scholarly journals On geometric and differentiation index of nonlinear differential-algebraic equations

2021 ◽  
Vol 54 (9) ◽  
pp. 186-191
Author(s):  
Yahao Chen ◽  
Stephan Trenn
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Differentiation Index

scholarly journals Regularization of Operator DAEs

2015 ◽  
Author(s):  
Robert Altmann
Keyword(s):  
General Framework ◽  
Stokes Equations ◽  
Differential Algebraic Equations ◽  
Navier Stokes ◽  
Algebraic Equations ◽  
Spatial Discretization ◽  
Navier Stokes Equations ◽  
First Order ◽  
Index 2 ◽  
Differentiation Index

A general framework for the regularization of constrained PDEs, also called operator differential-algebraic equations (DAEs), is presented. For this, we consider semi-explicit systems of first order which includes the Navier-Stokes equations. The proposed reformulation is consistent in the sense that the solution of the PDE remains untouched. However, one can observe improved numerical properties in terms of the sensitivity to perturbations and the fact that a spatial discretization leads to a DAE of lower index, i.e., of differentiation index $1$ instead of differentiation index 2.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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