Rare but crippling breakdowns of the electric supply system are due as much to our lack of appreciation of stability issues and thus our inability to formulate security criteria as because of the occurrence of unforeseen triggering events. Our research seeks to develop conceptual and computational tools to examine power system behavior near stability limits. The principle objectives are the qualitative characterization of instability mechanisms in electric power networks, the development of an analytical strategy for stability assessment, and the development of computer software tools which combine symbolic and numerical computation for the implementation of that strategy. The central analytical themes are the application of energy methods and bifurcation theory to constrained differential equations.
Our research program has made basic contributions to the modeling and stability analysis of electrical networks. These include an extension of Hamilton-Lagrange methods to nonlinear RLC networks with general topologies, the development of a local stability theory for electric power networks with transfer conductances based on Liapunov analysis, and the development of a rigorous theory of power system voltage collapse based on bifurcation theory. This work has provided a rigorous characterization of power system static stability which unifies and expands prevailing definitions. It demonstrated that the voltage collapse is actually a family of instability mechanisms of varying degrees of complexity and began a program of classification. Current work is focused on development of an analytical framework and computer tools for voltage stability analysis and control.
Some representative publications are:
1. "Derivation of the Brayton-Moser Equations From a Topological Mixed Potential Function", F.M. Massimo, H.G. Kwatny and L.Y. Bahar, Proceedings 17th Allerton Conference on Communication, Control and Computing, pp. 410-419, October, 1979; and Jrl. Franklin Institute, Vol. 310, No. 45, pp. 259-269, October/November, 1980.
2. "The Generalized Lagrange Formulation for Nonlinear RLC Networks", H.G. Kwatny, F.M. Massimo and L.Y. Bahar, IEEE Trans. on Circuits and Systems, Vol. CAS-29, No. 4, pp. 220-233, April, 1982.
3. "Energy-Like Lyapunov Functions for Power System Stability Analysis," H.G. Kwatny, L.Y. Bahar and A.K. Pasrija, IEEE Trans. on Circuits and Systems, Vol. CAS-32, No. 11, pp. 1140-1149, November 1985.
4. "Conservation Laws for Dissipative Systems Possessing Classical Normal Modes," L.Y. Bahar and H.G. Kwatny, Jrl. of Sound and Vibration, Vol. 102, No. 4, pp. 551-562, October 1985.
5. "Static Bifurcations in Electric Power Networks: Loss of Steady State Stability and Voltage Collapse," H.G. Kwatny, A.K. Pasrija and L.Y. Bahar IEEE Trans on Circuits and Systems, Vol. CAS-33, No. 10, pp. 981- 991, October, 1986.
6. "Extension of Noether's Theorem to Constrained Nonconservative Dynamical Systems,Ó L.Y. Bahar and H.G. Kwatny Int. Jrl. Nonlinear Mech.,vol.22, no.2, pp.125-38, 1987.
7. "Energy Analysis of Load-Induced Flutter Instability in Classical Models of Electric Power Networks," IEEE Trans on Circuits and Systems, H. G. Kwatny and Xiao-Ming Yu, Vol. 36, N0. 12, pp. 1544-57, Dec.1989.
8. "Dynamic Response of Some Dissipative Systems by Means of Functions of Matrices,Ó L. Y. Bahar and H. G. Kwatny, Jrl. of Sound and Vibration, Vol. 137, No. 3, pp. 433-442, 1990.
9. "Dynamic Response of Some Dissipative Systems by Means of Functions of Matrices,Ó L. Y. Bahar and H. G. Kwatny, Jrl. of Sound and Vibration, Vol. 137, No. 3, pp. 433-442, 1990.
