Critical Reviews of Load Flow Methods for Well, Ill and Unsolvable Condition

Shahriari, A.; Mokhlis, Hazlie; Bakar, Ab Halim Abu

doi:10.2478/v10187-012-0022-x

Cited by 10 publications

(4 citation statements)

References 45 publications

(104 reference statements)

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“…As systems start to operate closer to their limits, picking better initialization points becomes insufficient. Since the Jacobians for all points that are close to the boundary of the feasible power flow region have eigenvalues close to 0 (they loose rank), they necessarily become ill-conditioned and iterative algorithms may diverge [16], [17]. To avoid this phenomenon, a class of non-divergent power flow algorithms was developed to accelerate or decelerate the updates based on the conditioning of the Jacobian [18]- [21].…”

Section: Introductionmentioning

confidence: 99%

A Matrix-Inversion-Free Fixed-Point Method for Distributed Power Flow Analysis

Guddanti

Weng

Zhang

2022

IEEE Trans. Power Syst.

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The power flow (PF) problem is a fundamental problem in power system engineering. Many popular solvers like PF and optimal PF (OPF) face challenges, such as divergence and network information sharing between multi-areas. One can try to rewrite the PF problem into a fixed point (FP) equation (more stable), which can be solved exponentially fast. But, existing FP methods are not distributed and also have unrealistic assumptions such as requiring a specific network topology. While preserving its stable nature, a novel FP equation that is distributed in nature is proposed to calculate the voltage at each bus. This distributed computation enables the proposed algorithm to compute the voltages for multi-area networks without sharing private topology information. Unlike existing distributed methods, the proposed method does not use any approximate network equivalents to represent the neighboring area. Thus, it is approximation-free, and it also finds use cases in distributed AC OPFs. We compare the performance of our FP algorithm with state-of-the-art methods, showing that the proposed method can correctly find the solutions when other methods cannot, due to high condition number matrices. In addition, we empirically show that the FP algorithm is more robust to bad initialization points than the existing methods. Index Terms-Distributed power flow, fixed-point equation, multi-area network power flow, ill-conditioned problems. NOMENCLATUREBold signifies a vector.Three tuple describing the circle representing the real power equation. (a q , b q , c q )Three tuple describing the circle representing the reactive power equation. 1Vector of 1's of appropriate length. ΔSApparent power mismatch of a bus with the largest mismatch in the entire power network. ΔVVector of change in voltage state at all buses in the network.

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Section: Introductionmentioning

confidence: 99%

A Matrix-Inversion-Free Fixed-Point Method for Distributed Power Flow Analysis

Guddanti

Weng

Zhang

2022

IEEE Trans. Power Syst.

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“…Standard LF solvers do not have good performance in ill‐conditioned systems; hence, the standard NR and FD often fail in these cases. Different robust LF solvers have been developed to solve the ill‐conditioned cases .…”

Section: Introductionmentioning

confidence: 99%

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Tostado‐Véliz

Kamel

2018

Int Trans Electr Energ Syst

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Summary In this paper, several methods are proposed to find the load flow (LF) solution of large‐scale ill‐conditioned systems. These methods are based on the Adams‐Bashforth formulation. With the use of the proposed methods, the convergence problems of the most popular LF methods are addressed especially when the flat initial guess point is considered. The proposed methods are validated using three ill‐conditioned systems: the modified IEEE 300‐bus system, the 3375‐bus Polish system, and a 13 659‐bus portion of the European transmission system. The obtained results prove that the proposed methods constitute a family of robust and efficient methods for the LF problem.

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“…Ill‐conditioned cases may provoke convergence problems in most of standard LF methods [15]. Consequently, several robust LF methods have been developed in order to solve the ill‐conditioned systems.…”

Section: Introductionmentioning

confidence: 99%