On the Applicability of Two Families of Cubic Techniques for Power Flow Analysis

Tostado‐Véliz, Marcos; Kamel, Salah; Ruíz-Rodríguez, F.J.

doi:10.3390/en14144108

Cited by 5 publications

(14 citation statements)

References 44 publications

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“…As a sake of example, it is desirable that robust methodologies meet the Contraction Mapping Theorem (e.g. see [8]). However, this kind of analysis is infrequent in the related literature.…”

Section: A Motivationmentioning

confidence: 99%

“…Definition 2 [8]. Nonexpansive and Contractive Mappings: let ⊂ ℝ be a nonempty convex subset of a real Banach space.…”

Section: B Theoretical Backgroundmentioning

confidence: 99%

“…One expects that fixed points of an iterative map to be sinks, in order to ensure its stability. The following Theorem provides a sufficient condition about a sequence { } =0 ∞ , defined by an iterative map +1 = ( ), for converging to * Theorem 1 [8]. Contraction-Mapping Theorem: suppose that ∶ ⊂ ℝ → ℝ maps a closed set 0 ⊂ into itself and that:…”

Section: B Theoretical Backgroundmentioning

confidence: 99%

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Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

et al. 2021

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Power Flow solution of realistic ill-conditioned systems has recently attracted huge attention. Nevertheless, there are still some gaps in this field. For example, most of available references do not provide exhaustive theoretical analysis about convergence properties of proposed approaches. In addition, efficient solution of large-scale ill-conditioned systems is still an open topic. This paper tackles these issues by comprehensively studying the suitability of the Mann Iteration Process for the solution of ill-conditioned systems. A comprehensive theoretical analysis is provided, from which is demonstrated that the Mann Iteration Process has with asymptotic stability, may achieve a high convergence rate and constitutes a robust methodology, improving the contractive properties of the Newton-Raphson method. Moreover, some interesting links with other Power-Flow approaches are obtained as by-product. Several numerical experiments serve to confirm the theoretical findings and to compare the performance of the Mann Iteration Process with other well-known PF solvers. In all cases, the results obtained with the Mann Iteration Process are superior to that obtained using other methodologies, being able to efficiently solve various large-scale ill-conditioned systems.INDEX TERMS power-flow analysis, ill-conditioned systems, large-scale systems, Mann iteration process

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Section: A Motivationmentioning

confidence: 99%

“…Definition 2 [8]. Nonexpansive and Contractive Mappings: let ⊂ ℝ be a nonempty convex subset of a real Banach space.…”

Section: B Theoretical Backgroundmentioning

confidence: 99%

Section: B Theoretical Backgroundmentioning

confidence: 99%

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Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

et al. 2021

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“…This feature allows Darvishi's method to usually converge faster than NR employing less number of iterations and consuming less computation time 39 . However, this technique is quite weak 40 . To compensate for this drawback, Darvishi's method is combined with the Trapezoidal rule, 17 which provides robustness to the algorithm 40 …”

Section: Foundations and Remarksmentioning

confidence: 99%

“…Thus, if a PF solver is stable, its convergence is not guaranteed, but, if contrary, the PF solver would be unable to successfully converge. Unstable solvers are normally characterized by an erratic pattern in which the residuals tend to exponentially grow each iteration 40 …”

Section: Mathematical Backgroundmentioning

confidence: 99%

Solving realistic large‐scale ill‐conditioned power flow cases based on combination of numerical solvers

Tostado‐Véliz

Hasanien

Turky

et al. 2021

Int Trans Electr Energ Syst

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With the increasing electricity consumption and difficulty in upgrading existing infrastructures, ill-conditioned power flow (PF) cases are becoming more frequent nowadays. In this context, classical robust solvers may be unsuitable for realistic networks, which typically encompass thousands of buses, because of their high computational burden or low convergence rate. This article tackles this issue by proposing a novel PF solver, which presents acceptable robustness and efficiency in solving large-scale ill-conditioned systems. The proposed algorithm collects the advantage of various numerical solvers, which by separate present different weaknesses, but actuating in coordination their strengths can be jointly exploited. More precisely, the robust Forward-Euler and Trapezoidal rules are combined with the efficient Darvishi cubic technique. Thereby, an original predictor-corrector algorithm is developed to effectively coordinate the different numerical algorithms involved, obtaining a robust but efficient yet solution procedure. Various large-scale illconditioned benchmark systems are studied under different stressing conditions. The results obtained with the developed technique are promising, outperforming other robust and standard PF solvers. K E Y W O R D S computational efficiency, ill-conditioned cases, large-scale systems, power flowList of Symbols and Abbreviations: t, time instant; (.) sch , scheduled value; i, denotes the ith bus of the system; k, Denotes the kth iteration of an iterative algorithm; n l , total number of PQ buses; n g , total number of PV buses; n, size of the power flow state vector (n = 2n l + n g in polar coordinates); N, number of iterative loops; ω, state vector of a dynamic system; Δt, time step; P, nodal active power injection; Q, nodal reactive power injection; V∠δ, nodal voltage; Y∠θ, element of the admittance matrix; h, step size; ε, convergence tolerance; k max , maximum number of iterations allowed; g, power flow equations; [Á] T , transpose operator; [Á] À1 , inverse operator; kÁk ∞ , infinity norm; r x , vector/matrix gradient (first derivative) with respect to x; max{a,b}, returns b if b > a and a otherwise; min{a,b}, returns b if b < a and a otherwise; x, y, z, power flow state vector; δ PV , voltage angles at PV buses; δ PQ , voltage angles at PQ buses; V PQ , voltage magnitudes at PQ buses; g x , Jacobian matrix formed by the first partial derivatives of g with respect x; I, identity matrix; BEM, Backward-Euler method; HKW, Heun-King Werner approach; HOLM, high order Levenberg-Marquardt solver; LU, lower-upper; NR, Newton-Raphson technique; OMP, optimal multiplier method in polar coordinates; PF, power flow; TR, trapezoidal rule applied to PF analysis; 3OD, darvishi's cubic method applied to PF analysis.

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A novel Newton‐like method with high convergence rate for efficient power‐flow solution in isolated microgrids

Tostado‐Véliz

Bayat

Ghadimi

2022

IET Generation Trans & Dist

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Power‐Flow (PF) solution in isolated microgrids has attracted notable attention recently, because these systems present various particularities compared with the traditional PF solution in large meshed transmission networks. In this sense, this paper develops a novel Newton‐like PF solver for isolated microgrids. The new proposal is based on the Modified Midpoint method and shows high convergence order with relatively low computational burden. These characteristics bring superior theoretical performance compared with the standard Newton–Raphson (NR) method and other high order techniques, which has been conventionally used. Extensive simulations are performed on various small‐, and large‐scale benchmark Microgrids under different loading conditions and R/X ratios. Results provided serve to confirm the theoretical features of the developed solver, outperforming the NR technique as well as other recently developed solvers in all the studied systems with acceptable reliability even under high stressed conditions.

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On the Applicability of Two Families of Cubic Techniques for Power Flow Analysis

Cited by 5 publications

References 44 publications

Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

Solving realistic large‐scale ill‐conditioned power flow cases based on combination of numerical solvers

A novel Newton‐like method with high convergence rate for efficient power‐flow solution in isolated microgrids

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