Sensitivity of Transient Stability Critical Clearing Time

Abstract

Once the critical clearing time of a fault leading to transient instability has been computed, it is desirable to quantify its dependence on system parameters. We derive for a general power system model a new and exact formula for the first order sensitivity of the critical clearing time with respect to any system parameter. The formula is evaluated by integrating variational equations forward in time along the base case faulton trajectory and integrating adjoint variational equations backward in time along the post-fault trajectory. The computation avoids recomputing the critical clearing time for each parameter change and gives insight into how parameters influence power system transient stability. The computation of the sensitivity of the critical clearing time with respect to load impedances and generator inertias is illustrated on a 39-bus system.

Research Roadmap on Grid-Forming Inverters

“…If uncertainties are not considered in simulations, deterministic simulations might be unable to predict adverse dynamic behavior introduced by variable initial conditions and inputs. At the present time, a variety of tools have been proposed that are capable of handling uncertainties pertaining to fault clearing time (Sharma et al 2018) and initial conditions, such as trajectory sensitivity (Hiskens and Pai 2000), probabilistic collocation (Hockenberry and Lesieutre 2004), semidefinite programming (Choi, Seiler, and Dhople 2017), Lyapunov function families (Vu and Turitsyn 2016), and Taylor polynomials (Villegas Pico, Aliprantis, and Lin 2017). A common problem with these tools is the curse of dimensionality, which could be addressed by proper computational algorithms.…”

Critical Clearing Time Sensitivity for Inequality Constrained Systems

“…However, needs to tend to ∞ such that → ( ) for that characterization to be used. An effective approach was proposed in [13] to get a local characterization of ( ( )) at ; that approach will be used here directly. More details about the approach can be found in [13].…”

“…Finally, differentiating (13) and evaluating at for a sufficiently large value of using (15), we get,…”

Probabilistic framework for transient stability contingency ranking of power grids with active distribution networks: application in post disturbance security assessment

“…Deterministic approaches are usually designed to predict TS for online application. Conventionally, time‐domain simulation (TDS) [2], and the transient energy function [15–22] approaches have been used for dealing with TS issues in a deterministic way. Modern analysis, which is based on the machine learning algorithms and pattern recognition methods, provides more feasibility and flexibility in TS awareness and power system security classification [23–25].…”