Novel iterative T-network equivalent circuits are derived for the direct and quadrature axes of a generator with superconducting field winding and stator air-gap winding. They enable the treatment of the complex skin effect phenomena in a multi-shell damper system for any non- periodical time variation as well as of the mutual inductive couplings of the various rotor damper cylinders and the field and statorwindings. Consisting of linear RL networks, similar to the equivalent circuits of conventional generators, they can be included in existing computer programs for power system and machine dynamics. In this way an efficient tool is obtained to analyze the transient performance of a superconducting generator in the power system, including the torsional behavior, flux density distribution in the superconducting field winding and design optimization of the damper system.

Superconducting Generator Modeling by Iterative T-Network Equivalent Circuits for Investigation of Transient Performance

A vector potential is formulated for three-dimensional steady groundwater flow within a framework that is consistent with the Lagrange stream function for twodimensional flow. Analytical expressions are developed for vector potentials of a point–sink and a line–sink (of both finite and infinite length). A previously unpublished vector potential for a partly penetrating well in a horizontal confined aquifer is obtained using the method of images, where an infinite series of image line–sinks is approximated using a finite number of images and two semi–infinite elements. Singularities and discontinuities within these vector potentials are interpreted as producing a virtual discharge connecting vortex lines into continuous loops over infinity. The vector potential is used to accurately and efficiently compute the net flux through surfaces containing singularities in the specific discharge. This net flux quantifies errors in the elevation of streamlines associated with a finite number of images, and provides a measure to ensure a relatively seamless link between local three–dimensional flow and farfield two–dimensional flow.

A vector potential for a partly penetrating well and flux in an approximate method of images

This paper addresses the problem of the numerical calculation of three-dimensional magnetostatic fields. The basic equations for the vector potential method and for an extended scalar potential method are derived and the duality of both methods is shown. The superior applicability of the extended scalar potential method for three-dimensional field calculation is derived and recent results obtained for a superconducting coil are described.

Josef Spiegl

Papers

Comparison of Vector Potential and Extended Scalar Potential Methods and True Three-Dimensional Magnetostatic Field Calculation