Co-Simulation of Transient Effects in Superconducting Accelerator Magnets

Numerical modeling of complex physical systems involving several coupled physical domains, so called multi-domain and multi-physics systems, poses considerable challenges w.r.t. consistency of the formulation and selection of a suitable representation. The landscape is further complicated in case these phenomena occur at a wide range of temporal (multi-rate) and spatial (multi-scale) scales. Resolving all in one scale may result in unacceptable computational time. Recent development in port-based modeling techniques, in particular the port-Hamiltonian framework originating from control theory, made it possible to model complex multi-domain and multi-physics phenomena represented by means of both ordinary and partial differential equations in a generic and consistent way. The port-Hamiltonian models capture in an elegant way the internal energy flow, storage, dissipation as well as interaction through lumped, distributed, and boundary ports. In the thesis, we employ the port-Hamiltonian formalism to characterize the coupling between the electromagnetic and thermodynamic systems in a superconducting magnet along with an accompanying electrical circuit. In addition, we employ bond graph modeling to graphically represent the energy flow in the considered systems. These methods allow to study the model consistency as well as the computational causality. Similarly, the advances in cooperative simulation, in particular the application of the waveform relaxation algorithm to field/circuit coupling along with the use of preconditioners for field models allowed to achieve satisfactory convergence rates and accurate results. This method is particularly suited to approach multi-rate and multi-scale problems such as the simulation of a superconducting magnet and circuit. In this thesis, an architecture, data structures, and algorithms for automatic handling of hierarchical co-simulation are presented. The resulting framework supports four main co-simulation algorithms (one-way coupling, weak coupling, strong coupling, and waveform relaxation). Furthermore, the evolution of a transient in a co-simulation scenario may call for the adjustment of the model fidelity in order to accurately reproduce a given phenomenon. This is achieved by switching models and coupling algorithms during the co-simulation execution. The performance of the presented co-simulation framework is illustrated with several relevant examples of transient effects in accelerator magnets. The studied co-simulation scenarios involve superconducting accelerator magnets, circuits, and controllers of power converters in nominal and failure conditions. The developed energy-based models support the analysis of the performance of the co-simulation scenarios.