The Holomorphic Embedding Method<?Pub _newline ?>Applied to the Power-Flow Problem

Rao, Shruti; Yang, Feng; Tylavsky, Daniel; Subramanian, Muthu Kumar

doi:10.1109/tpwrs.2015.2503423

Cited by 135 publications

(88 citation statements)

References 22 publications

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“…The HELM is based on the embedding of the classical PBEs into a holomorphic functional extension of them, which allows to take advantage of the properties granted by complex analyticity . In this case, the property of representing holomorphic functions by their corresponding power series is of special interest . As it is well known in power flow methods, buses are classified into PV, PQ, and slack buses, depending on specified parameters and unknown variables.…”

Section: Helm Reviewmentioning

confidence: 99%

“…

U_{i} = U_{i}^{s p}, i \in s l a c k,

where

U_{i}^{s p}

is the specified bus voltage magnitude. The corresponding embedded equation becomes:

U_{i} false(s false) = 1 + false(U_{i}^{s p} - 1 false) s, i \in s l a c k .

PQ buses: …”

Section: Helm Reviewmentioning

confidence: 99%

“…In PV buses, the PBE equation associated with the active power balance can be written as

P_{i} = Re ((), U_{i} true \sum_{k = 1}^{N} {Y_{i k}}^{*} {U_{k}}^{*}), i \in u,

where P i is the active power injection at bus i , which is a known parameter. The voltage magnitude is specified as follows:

(||, U_{i}) = U_{i}^{s p}, i \in u,

this equation is embedded yielding the following:

U_{i} false(s false) {U_{i}}^{*} false(s^{*} false) = 1 + ((), {(||, U_{i}^{s p})}^{2} - 1) s, i \in u .

…”

Section: Helm Reviewmentioning

confidence: 99%

“…The original HELM proposal only raised an embedding for the slack bus and the PQ buses . Further studies carried out embeddings of PV buses . Also, a polynomial ZIP load model is devised for HELM applications, and HELM‐based approaches are proposed to estimate saddle node bifurcations .…”

Section: Introductionmentioning

confidence: 99%

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Distributed slack bus model formulation for the holomorphic embedding load flow method

Ortega

Molina

Muñoz

et al. 2020

Int Trans Electr Energ Syst

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Summary Distributed slack bus (DSB) models for the resolution of power flow problems are a more realistic approach than the classical single slack bus concept. DSB models have been widely implemented in iterative approaches such as in Newton‐Raphson power flow methods. However, iterative algorithms may lead to incorrect solutions or may fail to reach convergence under inappropriate initial estimations. The holomorphic embedding load‐flow method (HELM) deals with the solution of the nonlinear power flow equations by means of complex analysis techniques, resulting in a deterministic and noniterative method, which is independent of initial estimations. As such, this paper proposes, from two different methodologies, a novel formulation and implementation of the DSB model for the HELM, which overcomes in that way the disadvantages of iterative methods and also incorporates the inherent advantages of DSB models. Moreover, this paper performs convergence and speed capability tests of the two proposed methodologies using two real‐size benchmark systems.

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Section: Helm Reviewmentioning

confidence: 99%

“…

U_{i} = U_{i}^{s p}, i \in s l a c k,

where

U_{i}^{s p}

is the specified bus voltage magnitude. The corresponding embedded equation becomes:

U_{i} false(s false) = 1 + false(U_{i}^{s p} - 1 false) s, i \in s l a c k .

PQ buses: …”

Section: Helm Reviewmentioning

confidence: 99%

“…In PV buses, the PBE equation associated with the active power balance can be written as

P_{i} = Re ((), U_{i} true \sum_{k = 1}^{N} {Y_{i k}}^{*} {U_{k}}^{*}), i \in u,

where P i is the active power injection at bus i , which is a known parameter. The voltage magnitude is specified as follows:

(||, U_{i}) = U_{i}^{s p}, i \in u,

this equation is embedded yielding the following:

U_{i} false(s false) {U_{i}}^{*} false(s^{*} false) = 1 + ((), {(||, U_{i}^{s p})}^{2} - 1) s, i \in u .

…”

Section: Helm Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Distributed slack bus model formulation for the holomorphic embedding load flow method

Ortega

Molina

Muñoz

et al. 2020

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

show abstract

“…Its mathematical foundation is complex analysis instead of iterative methods, and advanced mathematical theory is used. Some application cases have been reported [37][38][39][40]. Table 1.…”

Section: Introductionmentioning

confidence: 99%

A Novel Power Flow Algorithm for Traction Power Supply Systems Based on the Thévenin Equivalent

2018

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Abstract:With the rapid development of high-speed and heavy-haul railways throughout China, modern large power locomotives and electric multiple units (EMUs) have been applied in main railway lines. The high power requirements have brought about the problem of insufficient power supply capacity (PSC) of traction power supply systems (TPSSs). Thus, a convenient method of PSC assessment is meaningful and urgently needed. In this paper, a novel algorithm is proposed based on the Thévenin equivalent in order to calculate the PSC. In this algorithm, node voltage equations are converted into port characteristic equations, and the Newton-Raphson method is exploited to solve them. Based on this algorithm, the PSC of a typical high-speed railway is calculated through the repeated power flow (RPF). Subsequently, the effects of an optimized organization of train operations are analyzed. Compared to conventional algorithms, the proposed one has the advantages of fast convergence and an easy approach to multiple solutions and PV curves, which show vivid and visual information to TPSS designers and operators. A numerical analysis and case studies validate the effectiveness and feasibility of the proposed method, which can help to optimize the organization of train operations and design lines and enhance the reliability and safety of TPSSs.

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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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The Holomorphic Embedding MethodApplied to the Power-Flow Problem

Cited by 135 publications

References 22 publications

Distributed slack bus model formulation for the holomorphic embedding load flow method

Distributed slack bus model formulation for the holomorphic embedding load flow method

A Novel Power Flow Algorithm for Traction Power Supply Systems Based on the Thévenin Equivalent

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

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