Copyright © lFAC Nonlinear Control Systems, Stuttgart, Gennany, 2004 TRANSIENT STABILIZATION OF MULTIMACmNE POWER SYSTEMS WITH NONTRIVIAL TRANSFER CONDUCTANCES Martha Galaz .,1, Romeo Ortega " Alessandro Astolfi •• Yuanzhang Sun ••• Tielong Shen •••• • Lab. des Signaux et Systemes, Supelec, Plateau du Moulon, 91192 Gif-sur-Yvette, France, ortega@lss. supelee. fr •• Electrical Engineering Department, Imperial College, Exhibition Road, London, SW72BT, UK, a.astolfi@ie.ae.uk ••• Department of Electrical Engineering, Tsinghua University, Beijing, 10084, China, yzsun@mail. tsinghua. edu. en •••• Department of Mechanical Engineering, Sophia University, Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan, tetu-sin@sophia.ae.jp ELSEVIER PUBLICATIONS www.elsevier.com/locatelifac Abstract: In this paper we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with non-negligible transfer conductances. More specifically, we consider the full 3n-<iimensional model of the n-generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. Our derivations underscore the deleterious effects of resistive elements which, as is well-known, hamper the assignment of simple "gradient" energy functions and compel us to include non-standard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system that play the role of multipliers in classical passivity theory. Copyright © 2004 [FAC Keywords: Power systems, nonlinear control, passivity-based control, stabilization. 1. INTRODUCTION In this paper we study the fundamental problem of transient stability of power systems, whose reliable assessment has become a major operating constraint, as illustrated by the recent dramatic blackouts in North America and Italy. Transient stability is concerned with a power system's ability to reach an accept- able steady-state following a fault, e.g., a short cir- 1 The work of Martha Galaz was partially sponsored by the GEO- PLEX programme of the European Commission 1033 cuit or a generator outage, that is later cleared by the protective system operation, see (Anderson and Fouad, 1994; Lu et al., 2(01) and the tutorial pa- per (Chiang et aI., 1995) for more details. The fault temporarily modifies the circuit topology-driving the system away from the stable operating point-and the question is whether the trajectory will remain in the basin of attraction of this (or other) equilibrium after the fault is cleared. The key analysis issue is then the evaluation of the domain of attraction of the system's