Small Signal Stability Analysis for Non Index 1 Hessenberg Form Systems of Delay Differential Algebraic Equations
This paper focuses on the small signal stability analysis of systems modelled as differential algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines.
IEEE Transactions on Circuits and Systems I: Regular Papers