Robust Stability Assessment in the Presence of Load Dynamics Uncertainty

Abstract

Abstract-Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical "robust stability" criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of Robust Stability Assessment (RSA) that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies.

Stochastic Small Signal Stability of a Power System with Uncertainties

“…Based on Section 3.2, P can be obtained by solving the linear matrix inequality (LMI) (11). Then the Lyapunov function can be selected as V(x) = x T Px.…”

“…Then, from (11), α 4 can be chosen such that 1 2 Tr(Σ T PΣ) ≤ α 4 ( ΣΣ T ) (A8) α 1 and α 2 can be selected as the minimum eigenvalue and the maximum eigenvalue of P, respectively. Then the system (9) satisfies the stochastic stability index (3) and (12) is satisfied.…”

“…Furthermore, the adaptive control based strategies [7,8], frequency-domain approach [9], and particle swarm optimization-based methods [10] are adopted to enhance power system stability with stochastic disturbances. In [11], uncertainties are characterized by a compact set, then robust optimization is carried out for the worst-case scenario, or the random factors are measured in real time in the context of the adaptive control. However, these approaches rely on a deterministic modeling of the power system, and this means that the electromechanical transient of the power system is still governed by ordinary differential equations, and hence, the stochastic nature of the system dynamic process is neglected.…”

Optimal Steady-State Voltage Control Using Gaussian Process Learning

“…Another contemporary trend in voltage control research focuses on the uncertainties such as those brought by intermittent renewable sources and electrical vehicles [2], [11], [12]. As such uncertainties pose additional challenges in operation, most of the proposed voltage control algorithms, including decentralized controls under limited communication conditions, require certain assumptions/simplifications to perform well [8], [13]. Some important assumptions are negligible line losses [14], adjustable P Q injections located at all nodes [10], [15], or purely resistive network [16].…”

On differential equations with interval coefficients

“…Differential equations with interval coefficients arise also when stability problems are examined. We naturally encounter with the robust (or interval) stability concept when we study real‐life problems in control theory . A system is called robust (interval absolutely stable), if it is absolutely stable for each matrix, the elements of which lie in the specified intervals .…”