Toward Simulation-Free Estimation of Critical Clearing Time

Abstract

Abstract-Contingency screening for transient stability of large scale, strongly nonlinear, interconnected power systems is one of the most computationally challenging parts of Dynamic Security Assessment and requires huge resources to perform time-domain simulations-based assessment. To reduce computational cost of time-domain simulations, direct energy methods have been extensively developed. However, these methods, as well as other existing methods, still rely on time-consuming numerical integration of the fault-on dynamics. This task is computationally hard, since possibly thousands of contingencies need to be scanned and thousands of accompanied fault-on dynamics simulations need to be performed and stored on a regular basis. In this paper, we introduce a novel framework to eliminate the need for fault-on dynamics simulations in contingency screening. This simulationfree framework is based on bounding the fault-on dynamics and extending the recently introduced Lyapunov Function Family approach for transient stability analysis of structure-preserving model. In turn, a lower bound of the critical clearing time (CCT) is obtained by solving convex optimization problems without relying on any time-domain simulations. A comprehensive analysis is carried out to validate this novel technique on a number of IEEE test cases.

Inverse Stability Problem and Applications to Renewables Integration

“…Theorem 1: Consider a given initial state δ 0 inside the set P. Assume that the EP of the system takes different values in the set A(δ 0 ) = Λ ∩ B(δ 0 ), where the set B(δ 0 ) is defined as in (9). Then, the system state always converges from the given initial state δ 0 to the EP.…”

“…Here a kj = V k V j B kj , where B kj is the (normalized) susceptance of the transmission line {k, j} connecting the k th bus and j th bus. N k is the set of neighboring buses of the k th bus (see [9] for more details). Let δ(t) = [δ 1 (t) ... δ |N | (t)δ 1 (t) ...δ |N | (t)] be the state of the system (1) at time t (for simplicity, we will denote the system state by δ).…”

Sensitivity of Transient Stability Critical Clearing Time

“…For definiteness we could now choose the sign of w(α) so that S(x, α 0 ) > 0 for unstable trajectories and S(x, α 0 ) < 0 for stable trajectories. However, any consistent sign for w(α) and S can be used, since the sensitivity formula (13) does not depend on the sign of S.…”

“…To compute the sensitivity of the critical clearing time with respect to load impedances α Z and generator inertias α H as parameters, we use MATLAB to evaluate all the steps in Section V and hence evaluate formula (13). All the numerical integrations use the MATLAB ode15s solver.…”

“…An exact computation of critical clearing time requires numerical integration of fault-on and post-fault trajectories and identification of the controlling unstable equilibrium point that determines the relevant portion of the stability boundary. Critical clearing time is a well-established engineering metric of transient stability and its exact computation by nonlinear analysis and numerical integration [1]- [3] and its approximate computation by energy methods [4]- [13] has been extensively studied.…”