Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

Wu, Dan; Wang, Bin

doi:10.1109/access.2019.2925384

Cited by 21 publications

(11 citation statements)

References 42 publications

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“…Due to the promising results obtained, MIP should be taken into account and deeply explored for PF calculation of realistic large-scale ill-conditioned systems. In that sense, its suitability in other related problems like the Continuation Power Flow [36] or contingency analysis [65] should be analysed in future works. Maybe, the main issue relative to the PF calculation using MIP is its local convergence, which entails sensitivity with respect the initial guess 0 .…”

Section: Discussionmentioning

confidence: 99%

“…Instead of using conventional nonlinear iterative solvers, other authors have tried to address PF ill-conditioned problems from alternative point of views. Such is the case of the metaheuristic-like solvers [35]; Continuation approaches [6], [36], [37] and homotopy/holomorphic algorithms [38]- [40]. Nevertheless, these solvers still present serious problems.…”

Section: B Literature Reviewmentioning

confidence: 99%

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Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

et al. 2021

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Power Flow solution of realistic ill-conditioned systems has recently attracted huge attention. Nevertheless, there are still some gaps in this field. For example, most of available references do not provide exhaustive theoretical analysis about convergence properties of proposed approaches. In addition, efficient solution of large-scale ill-conditioned systems is still an open topic. This paper tackles these issues by comprehensively studying the suitability of the Mann Iteration Process for the solution of ill-conditioned systems. A comprehensive theoretical analysis is provided, from which is demonstrated that the Mann Iteration Process has with asymptotic stability, may achieve a high convergence rate and constitutes a robust methodology, improving the contractive properties of the Newton-Raphson method. Moreover, some interesting links with other Power-Flow approaches are obtained as by-product. Several numerical experiments serve to confirm the theoretical findings and to compare the performance of the Mann Iteration Process with other well-known PF solvers. In all cases, the results obtained with the Mann Iteration Process are superior to that obtained using other methodologies, being able to efficiently solve various large-scale ill-conditioned systems.INDEX TERMS power-flow analysis, ill-conditioned systems, large-scale systems, Mann iteration process

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Section: Discussionmentioning

confidence: 99%

Section: B Literature Reviewmentioning

confidence: 99%

Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

et al. 2021

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“…This section applies an efficient method [21], [22] to solve (12) for multiple equilibra of the DAE model (7). We gradually change the load model from constant power to constant impedance and observe the change of equilibra.…”

Section: Equilibria With Different Load Modelsmentioning

confidence: 99%

Influence of Load Models on Equilibria, Stability and Algebraic Manifolds of Power System Differential-Algebraic System

Wang

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper presents a comprehensive study to investigate the geometric and topological changes induced by different load models for the traditional power system differential-algebraic equations. Specifically, we attempt to reveal the deformation of equilibria, stability regions, and algebraic manifolds during a continuous evolution of load model. Several findings are presented in the paper, some of which countering traditional recognitions and intuitions. A major discovery is that the load model with a large proportion of constant impedance and a small proportion of constant power exhibits much more complex features than the load model with the reversed proportions of impedance and power. The increase of complexity is thoroughly recorded and investigated by the changes of geometric properties and mutations of topological invariants in the sense of equilibria, stability regions, and algebraic manifolds for the DAE system. However, most of the changes seem to occur on unstable components of algebraic manifolds or near the singular boundary surfaces, suggesting a limited variation of dynamical behaviors on the stable component.

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“…The considerable work on modeling of slack bus, load bus, and generator bus along-with reactive power limit constraints of generator bus have been found in [5,6,7,8,9,10,11]; and other significant advancements in the area of HELM can be found in [12,13,14,15,16]. The holomorphic embedded equations have been obtained by separating the shunt and series part of the admittance matrix; and initially the system is assumed to be without load and generation except the slack bus.…”

Section: Introductionmentioning

confidence: 99%

Steady-State Model of VSC based FACTS Devices using Flexible Holomorphic Embedding: (SSSC and IPFC)

Singh¹,

Senroy²

2021

Preprint

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For proper planning, operation, control and protection of the power system, the development of suitable steady-state mathematical model of FACTS devices is a key issue. The Fast and Flexible Holomorphic Embedding (FFHE) method converges faster and provides the flexibility to use any state as an initial guess. But to investigate the effect and ability of FACTS devices using FFHE technique, it is necessary to develop an embedded system for these devices. Therefore, this paper presents FFHE-based embedded system for VSC-based FACTS controllers, such as, SSSC and IPFC. The embedded system is also proposed for their controlling modes.The introduced embedded system is flexible which allows to take any state as an initial guess instead of fixed state, which leads towards the reduced runtime and decrease the required number of terms, as compared to standard HELM. To demonstrate the effectiveness and practicability, the proposed FFHE-based models of FACTS devices have been tested for several cases. Further, the developed recursive formulas for power balance equations, devices' physical constraints and their controlling modes are thoroughly investigated and examined. From several tests, it is found that the proposed FFHE-based FACTS models requires less execution time and reduce the error at higher rate.

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Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

Cited by 21 publications

References 42 publications

Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

Mann-Iteration Process for Power Flow Calculation of Large-Scale Ill-Conditioned Systems: Theoretical Analysis and Numerical Results

Influence of Load Models on Equilibria, Stability and Algebraic Manifolds of Power System Differential-Algebraic System

Steady-State Model of VSC based FACTS Devices using Flexible Holomorphic Embedding: (SSSC and IPFC)

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