High-Order Approximate Power Flow Solutions and Circular Arithmetic Applications

2019 ◽  
Vol 34 (6) ◽  
pp. 5053-5062 ◽  
Author(s):  
Rabih A. Jabr
Keyword(s):  
Power Flow ◽  
High Order ◽  
Circular Arithmetic ◽  
Approximate Power

Application of high-order Newton-like methods to solve power flow equations

2016 ◽  
Vol 10 (8) ◽  
pp. 1853-1859 ◽  
Author(s):  
Sayed Yaser Derakhshandeh ◽  
Rohallah Pourbagher
Keyword(s):  
Power Flow ◽  
High Order ◽  
Flow Equations

scholarly journals A Novel Probabilistic Power Flow Algorithm Based on Principal Component Analysis and High-Dimensional Model Representation Techniques

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3520 ◽  
Author(s):  
Hang Li ◽  
Zhe Zhang ◽  
Xianggen Yin
Keyword(s):  
Principal Component Analysis ◽  
Power System ◽  
Power Flow ◽  
Random Variables ◽  
Principal Component ◽  
Component Analysis ◽  
High Order ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Dimensional Model

Because the penetration level of renewable energy sources has increased rapidly in recent years, uncertainty in power system operation is gradually increasing. As an efficient tool for power system analysis under uncertainty, probabilistic power flow (PPF) is becoming increasingly important. The point-estimate method (PEM) is a well-known PPF algorithm. However, two significant defects limit the practical use of this method. One is that the PEM struggles to estimate high-order moments accurately; this defect makes it difficult for the PEM to describe the distribution of non-Gaussian output random variables (ORVs). The other is that the calculation burden is strongly related to the scale of input random variables (IRVs), which makes the PEM difficult to use in large-scale power systems. A novel approach based on principal component analysis (PCA) and high-dimensional model representation (HDMR) is proposed here to overcome the defects of the traditional PEM. PCA is applied to decrease the dimension scale of IRVs and eliminate correlations. HDMR is applied to estimate the moments of ORVs. Because HDMR considers the cooperative effects of IRVs, it has a significantly smaller estimation error for high-order moments in particular. Case studies show that the proposed method can achieve a better performance in terms of accuracy and efficiency than traditional PEM.

Propagation and power flow of high-order three-Airy beams

2017 ◽  
Vol 405 ◽  
pp. 120-126 ◽  
Author(s):  
Yi Liang ◽  
Yingkang Chen ◽  
Lingyu Wan
Keyword(s):  
Power Flow ◽  
High Order ◽  
Airy Beams

An Approximate Power Flow for Distribution Systems

2014 ◽  
Vol 12 (8) ◽  
pp. 1432-1440 ◽  
Author(s):  
Antonio Jose Gil Mena ◽  
Juan Andres Martin Garcia
Keyword(s):  
Power Flow ◽  
Distribution Systems ◽  
Approximate Power

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

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2019
Author(s):  
Talal Alharbi ◽  
Marcos Tostado-Véliz ◽  
Omar Alrumayh ◽  
Francisco Jurado
Keyword(s):  
Power Flow ◽  
Order Of Convergence ◽  
Computational Cost ◽  
High Order ◽  
Sixth Order ◽  
Power Networks ◽  
Power Flow Calculation ◽  
Flow Problems ◽  
High Computational Cost ◽  
Very High

Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarrat’s method as applied to power flow calculation (PFC). Despite the 4th order of convergence of this technique, it is not competitive with the conventional solvers due to its very high computational cost. This paper addresses this issue by proposing two efficient modifications of the 4th order Jarrat’s method, which present the fourth and sixth order of convergence. In addition, continuous versions of the new proposals and the 4th order Jarrat’s method extend their applicability to ill-conditioned cases. Extensive results in multiple realistic power networks serve to sow the performance of the developed solvers. Results obtained in both well and ill-conditioned cases are promising.

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