Bilevel Optimization Approaches to Decide the Feasibility of Bookings in the European Gas Market

The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. This results in a highly challenging mathematical problem. Using potential-based flows to model stationary gas physics, feasible bookings on passive networks, i.e., networks without controllable elements, have been characterized in the recent literature. In this paper, we consider networks with linearly modeled active elements such as compressors and control valves that do not lie on cycles of the network. Since these active elements allow the TSO to control the gas flow, the single-level approaches from the literature are no longer applicable. We thus present a bilevel approach to decide the feasibility of bookings in networks with active elements. Besides the classical Karush-Kuhn-Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations, which also lead to novel characterizations of feasible bookings in active networks. We compare the performance of our methods by a case study based on data from the GasLib

Modeling Hydrogen Networks for Future Energy Systems: A Comparison of Linear and Nonlinear Approaches

Common energy system models that integrate hydrogen transport in pipelines typically simplify fluid flow models and reduce the network size in order to achieve solutions quickly. This contribution analyzes two different types of pipeline network topologies (namely, star and tree networks) and two different fluid flow models (linear and nonlinear) for a given hydrogen capacity scenario of electrical reconversion in Germany to analyze the impact of these simplifications. For each network topology, robust demand and supply scenarios are generated. The results show that a simplified topology, as well as the consideration of detailed fluid flow, could heavily influence the total pipeline investment costs. For the given capacity scenario, an overall cost reduction of the pipeline costs of 37% is observed for the star network with linear cost compared to the tree network with nonlinear fluid flow. The impact of these improvements regarding the total electricity reconversion costs has led to a cost reduction of 1.4%, which is fairly small. Therefore, the integration of nonlinearities into energy system optimization models is not recommended due to their high computational burden. However, the applied method for generating robust demand and supply scenarios improved the credibility and robustness of the network topology, while the simplified fluid flow consideration can lead to infeasibilities. Thus, we suggest the utilization of the nonlinear model for post-processing to prove the feasibility of the results and strengthen their credibility, while retaining the computational performance of linear modeling

Shell evolution of stable N = 50-56 Zr and Mo nuclei with respect to low-lying octupole excitations

For the N = 50-56 zirconium (Z = 40) and molybdenum (Z = 42) isotopes, the evolution of subshells is evaluated by extracting the effective single-particle energies from available particle-transfer data. The extracted systematic evolution of neutron subshells and the systematics of the excitation energy of the octupole phonons provide evidence for type-II shape coexistence in the Zr isotopes. Employing a simplistic approach, the relative effective single-particle energies are used to estimate whether the formation of low-lying octupole-isovector excitations is possible at the proposed energies. The results raise doubts about this assignment

Quadrupole collectivity in neutron-rich Cd isotopes

4 pags., 2 figs. -- INPC 2013 – International Nuclear Physics ConferenceThe investigation of the excitation energies of the 21+ –states in the neutron-rich Cd isotopes shows an irregular behaviour when approaching the neutron shell-closure at N = 82. The energy of the 21+–state in 128Cd is lower than the one in 126Cd. The transition strength B(E2, 0gs+ → 21+) in the even isotopes 122−128Cd was measured in Coulomb excitation experiments with the high-purity germanium detector array MINIBALL at REXISOLDE (CERN). The values for 122,124Cd coincide with beyond-mean-field calculations with a resultant prolate deformation, whereas 126,128Cd are better described by shell-model calculations.This project is supported by BMBF (No. 06 DA 9036I, No. 05 P12 RDCIA, No. 05 P12 RDCIB and No. 05 P12 PKFNE), HIC for FAIR, EU through EURONS (No. 506065) and ENSAR (No. 262010) and the MINIBALL and REX-ISOLDE collaborations

Quadrupole collectivity in neutron-rich Cd isotopes

The investigation of the excitation energies of the 2(1)(+)-states in the neutron-rich Cd isotopes shows an irregular behaviour when approaching the neutron shell-closure at N = 82. The energy of the 2(1)(+)-state in Cd-128 is lower than the one in Cd-126. The transition strength B(E2, 0(gs)(+) -> 2(1)(+)) in the even isotopes Cd122-128 was measured in Coulomb excitation experiments with the high-purity germanium detector array MINIBALL at REX-ISOLDE (CERN). The values for Cd-122,Cd-124 coincide with beyond-mean-field calculations with a resultant prolate deformation, whereas Cd-126,Cd-128 are better described by shell-model calculations