Critical Clearing Time Sensitivity for Inequality Constrained Systems

TL;DR

This paper introduces a new approach to analyze how the critical clearing time in power systems with constraints depends on system parameters, aiding in better protection and operation strategies during disturbances.

Contribution

It derives the first-order sensitivity of critical clearing time for constrained power systems using trajectory sensitivity analysis, providing insights into system stability and constraints.

Findings

CCT sensitivity depends on system parameters like inertia and power input.

The method is demonstrated on single-machine and multi-machine systems.

Results help improve protection settings and operational planning.

Abstract

With the growth of renewable generation (RG) and the development of associated ride through curves serving as operating limits, during disturbances, on violation of these limits, the power system is at risk of losing large amounts of generation. In order to identify preventive control measures that avoid such scenarios from manifesting, the power system must be modeled as a constrained dynamical system. For such systems, the interplay of feasibility region (man-made limits) and stability region (natural dynamical system response) results in a positively invariant region in state space known as the constrained stability region (CSR). After the occurrence of a disturbance, as it is desirable for the system trajectory to lie within the CSR, critical clearing time (CCT) must be defined with respect to the CSR instead of the stability region as is done traditionally. The sensitivity of CCT to system parameters of constrained systems then becomes beneficial for planning/revising protection settings (which impact feasible region) and/or operation (which impact dynamics). In this paper, we derive the first order CCT sensitivity of generic constrained power systems using the efficient power system trajectory sensitivity computation, pioneered by Hiskens in [1]. The results are illustrated for a single-machine infinite-bus (SMIB) system as well as a multi-machine system in order to gain meaningful insight into the dependence between ability to meet constraints, system stability, and changes occurring in power system parameters, such as, mechanical power input and inertia.