In the study of nonlinear dynamical systems, it is useful to determine the (parameter space) phase boundary that separates stable from unstable behaviour. This presentation will consider algorithms which achieve that goal through the use of shooting methods and Euler homotopy continuation. Firstly, the trajectory is forced to remain in the proximity of an unstable equilibrium point (UEP) for a specified time. That time is then progressively increased, ensuring the trajectory approaches the UEP arbitrarily closely. This process can be used to explore trade-offs between parameters. It also forms the basis for robustness assessment by establishing the minimum distance (in parameter space) from a given operating point to the phase boundary. The various concepts will be illustrated through examples that consider "fault induced delayed voltage recovery" (FIDVR), a vulnerability of distribution networks where residential air-conditioning is prevalent.
Ian A. Hiskens received the B.Eng. degree in electrical engineering and the B.App.Sc. degree in mathematics from the Central Queensland University, Rockhampton, Australia, in 1980 and 1983 respectively, and the Ph.D. degree in electrical engineering from the University of Newcastle, Australia, in 1991. He is the Vennema Professor of Engineering in the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor. He has held prior appointments in the Queensland electricity supply industry, and various universities in Australia and the United States. His research interests lie at the intersection of power system analysis and systems theory, with recent activity focused largely on integration of renewable generation and controllable loads. Dr. Hiskens is actively involved in various IEEE societies, and is VP-Finance of the IEEE Systems Council. He is a Fellow of the IEEE, a Fellow of Engineers Australia and a Chartered Professional Engineer in Australia.