Stability Analysis Sample Clauses

Stability Analysis. ▇▇▇▇’s stability analysis examined the impact of the Retiring Generating Facility by evaluating local and regional stability performance on the MISO transmission system in the Bench and Study cases. The most recent dynamics data from Ameren was used to develop these cases. DSATools – TSAT was used to perform transient voltage analyses. Fault analysis was performed on bench and study cases for the fault lists as specified by Ameren. The results were compared to find if there are any criteria violations due to the unit(s) change of status.

Stability Analysis. ∈ ∈ ∈ In this section, we analyze whether the system (186), (187), with given Kσk and Lσk , is stable for some given bounds on the sampling interval, i.e. hk [h, h] for all k N. The stability analysis is based on the ideas in [17], in which stability of networked control systems is discussed. As in [17], the uncertain parameter hk, k N appears nonlinearly in (187) through A¯hk and B¯hk . To make the system amenable for analysis, a procedure is proposed to overapproximate system (186), (187) by a polytopic system with norm-bounded additive uncertainty, i.e., ▇ x¯k+1 = Σ αl (Fσ ,j + Gj∆kHσ ) x¯k, (188) j=1 ▇ ▇ where Fl,j ∈ Rn×n, Gj ∈ Rn×q, Hl ∈ Rq×n, for l ∈ {1, . . . , nF } and j ∈ {1, . . . , M }, with M the number of vertices of the polytope. The vector αk = [α1 . . . αM ]T ∈ A, k ∈ N, is time-varying with j=1 A =nα ∈ RM ΣM αj = 1 and αj ≥ 0 for j ∈ {1, . . . , M }, ∈ { } ∈ and ∆k ∆, where ∆ is a norm-bounded set of matrices in Rq×q that describes the additive un- certainty. Equation (188) is an overapproximation of (186) in the sense that for all l 1, . . . , nF , it holds that n Σ⊆ nA˜c,h,l | h ∈ [h, h], M j=1 αj (Fl,j + Gj∆Hl) | α ∈ A, ∆ ∈ ∆,. (189) We now provide a gridding-based procedure to overapproximate system (186), such that (189) holds, after which we can provide conditions for stability. Procedure 1. Select M distinct sampling intervals h˜1, . . . , h˜M as grid points, such that h =: h˜1 ≤ h˜2 < . . . < h˜M —1 ≤ h˜M := h. • Define c,▇▇ ,l Fl,j := A˜ ˜ .