TY - BOOK

T1 - Dynamic optimization of gas transmission networks for storage of renewable energy

AU - Thiedau, Jan

N1 - Doctoral thesis

PY - 2018

Y1 - 2018

N2 - To ensure security of supply in the presence of highly volatile generation of renewable electric energy, extensive storage is required. In this thesis the application of mathematical optimization methods to gas transmission networks with electricity driven compressor stations, operated as electricity storage, is discussed. Therefore, a transient network model that incorporates the gas dynamics described by the isothermal Euler equations as well as technical network elements is introduced and reviewed as coupled systems of hyperbolic balance laws. For optimization problems on networks these PDEs are commonly discretized by finite differences using an implicit box-scheme. The comparison with finite volume simulations, obtained using a high order ADER method, shows that the finite difference approximations represent sufficiently well the gas dynamics for typical flow situations on transmission networks while requiring much less computational effort. The optimization model is then applied to realistic test problems abstracting parts of the German gas transmission network. The results for different price scenarios, which are used as indicator for the availability of renewable energy, show the potential of using pipelines as short term storage for electric energy but also the limitations. The thesis is concluded by a discussion of the recently proposed distributed optimization algorithm ALADIN and its application to the structured gas network optimization problems. Therefore, an implementation of this algorithm as well as the experiences applying it to the introduced model are presented. Compared to a general purpose interior-point method, this approach of exploiting the problem structure shows promising performance for simple examples but fails for more complicated model instances.

AB - To ensure security of supply in the presence of highly volatile generation of renewable electric energy, extensive storage is required. In this thesis the application of mathematical optimization methods to gas transmission networks with electricity driven compressor stations, operated as electricity storage, is discussed. Therefore, a transient network model that incorporates the gas dynamics described by the isothermal Euler equations as well as technical network elements is introduced and reviewed as coupled systems of hyperbolic balance laws. For optimization problems on networks these PDEs are commonly discretized by finite differences using an implicit box-scheme. The comparison with finite volume simulations, obtained using a high order ADER method, shows that the finite difference approximations represent sufficiently well the gas dynamics for typical flow situations on transmission networks while requiring much less computational effort. The optimization model is then applied to realistic test problems abstracting parts of the German gas transmission network. The results for different price scenarios, which are used as indicator for the availability of renewable energy, show the potential of using pipelines as short term storage for electric energy but also the limitations. The thesis is concluded by a discussion of the recently proposed distributed optimization algorithm ALADIN and its application to the structured gas network optimization problems. Therefore, an implementation of this algorithm as well as the experiences applying it to the introduced model are presented. Compared to a general purpose interior-point method, this approach of exploiting the problem structure shows promising performance for simple examples but fails for more complicated model instances.

U2 - 10.15488/3177

DO - 10.15488/3177

M3 - Doctoral thesis

CY - Hannover

ER -