## Efficient Reduction Techniques for a large-scale Transmission Expansion Planning problem

##### Abstract

The aim of Transmission Expansion Planning (TEP) studies is to decide which, where, and when new grid elements should be built in order to minimize the total system cost. The lumpiness of the investment decisions, together with the large size of the problem, make the problem very hard to solve. Consequently, methods should be put in place to reduce the size of the problem while providing a similar solution to the one that would be obtained considering the full size problem.
Techniques to model the TEP problem in a compact way, also called reduction methods, can reduce the size of the TEP problem and make it tractable. This thesis provides new techniques to reduce the size of the TEP problem in its main three dimensions: the representation made of the grid (spatial dimension), the representation made of the relevant operation situations (temporal representation), and the number of candidate grid elements to consider.
In each of the three reduction techniques proposed in this thesis work, the first step consists in solving a linear relaxation of the TEP problem. Then, they make use of information that is relevant to make the network investment decisions to formulate the TEP problem in a compact way for a certain dimension. I use the potential benefits brought by candidate lines to reduce the size of the representation made of the temporal variability in the problem. Besides, I reduce the size of the network by preserving the representation made of the congested lines and partially installed lines while computing an equivalent for other network elements. Lastly, I manage to reduce the set of candidate lines to consider based on the set of expanded corridors and the amount of new capacity built in them.
I also compare each of the reduction techniques that I have developed to alternative reduction methods discussed in the literature within various case studies. In each of the three reduction methods proposed, the TEP solution computed solving the TEP problem resulting from applying the proposed reduction methods is more accurate (efficient) than the ones computed applying alternative reduction methods. Besides, this solution is almost as efficient as the solution of the original TEP problem, i.e. the TEP problem that has not been reduced by the proposed reduction method.
As a next step, one may explore combining the three reduction methods proposed to maximize the reduction achieved in the size of the TEP problem.

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**Tesis Doctoral**

Efficient Reduction Techniques for a large-scale Transmission Expansion Planning problem#####
**Titulación / Programa**

Programa de Doctorado Erasmus Mundus en Tecnologías y Estrategias Energéticas Sostenibles / Erasmus Mundus Joint Doctorate in Sustainable Energy Technologies and Strategies#####
**Materias/ UNESCO**

12 Matemáticas1201 Álgebra

120110 Álgebra lineal

1206 Análisis numérico

120609 Ecuaciones lineales

120610 Matrices

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**Collections**

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