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Constrained optimization over manifolds for power system application


A. Zanardi

Semester Thesis, SS16 (10525)

In the recent years power distribution grids are experiencing the integration of a huge array of new devices, ranging from renewable energy sources to electrical vehicles. Hence, the distribution networks are shifting away from the paradigm of mono-directional power flows, which gives rise to many new control challenges to operate the grid in an efficient and safe way. Recent works [14] have shown that local voltage control is not sufficient anymore and, therefore, it becomes vital to develop more sophisticated tools. This project concerns the issues of real-time power flow control in distribution networks. We take as initial point of the project previous works [2] which have shown how the set of all possible power flow solutions is described by a regular manifold, hence we want to formulate our optimization problem as a flow on manifold. Altough many optimization problems have been recently reformulated as flows on manifolds with the tools of differential geometry [1], very few have considered optimization schemes with additional constraints on top of the manifold [6]. Nevertheless, when it comes to power grids additional constraints such as voltage or current limits are unavoidable. Hence, the aim of this project has been to explore techniques in the field of constrained optimization over manifolds to continuously steer the system toward an optimal solution. With this goal in mind, the first idea to tackle the problem, is to adapt optimization techniques used in Rn to this new framework. We will show that, with some carefulness, this already produces very satisfactory results. Additionally, in the final part of this report (chapter 5), we will show that the problem can also be treated in a different way, which does not need the concept of manifold. Finally, the reader should keep in mind that the level of formalism required by differential geometry has been kept to the minimum for the sake of clarity. Moreover, the particular power system application endows us with many assumptions on the manifold that are not true in general cases. Smoothness of the manifold and proper embedding Euclidean space are guaranteed to exist [2], hence allowing us to avoid cumbersome notation.

Supervisors: Saverio Bolognani, Adrian Hauswirth, Prof. Florian Dörfler


Type of Publication:

(13)Semester/Bachelor Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2016:IFA_5501
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