HELM: The Holomorphic
        Embedding Load-Flow Method.
        Foundations and Implementations

Trias, Antonio

doi:10.1561/3100000015

Cited by 14 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1) faster evaluation to obtain results for a specific value of s1, s2, …, sD; 2) more computationally efficient to obtain the diagonal Padé approximants for an MPS; 3) less computation burden: the computation complexity of univariate quotient-difference algorithm is O(K 2 ) (K is the order of the denominator of MPA), which is obviously less than the traditional matrix method (i.e. O(M 3 )) [23]. The superiority of using the MQD method to enlarge the ROC of the analytical solutions will be demonstrated in Section V.…”

Section: Multivariate Quotient-difference Methods For Multivariate Pa...mentioning

confidence: 99%

Power flow analytical solutions and multi-dimensional voltage stability boundary based on the multivariate quotient-difference method

Liu

Lai

2021

CSEE JPES

View full text Add to dashboard Cite

This paper proposes a novel Multivariate Quotient-Difference (MQD) method to obtain the approximate analytical solution for AC power flow equations. Hence, in the online environment, the power flow solutions covering different operating conditions can be directly obtained by plugging in values into multiple symbolic variables, such that the power injections and consumptions of selected buses or areas can be independently adjusted. This method first derives a power flow solution by Multivariate Power Series (MPS). Next, the MQD method is applied to transform the obtained MPS to Multivariate Padé Approximants (MPA) to expand the Radius of Convergence (ROC), so that the accuracy of the derived analytical solution can be significantly increased. Besides, the hypersurface of voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA. This direct method for power flow solution and voltage stability boundary is fast for many online applications, since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions. The proposed method is validated in detail on the New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.

show abstract

Section: Multivariate Quotient-difference Methods For Multivariate Pa...mentioning

confidence: 99%

Power flow analytical solutions and multi-dimensional voltage stability boundary based on the multivariate quotient-difference method

Liu

Lai

2021

CSEE JPES

View full text Add to dashboard Cite

show abstract

“…It uses the techniques of complex and deterministic analysis. In brief, the HELM mechanism comprises the following steps [13,14]:…”

Section: Holomorphic Embeddingmentioning

confidence: 99%

“…Figure 3 depicts the relation between the generator-modelled prototypes, the inverse of which is the motor prototype. The following are the equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) developed to determine the generator model steps and calculation for the range of voltage, resistance and load [15][16][17]: The following are the Equations (1)- (14) developed to determine the generator model steps and calculation for the range of voltage, resistance and load [15][16][17] (3)…”

Section: Generatormentioning

confidence: 99%

Turboelectric Uncertainty Quantification and Error Estimation in Numerical Modelling

Alrashed¹,

Nikolaidis²,

Pilidis³

et al. 2020

Applied Sciences

View full text Add to dashboard Cite

Turboelectric systems can be considered complex systems that may comprise errors and uncertainty. Uncertainty quantification and error estimation processes can, therefore, be useful in achieving accurate system parameters. Uncertainty quantification and error estimation processes, however, entail some stages that provide results that are more positive. Since accurate approximation and power optimisation are crucial processes, it is essential to focus on higher accuracy levels. Integrating computational models with reliable algorithms into the computation processes leads to a higher accuracy level. Some of the current models, like Monte Carlo and Latin hypercube sampling, are reliable. This paper focuses on uncertainty quantification and error estimation processes in turboelectric numerical modelling. The current study integrates the current evidence with scholarly sources to ensure the incorporation of the most reliable evidence into the conclusions. It is evident that studies on the current subject began a long time ago, and there is sufficient scholarly evidence for analysis. The case study used to obtain this evidence is NASA N3-X, with three aircraft conditions: rolling to take off, cruising and taking off. The results show that the electrical elements in turboelectric systems can have decent outcomes in statistical analysis. Moreover, the risk of having overload branches is up to 2% of the total aircraft operation lifecycle, and the enhancement of the turboelectric system through electrical power optimisation management could lead to higher performance.

show abstract

“…In connection with the new approach of [30] to the problem of efficient continuation of a given germ of a multivalued analytic function, this fact seems to be one of the main motivations for the study of equilibrium problems associated with complex Nikishin systems. Moreover, there are other applications of Hermite-Padé polynomials to the study of actual problems from various fields of theoretical and applied mathematics; see, for example, [19], [34], [16] and the references found there. It is the field of Nikishin systems which has received most attention in recent years.…”

Section: Introduction and Statement Of The Problemmentioning

confidence: 99%

Scalar equilibrium problem and the limit distribution of the zeros of Hermite-Padé polynomials of type II

Ikonomov¹,

Suetin²

2019

Preprint

View full text Add to dashboard Cite

The existence of the limit distribution of the zeros of Hermite-Padé polynomials of type II for a pair of functions forming a Nikishin system is proved using the scalar equilibrium problem posed on the two-sheeted Riemann surface.The relation of the results obtained here to some results of H. Stahl (1988) is discussed. Results of numerical experiments are presented. The results of the present paper and those obtained in the earlier paper of the second author [28], [32], [33] are shown to be in good accordance with both H. Stahl's results and with results of numerical experiments. Bibliography: [35] titles. 4 figures.

show abstract

HELM: The Holomorphic Embedding Load-Flow Method. Foundations and Implementations

Cited by 14 publications

References 0 publications

Power flow analytical solutions and multi-dimensional voltage stability boundary based on the multivariate quotient-difference method

Power flow analytical solutions and multi-dimensional voltage stability boundary based on the multivariate quotient-difference method

Turboelectric Uncertainty Quantification and Error Estimation in Numerical Modelling

Scalar equilibrium problem and the limit distribution of the zeros of Hermite-Padé polynomials of type II

Contact Info

Product

Resources

About