Optimization of Distributed Energy Supply Systems by Branch-and-Price Optimierung von dezentralen Energieversorgungssystemen mit Branch-and-Price

This work evaluates whether optimization problems resulting from modelling the optimal synthesis, design and operation of a decentralized energy supply system have an embedded structure which can be exploited by decomposition methods in solution algorithms. The objective is to determine if the the accuracy and/or the problem size in terms of number of periods of time and number of units considered may be increased, as these are limited if the branch-and-bound method combined with the simplex method is used to solve the problems. A model of the problem is formulated as a mixed-integer linear program as proposed by Yokoyama et al. (2002) and Voll (2013). The model is analyzed and two embedded structures suitable for decomposition are identified. The first structure emphasizes the independent operation and design of every component. The second structure emphasizes the design and operation of all components and focuses on the independence of every period of time considered. The model is reformulated using the Dantzig-Wolfe decomposition principle for both proposed embedded structures. A numerical study is conducted where the synthesis, design and operation of a fictional energy supply system is optimized by both the branch-and-bound method combined with the simplex method and by the branch-and-price method. A set of instances is created for different degrees of complexity in terms of the number of units and the number of periods of time considered. The results show that the dual bounds obtained by solving the rootnode LP relaxation can be improved in comparison to the conventional solution approach, if the reformulation emphasizing independent components is utilized. The results provide no evidence on improvements on the considered test set for the reformulation emphasizing design and operation. For the case of an optimal solution computing times required to solve the considered instances of a test set are found to be reduced by utilizing the branch-and-price method and the reformulation emphasizing components, if identical components are considered in the energy supply system in comparison to the non-commercial solver SCIP.

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