Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Тутуева, Александра; Butusov, Denis N.

doi:10.3390/math9192463

Cited by 4 publications

(11 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be noted that using the DF (PEC) methods requires twice the amount of memory compared to using ABM. However, these algorithms can be further optimized using the approach given in [17].…”

Section: Discussionmentioning

confidence: 99%

“…In terms of computational efficiency, ref. [17] showed that semi-explicit and semiimplicit ABM methods are efficient methods compared to other linear multistep methods (such as ABM and BDF). Furthermore, it was shown in [17] that semi-explicit and semiimplicit ABM methods are sufficiently flexible to optimize the computations according to the problem features.…”

Section: Discussionmentioning

confidence: 99%

“…Let us consider the semi-explicit and semi-implicit modifications of the predictorcorrector Adams-Bashforth-Moulton formula as described in [15]. In this section, we use the same methodology as in [17]. In the original ABM integration, all calculations are explicit.…”

Section: Methodsmentioning

confidence: 99%

“…Following the ideas of [17] and particularly [18] for a two-dimensional problem, matrix A of the test problem is built such that the conjugate eigenvalues λ 1,2 defined in Section 2.2 are the eigenvalues of this matrix A. This will allow us to study the same stability regions with values R(|λ 1,2 |).…”

Section: Test Problem For Estimating Methods Stabilitymentioning

confidence: 99%

“…Since semi-explicit methods do not exist for ODEs with less than two dimensions, we cannot use Dahlquist's first-order test equation. Instead, we choose the similar approach used in [17] that applies a two-dimensional test problem. Let us compose a matrix A of dimension 2 × 2 for the studied problem:…”

Section: Stability Analysismentioning

confidence: 99%

See 4 more Smart Citations

Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods

et al. 2022

Self Cite

View full text Add to dashboard Cite

Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-implicit predictor–corrector methods based on the backward differentiation formula and Adams–Bashforth methods. We provide a thorough study of the numerical stability and performance of new methods and compare their stability with semi-explicit and semi-implicit Adams–Bashforth–Moulton methods and their performance with conventional linear multistep methods: Adams–Bashforth, Adams–Moulton, and BDF. The numerical stability of the investigated methods was assessed by plotting stability regions and their performances were assessed by plotting error versus CPU time plots. The mathematical developments leading to the increase in numerical stability and performance are carefully reported. The obtained results show the potential superiority of semi-explicit and semi-implicit methods over conventional linear multistep algorithms.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Test Problem For Estimating Methods Stabilitymentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

See 3 more Smart Citations

Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

Evaluation of Numerical Methods for TSCOPF in a Large Interconnected System

et al. 2022

View full text Add to dashboard Cite

Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of power systems. However, they require a high computational effort and can suffer from convergence problems when applied to large systems. This study analyzes the performance of eleven numerical integration algorithms applied to ordinary differential equations that represent power system dynamics in a TSCOPF model. The analyzed algorithms cover a range of explicit and implicit methods, including the recently published semi-explicit and semi-implicit Adams-Bashforth-Moulton formulas, together with several initialization techniques. The integration methods are applied to a model of the Iberian Peninsula power system, and their performance is discussed in terms of convergence, accuracy, and computational effort. The results show that most implicit methods converge to the solution, even for large time steps. In particular, the Adams-Moulton method of order two and Simpson's rule, both initialized with RK4, outperform the trapezoidal rule, which is the default method in TSCOPF models.INDEX TERMS numerical methods, optimal power flow, power system stability, transient stability,Number of synchronous generators and buses, respectively. c iCost coefficient of the synchronous generator at bus i (in e M W h ). P g,i,0 , Q g,i,0Steady-state active and reactive power generated by the synchronous generator at bus i (in p.u.). P g,i,t , Q g,i,tActive and reactive power generated by the synchronous generator at bus i and time t (in p.u.).Active and reactive load at bus i and time t (in p.u.). P e,i,t , Q e,i,tElectric output active and reactive power in the rotor of the synchronous generator at bus i and time t (in p.u.). P m,iMechanical input power of the synchronous generator at bus i (in p.u.).V i,0 , α i,0 Steady state voltage magnitude and angle at bus i (in p.u. and rad, respectively). V i,t , α i,tVoltage magnitude and angle at bus i and time t (in p.u. and rad, respectively). I brSteady state current of branch br (in p.u.). Y i,j , θ i,jMagnitude and angle of the element (i, j) in the bus admittance matrix Y (in p.u. and rad, respectively). Y L,br,j , θ L,br,j Magnitude and angle of the element (br, j) in the line admittance matrix Y L (in p.u. and rad, respectively). δ i,tRotor angle of synchronous generator i at time t in synchronously rotating reference frame (in rad). δ COI,tThe rotor angle corresponds to the center of inertia (COI) at time t (in rad). ω s Synchronous rotor speed (in rad s ). ∆ω i,0Steady-state rotor speed deviation of the

show abstract

On the existence and numerical simulation of Cholera epidemic model

Shah,

Ahmad,

Shafiullah

et al. 2024

Open Physics

View full text Add to dashboard Cite

A model describing the transmission dynamics of cholera is considered in this article. The concerned model is investigated under the Caputo-Fabrizio fractal fractional derivative. The objective of this article is to study theoretical and numerical results for the model under our consideration. Classical fixed point approach is used to obtain sufficient conditions for the existence of solution to the proposed model. Adam’s Bashforth numerical method is utilized for the numerical interpretation of the suggested model. The considered technique is a powerful mathematical tool, that provides a numerical solution for the concerned problem. To discuss the transmission dynamics of the considered model, several graphical presentations are given.

show abstract

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Cited by 4 publications

References 22 publications

Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods

Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods

Evaluation of Numerical Methods for TSCOPF in a Large Interconnected System

On the existence and numerical simulation of Cholera epidemic model

Contact Info

Product

Resources

About