Families of moment matching based, low order approximations for linear systems

IEEE Trans. Automat. Contr.

2017

Abstract-The problem of model reduction for nonlinear differential-algebraic systems is addressed using the notions of moment and of steady-state response. These notions are formally introduced for this class of systems and families of nonlinear differential-algebraic reduced order models achieving moment matching with additional properties are presented. Stronger results for the special class of linear singular systems are provided. Two simple examples illustrate the proposed technique.

“…Proof of Theorem 4: Claim (C1): Since G 1 is such that σ(S) ∩ σ(S − G 1 L) = ∅, ξ 1 = (S − G 1 L)ξ 1 + G 1 u is controllable, see [44]. Claim (C2): Recall that…”

Section: Acknowledgmentmentioning

confidence: 98%

Steady-State Matching and Model Reduction for Systems of Differential–Algebraic Equations

IEEE Trans. Automat. Contr.

2017

“…The family of systems (4) is a model of system (1) at S if G is such that σ(S) ∩ σ(S − GL) = ∅ and [17], [18] (−1)…”

Section: B Mimo Systemsmentioning

confidence: 99%

Model reduction of power systems with preservation of slow and poorly damped modes

2015 IEEE Power &Amp; Energy Society General Meeting

2015

Abstract-In this paper a recently proposed variation of the Krylov subspace method for model reduction is applied to power systems. The technique allows to easily enforce constraints on the reduced order model. Herein this is used to preserve the slow and poorly damped modes of the systems in the reduced order model. We analyze the role that these modes have in obtaining a good approximation and we show that the order of the reduced model can be decreased if the "right" modes are preserved. We validate the theory on the 68-Bus, 16-Machine, 5-Area benchmark system (NETS-NYPS).

“…Consider the purely fast fifth order singular system described by the equations Let σ(S) = {0, ±2.85j} and L and ω(0) in (9) be randomly generated. Then, system (17) is a third order reduced order model of system (22), namely…”

Section: A a Classical Fast Subsystem Examplementioning

confidence: 99%

Model reduction by moment matching for linear singular systems

2015 54th IEEE Conference on Decision and Control (CDC)

2015

Abstract-The paper presents a moment matching approach to the model reduction problem for singular systems. Combining the interpolation-based and the steady-state-based description of moment, a partitioned formulation of the Krylov projector is obtained. Several implications of this result are investigated and different families of reduced order models are proposed. The possibility to maintain structural properties of the fast subsystem is studied. Two examples illustrate the results of the paper.