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Distributed Optimization Based Control on the Example of Microgrids

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Computational Intelligence and Optimization Methods for Control Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 150))

Abstract

Model Predictive Control (MPC) is nowadays one of the most successful advanced process control methodologies and is used in a wide range of applications. While originally limited to processes with slow dynamics and a limited number of states, the applicability of MPC schemes increased dramatically over the past years due to the performance of modern microchips and the concurrent advancements of mathematical optimization, in particular, distributed optimization. In this paper, we outline the ideas of distributed optimization schemes embedded in MPC implementations on the example of the dual ascent algorithm and the alternating direction method of multipliers. The performance and the properties of the resulting distributed optimization based control schemes are illustrated on the example of a network of distributed energy systems. In particular, the overall power demand of the network is optimized by using flexibilities resulting from distributed storage devices and controllable loads.

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Notes

  1. 1.

    A function \(F:{\mathbb R}^n \rightarrow {\mathbb R}\) is said to be strongly convex with parameter \(\chi >0\) if \(F(\mu x+(1-\mu )y) \le \mu F(x) + (1-\mu )F(y)-\frac{\chi }{2}\mu (1-\mu )\Vert x-y\Vert _2^2\) holds for all \(x,y\in {\mathbb R}^n\) and all \(\mu \in [0,1]\).

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Acknowledgements

Funding from the German Research Foundation (DFG; grants WO 2056/2-1 and WO 2056/4-1) and the German Federal Ministry of Education (BMBF; grant 05M18SIA) is gratefully acknowledged.

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Authors and Affiliations

  1. School of Electrical Engineering and Computing, University of Newcastle, Newcastle, Australia

    Philipp Braun

  2. Institute for Mathematics, Technische Universität Ilmenau, Ilmenau, Germany

    Philipp Sauerteig & Karl Worthmann

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  1. Philipp Braun
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  2. Philipp Sauerteig
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  3. Karl Worthmann
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Corresponding author

Correspondence to Philipp Braun .

Editor information

Editors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA

    Maude Josée Blondin

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  3. Institute of Automation and Industrial Computer, Polytechnic University of Valencia, Valencia, Spain

    Javier Sanchis Sáez

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Braun, P., Sauerteig, P., Worthmann, K. (2019). Distributed Optimization Based Control on the Example of Microgrids. In: Blondin, M., Pardalos, P., Sanchis Sáez, J. (eds) Computational Intelligence and Optimization Methods for Control Engineering. Springer Optimization and Its Applications, vol 150. Springer, Cham. https://doi.org/10.1007/978-3-030-25446-9_8

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