On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Alharbi, Talal; Tostado‐Véliz, Marcos; Alrumayh, Omar

doi:10.3390/math9172019

Cited by 3 publications

(7 citation statements)

References 30 publications

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“…In [32], the authors analyzed various HONL solvers with cubic, 4th, and 5th order convergence. In this case, results were promising, which motivates further developments and studies in [33][34][35]. Nonetheless, this kind of solver must be further studied since, as shown in some recent works [8], they might be inefficient or even numerically unstable.…”

Section: Literature Reviewmentioning

confidence: 64%

On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

Tostado‐Véliz

Alharbi

et al. 2022

Mathematics

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Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of efficiently solving well- and ill-conditioned Power-Flow cases in a modern power-system paradigm. While the well-conditioned cases are easily solvable using standard methods, the ill-conditioned ones suppose a challenge for such solvers. In this regard, methods based on the Continuous Newton’s principle have demonstrated their ability to address ill-conditioned cases with acceptable efficiency. This paper demonstrates that the approaches proposed so far do not extract the best numerical properties of such solvers. To fill this gap, an optimization framework is proposed by which the parameters involved in the two-stage Runge–Kutta-based solvers are appropriately set, so that the stability and convergence order of the numerical mapping are maximized. By using the developed optimization technique, three solvers with quadratic, cubic, and 4th order of convergence are developed. The new proposals are tested on a variety of large-scale ill-conditioned cases. Results obtained were promising, outperforming other conventional and robust approaches.

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Section: Literature Reviewmentioning

confidence: 64%

On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

Tostado‐Véliz

Alharbi

et al. 2022

Mathematics

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“…N −2 . Keeping this in mind, it is clear that 𝛽 = 1 would yield the maximum order of convergence in (26), since this adoption would eliminate the error e (k) N −2 . Thus, assuming 𝛽 = 1, expression (26) can be developed, yielding…”

Section: Convergence Analysis Of the Developed Hommpmentioning

confidence: 99%

“…This way, it results useful comparing the developed solver with the Newton technique. In addition, we have included the sixth-order method (6OM) developed in [26] for comparison. This technique demonstrated a good performance in large-scale transmission networks, and it can be easily adapted to IMGs.…”

Section: Computational Comparison With Other Solversmentioning

confidence: 99%

“…This technique demonstrated a good performance in large-scale transmission networks, and it can be easily adapted to IMGs. In [26], the other two HONL solvers were developed; however, the 6OM turned out to be clearly superior. Therefore, it is reasonable including only the 6OM in the analysis.…”

Section: Computational Comparison With Other Solversmentioning

confidence: 99%

“…Proof. See [26]. □ It is also necessary to consider the computational cost of each function evaluation o(g) and Jacobian evaluation o(g ′ ).…”

Section: Computational Comparison With Other Solversmentioning

confidence: 99%

See 2 more Smart Citations

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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A Bus Privacy Preserving Decentralized Power Flow Algorithm Considering Neighbor Partial Derivative Information

Tan,

Peng,

et al. 2024

IEEE Access

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To ensure the privacy of power system users while maximizing the efficiency of decentralized computational resources, this paper presents a novel decentralized power flow algorithm. Its core focus lies in preserving bus privacy through the integration of neighboring partial derivative information. Initially, the algorithm utilizes partial derivative data from adjacent buses to formulate a bus-level voltage iterative function, rooted in the bus power balance equation. Each bus in the power network is treated as an individual computational unit managed by an agent. This process involves scanning the network's buses, computing estimated bus voltage values using a designated iteration formula, and iterating until convergence is achieved. Subsequent utilization of the latest neighbor information accelerates this iterative process. To fortify the algorithm's reliability, a strategy assessing local convergence, utilizing the Jacobian matrix at the solution's convergence, is proposed. The simulation results across various IEEE test systems unequivocally validate the proposed algorithm's efficacy in power flow computation, showcasing accelerated speed and robust antiinterference capabilities. Compared to the traditional decentralized power flow method at the bus level, this algorithm significantly optimizes the iterative process, slashing the number of iterations by a minimum of 1.36 times. Notably, this efficiency boost amplifies in larger system scales, boasting an impressive reduction of up to 9.21 times fewer iterations.

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On Various High-Order Newton-Like Power Flow Methods for Well and Ill-Conditioned Cases

Cited by 3 publications

References 30 publications

On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

On Optimal Settings for a Family of Runge–Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

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

A Bus Privacy Preserving Decentralized Power Flow Algorithm Considering Neighbor Partial Derivative Information

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