Dynamic Security Assessment of Small-Signal Stability for Power Grids Using Windowed Online Gaussian Process

Abstract

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. Note to Practitioners—This paper was motivated by the problem of online assessment of power systems security but it also applies to other industrial control systems that have stable state trajectories. Existing approaches to security assessment of power systems generally focus on the adoption of various machine-learning algorithms by treating power grid as a “black box,” which ignores the intrinsic characteristics of power systems and thus restricts the inference performance. This paper proposes a new approach using limited sampling data and system dynamics to construct a domain of stability for power grids, which can reflect the evolution of security zones and provide more accurate predictions. In this work, we mathematically characterize the domain of stability for a practical power grid by analyzing and learning its state trajectories. Then we show how the proposed approach can be efficiently implemented online, which can timely alert human operators to abnormalities. Preliminary validations suggest that this approach is feasible and effective. In future research, we will incorporate it into an energy management system and test it in other industrial processes.