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Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

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Abstract

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.

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Acknowledgements

The first two authors acknowledge the financial support of Ministerio de Economía y Competitividad, grant DPI2014-51844-C2-2-R. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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  1. Universidad Politécnica de Cataluña (LaCàN), Barcelona, Spain

    Raquel García-Blanco & Pedro Díez

  2. Ecole Central de Nantes (ICI), Nantes, France

    Domenico Borzacchiello & Francisco Chinesta

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  1. Raquel García-Blanco
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Correspondence to Pedro Díez.

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García-Blanco, R., Díez, P., Borzacchiello, D. et al. Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems. Arch Computat Methods Eng 25, 1003–1026 (2018). https://doi.org/10.1007/s11831-017-9223-6

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