A local-global stepsize control for multistep methods applied to semi-explicit index 1 differential-algebraic equations

1999 ◽  
Vol 6 (3) ◽  
pp. 463-492 ◽  
Author(s):  
G. Yu. Kulikov ◽  
S. K. Shindin
Keyword(s):  
Multistep Methods ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Stepsize Control

Convergence of Linear Multistep Methods and One-Leg Methods for Index-2 Differential-Algebraic Equations with a Variable Delay

2012 ◽  
Vol 4 (5) ◽  
pp. 636-646 ◽  
Author(s):  
Hongliang Liu ◽  
Aiguo Xiao
Keyword(s):  
Multistep Methods ◽  
Differential Algebraic Equations ◽  
Linear Multistep Methods ◽  
Variable Delay ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Convergence Results ◽  
Index 2

AbstractLinear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay. The corresponding convergence results are obtained and successfully confirmed by some numerical examples. The results obtained in this work extend the corresponding ones in literature.

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>

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