Variable order and variable step-size integration method for transient analysis programs

1991 ◽  
Vol 6 (1) ◽  
pp. 206-213 ◽  
Author(s):  
T. Kato ◽  
K. Ikeuchi
Keyword(s):  
Transient Analysis ◽  
Integration Method ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

Power System Stability Computer Simulation Using a Differential-Algebraic Equation Solver

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
Jose Eduardo Onoda Pessanha ◽  
Osvaldo Saavedra ◽  
Alex Paz ◽  
Carlos Portugal
Keyword(s):  
Computer Simulation ◽  
Power System ◽  
Time Domain ◽  
Differential Algebraic Equations ◽  
System Stability ◽  
Variable Step Size ◽  
Variable Order ◽  
Differential Algebraic Equation ◽  
Step Size ◽  
Variable Step

The preset work tested a freely domain software for solving index zero and one systems of differential-algebraic equations, named as DASSL. The code encompasses an efficient variable step size and variable order based on BDF methods to solve a system of DAEs or ODEs. The code was applied in power systems time domain studies, i.e., synchronous machine angular transient stability and long-term voltage stability, using the Brazilian South-Southeast Equivalent Power System. Using this real power system model including fast and slow response control devices, it was possible to investigate the code capability in simulating different stability phenomena in the same run. The variable step size and variable order algorithm implemented in DASSL results in a very powerful tool for power system time domain computer simulation.

A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2021 ◽  
Author(s):  
Alberto Carini ◽  
Markus V. S. Lima ◽  
Hamed Yazdanpanah ◽  
Simone Orcioni ◽  
Stefania Cecchi
Keyword(s):  
Adaptive Filters ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step

Active control for vehicle interior noise using the improved iterative variable step-size and variable tap-length LMS algorithms

2019 ◽  
Vol 67 (6) ◽  
pp. 405-414 ◽  
Author(s):  
Ningning Liu ◽  
Yuedong Sun ◽  
Yansong Wang ◽  
Hui Guo ◽  
Bin Gao ◽  
...  
Keyword(s):  
Steady State ◽  
Noise Control ◽  
Convergence Speed ◽  
Interior Noise ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Vehicle Interior ◽  
Vehicle Interior Noise ◽  
Variable Step

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

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