A powerful method for solving the power flow problem in the ill-conditioned systems

Pourbagher, Rohallah; Derakhshandeh, Sayed Yaser

doi:10.1016/j.ijepes.2017.06.032

Cited by 38 publications

(26 citation statements)

References 34 publications

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“…The adaptive scheme has been used for this method. High‐order LM (HLM) method Nonmonotone line search with corrected LM method (NM‐LM) Jacobian adjusted LM (LMJ) method .…”

Section: Resultsmentioning

confidence: 99%

“…19 • Nonmonotone line search with corrected LM method (NM-LM). 20 • Jacobian adjusted LM (LMJ) method. 30,31 The adaptive scheme 19 has been used for this solver.…”

Section: Resultsmentioning

confidence: 99%

“…An LF solver based on the Levenberg‐Marquardt (LM) method has been recently presented by Milano, which is a very promising technique for ill‐conditioned cases. Several improvements of the standard LM method have been proposed by Pourbagher and Derakhshandeh …”

Section: Introductionmentioning

confidence: 99%

“…Several improvements of the standard LM method have been proposed by Pourbagher and Derakhshandeh. 19,20 Second-order and Levenberg methods are suitable for small-and medium-scale ill-conditioned cases 8,19,20 ; nevertheless, their convergence becomes very slow in large-scale systems. Moreover, they may fail in large-scale ill-conditioned systems if the initial guess point is not good enough.…”

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confidence: 99%

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Development of different load flow methods for solving large‐scale ill‐conditioned systems

Tostado‐Véliz

Kamel

2018

Int Trans Electr Energ Syst

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Summary In this paper, several methods are proposed to find the load flow (LF) solution of large‐scale ill‐conditioned systems. These methods are based on the Adams‐Bashforth formulation. With the use of the proposed methods, the convergence problems of the most popular LF methods are addressed especially when the flat initial guess point is considered. The proposed methods are validated using three ill‐conditioned systems: the modified IEEE 300‐bus system, the 3375‐bus Polish system, and a 13 659‐bus portion of the European transmission system. The obtained results prove that the proposed methods constitute a family of robust and efficient methods for the LF problem.

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“…The adaptive scheme has been used for this method. High‐order LM (HLM) method Nonmonotone line search with corrected LM method (NM‐LM) Jacobian adjusted LM (LMJ) method .…”

Section: Resultsmentioning

confidence: 99%

“…19 • Nonmonotone line search with corrected LM method (NM-LM). 20 • Jacobian adjusted LM (LMJ) method. 30,31 The adaptive scheme 19 has been used for this solver.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Development of different load flow methods for solving large‐scale ill‐conditioned systems

Tostado‐Véliz

Kamel

2018

Int Trans Electr Energ Syst

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“…Recently, the Levenberg–Marquardt's method has been profusely studied for solving the PF problem of ill‐conditioned systems [5, 16]. These methodologies are quite robust; however, they may show slow convergence or produce an inaccurate solution [17].…”

Section: Introductionmentioning

confidence: 99%

Promising framework based on multistep continuous Newton scheme for developing robust PF methods

Tostado‐Véliz¹,

Kamel

2019

IET Generation, Transmission & Distribution

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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 powerful method for solving the power flow problem in the ill-conditioned systems

Cited by 38 publications

References 34 publications

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Promising framework based on multistep continuous Newton scheme for developing robust PF methods

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

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