station, thereby taking proactive remedial actions prior to emergencies.

Online transmission line outage detection over the entire network enables timely corrective action to be taken, which prevents a local event from cascading into a large scale blackout. Line outage detection aims to detect an outage as soon as possible after it happened. Traditional methods either do not consider the transient dynamics following an outage or require a full Phasor Measurement Unit (PMU) deployment. Using voltage phase angle data collected from a limited number of PMUs, we propose a real-time dynamic outage detection scheme based on alternating current (AC) power flow model and statistical change detection theory. The proposed method can capture system dynamics since it retains the time-variant and nonlinear nature of the power system. The method is computationally efficient and scales to large and realistic networks. Extensive simulation studies on IEEE 39-bus and 2383-bus systems demonstrated the effectiveness of the proposed method.

The significant penetration of renewable energy resources into power systems introduces intermittent disturbances that drive the system away from its stable operating point (i.e., equilibrium). Nevertheless, as long as the system states are still contained inside a region of attraction (ROA), the system will finally return to the normal operating equilibrium. Thus, the ROA plays a crucial role in the stability assessment of dynamical power systems under uncertainties. This brief introduces a novel framework to construct the ROA of a power system centered around a stable equilibrium by using stable state trajectories of system dynamics. Most existing works on estimating ROA rely on analytic Lyapunov functions, which are subject to two limitations: the analytic Lyapunov functions may not be always readily available and the resulting ROA may be overly conservative. This work overcomes these two limitations by leveraging the converse Lyapunov theorem in control theory to eliminate the need for an analytic Lyapunov function and learning unknown Lyapunov functions with the Gaussian process (GP) approach. In addition, a GP upper confidence bound (GP-UCB)-based sampling algorithm is designed to reconcile the tradeoff between the exploitation for enlarging the ROA and the exploration for enhancing the confidence level of the sample region. Within the constructed ROA, it is guaranteed in the probability that the system state will converge to the stable equilibrium with a confidence level. Extensive simulations and experimental validations are conducted to substantiate the assessment approach for the ROA of IEEE test systems and a real smartgrid using phasor measurement unit (PMU) data. It is demonstrated that the proposed approach can significantly enlarge the estimated ROA compared to that of the analytic Lyapunov counterpart.