An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems

Pourbagher, Rohallah; Derakhshandeh, Sayed Yaser; Golshan, Mohammad

doi:10.1016/j.ijepes.2021.107425

Cited by 23 publications

(12 citation statements)

References 31 publications

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“…Trivially, it can be deduced that findings encountered in Theorem 1 are also applicable to (6), since it is a particular case of (7). It is worth mentioning that Theorem 2 establishes the necessary conditions.…”

Section: Mip For Pf Analysismentioning

confidence: 83%

“…However, this trend is changing nowadays and illconditioned PF problems are becoming more frequent in power system operation [5]. The main reason for that is an overall growing demand along the impossibility of upgrading infrastructures, which is leading the power systems to be operated close to their operability limits [6]. Nevertheless, other reasons are provoking ill-conditioning in PF cases, like the increasing deployment of electronic devices (FACTS and D-FACTS) [7].…”

Section: A Motivationmentioning

confidence: 99%

“…The other category of solvers is based on the Levenberg method [6], [7], [30]- [33]. By this technique, stability of NR is improved by intentionally well conditioning the Jacobian matrix.…”

Section: B Literature Reviewmentioning

confidence: 99%

“…Instead of using conventional nonlinear iterative solvers, other authors have tried to address PF ill-conditioned problems from alternative point of views. Such is the case of the metaheuristic-like solvers [35]; Continuation approaches [6], [36], [37] and homotopy/holomorphic algorithms [38]- [40]. Nevertheless, these solvers still present serious problems.…”

Section: B Literature Reviewmentioning

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: Mip For Pf Analysismentioning

confidence: 83%

Section: A Motivationmentioning

confidence: 99%

“…The other category of solvers is based on the Levenberg method [6], [7], [30]- [33]. By this technique, stability of NR is improved by intentionally well conditioning the Jacobian matrix.…”

Section: B Literature Reviewmentioning

confidence: 99%

Section: B Literature Reviewmentioning

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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“…Therefore, one can consider that a PF solver is efficient if its computational burden is comparable or lower than that showed by NR. In this sense, operators may face important challenges due to the unsolvability of PF problems, especially in stressed systems 10,11 …”

Section: Introductionmentioning

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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Power system voltage stabilization using model predictive control

Das,

Sengupta

2023

Electr Eng

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An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems

Cited by 23 publications

References 31 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

Power system voltage stabilization using model predictive control

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