Bivariate holomorphic embedding applied to the power flow problem

Zhu, Yujia; Tylavsky, Daniel

doi:10.1109/naps.2016.7747975

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…It allows the HEM to extend from the physical germ solution while attributing physical meanings to the embedded variables , such as controlling the loading levels of load buses through loading scales. This special feature enhances the robustness of the HEM as any solution at is meaningful and could cooperate with other methods such as multi-stage strategy [37] . Also, the original HEM embeds one dimension into the power flow equations, making the solution a single-dimensional power series.…”

Section: Reviewmentioning

confidence: 95%

“…However, as noted by Ref. [37], the use of the Padé matrix in the HEM increases the condition number when the system approaches the nose point, consequently slowing down the HEM's convergence rate and introducing significant errors due to limited computational precision. Addressing this, a multi-stage HEM method MSHEM is proposed in Ref.…”

Section: Applications For Stability and Dynamic Problems 31 Voltage S...mentioning

confidence: 99%

“…Most of them embed only a single variable that uniformly controls generations or loads such as Refs. [11,37,71,72]. This approach proves inadequate when loads or generations change in varying proportions.…”

Section: Applications For Stability and Dynamic Problems 31 Voltage S...mentioning

confidence: 99%

“…While Stahl's theorem guarantees theoretical convergence, numerical convergence is not established. It is claimed and admitted that universal convergence cannot be guaranteed due to precision issues [32,37,81,82] . Specifically, finite computing precision restricts the meaningful number of power series terms when generating Padé approximants.…”

Section: Theoretical Convergence Vs Numerical Convergencementioning

confidence: 99%

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A Review on Applications of Holomorphic Embedding Methods

Huang,

Sun

2023

iEnergy

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The holomorphic embedding method (HEM) stands as a mathematical technique renowned for its favorable convergence properties when resolving algebraic systems involving complex variables. The key idea behind the HEM is to convert the task of solving complex algebraic equations into a series expansion involving one or multiple embedded complex variables. This transformation empowers the utilization of complex analysis tools to tackle the original problem effectively. Since the 2010s, the HEM has been applied to steady-state and dynamic problems in power systems and has shown superior convergence and robustness compared to traditional numerical methods. This paper provides a comprehensive review on the diverse applications of the HEM and its variants reported by the literature in the past decade. The paper discusses both the strengths and limitations of these HEMs and provides guidelines for practical applications. It also outlines the challenges and potential directions for future research in this field.

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Section: Reviewmentioning

confidence: 95%

Section: Applications For Stability and Dynamic Problems 31 Voltage S...mentioning

confidence: 99%

Section: Applications For Stability and Dynamic Problems 31 Voltage S...mentioning

confidence: 99%

Section: Theoretical Convergence Vs Numerical Convergencementioning

confidence: 99%

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A Review on Applications of Holomorphic Embedding Methods

Huang,

Sun

2023

iEnergy

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“…HELM has been implemented in voltage stability analysis [10] [11] and nonlinear network reduction [12]. Compared with step-by-step NR-based continuation flow methods, HELM is capable of calculating the load flow under different load scales simultaneously [13] [14], instead of step by step, which speeds up voltage stability. Moreover, the initial point of HELM is not necessarily10  , and it is applicable to large-scale transmission networks [15].…”

Section: A Related Workmentioning

confidence: 99%

Holomorphic Embedding Load Flow Modeling of the Three-phase Active Distribution Network

Ju¹

2018

Preprint

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With large-scale distributed generators (DGs) in an active distribution network (ADN), conventional load flow convergence failure is incurred by heavy power transmission. The Holomorphic Embedding Load Flow Method (HELM) has proven to be more robust than the Newton–Raphson method under heavy power transmission. At present, HELM is mainly designed for balanced transmission networks. In this study, we developed a three-phase HELM model to accommodate DGs, delta connection loads, and ZIP loads for ADN. The effectiveness and better performance of the proposed method under heavy load situations were validated using modified unbalanced IEEE 13, 34, 37, and 123 test feeders.

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A Multi-Dimensional Holomorphic Embedding Method to Solve AC Power Flows

Liu

Wang

et al. 2017

IEEE Access

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Bivariate holomorphic embedding applied to the power flow problem

Cited by 9 publications

References 13 publications

A Review on Applications of Holomorphic Embedding Methods

A Review on Applications of Holomorphic Embedding Methods

Holomorphic Embedding Load Flow Modeling of the Three-phase Active Distribution Network

A Multi-Dimensional Holomorphic Embedding Method to Solve AC Power Flows

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