Transient stability and discontinuous solution in electric power system with dc transmission: A study with DAE system Yoshihiko Susuki † , Takashi Hikihara † , and Hsiao-Dong Chiang ‡ †Department of Electrical Engineering, Kyoto University Katsura, Nishikyo-ku, Kyoto, 615-8510, Japan ‡Department of Electrical and Computer Engineering, Cornell University Ithaca, NY, 14853, The United States Email: susuki@dove.kuee.kyoto-u.ac.jp, hikihara@kuee.kyoto-u.ac.jp, chiang@ece.cornell.edu Abstract—This paper focuses on transient stabil- ity of an electric power system with dc transmis- sion. When the transient stability is numerically evalu- ated based on a differential-algebraic equation (DAE) system, associated trajectories become discontinuous since constraint sets are different among correspond- ing pre-fault, fault-on, and post-fault DAE systems. In this paper, several discontinuous solutions are numer- ically and analytically discussed for the DAE system. 1. Introduction This paper addresses transient stability of an elec- tric power system with dc transmission. DC transmis- sion has been widely recognized as a novel technology for future power supply networks [1, 2, 3, 4]. Tran- sient stability of ac/dc power systems is of important concern with their ability to reach an acceptable op- erating condition following an event disturbance. The transient stability is mainly analyzed based on the two different approaches: time-domain (numerical) simula- tion [1, 2] and dynamical system theory [5, 6] involving energy function method [7, 1, 6]. By combing the two approaches, we can obtain sufficient and practical in- formation about the transient stability. The present paper investigates discontinuous solu- tions in a differential-algebraic equation (DAE) system using the numerical simulation. In [5, 6] we examined transient stability boundaries of the ac/dc power sys- tem based on the DAE system. Our previous stud- ies focused on geometric and topological structures of the stability boundaries. Unfortunately, the relation has not been clarified between the stability boundaries and possible system trajectories relative to accidental faults. The understanding of the relation is inevitable in order to apply the obtained results in [5, 6] to prac- tical situations and reveal the transient stability. Here, to clarify the relation, we consider particular discontin- uous solutions caused by accidental faults in the ac/dc system; the solutions have a potential to provide with us a clue about the relation. This paper shows several discontinuous solutions of the DAE system and evalu- ates them via the singular perturbation technique. γ dc transmission generator infinite bus dc(ref) I Figure 1 System model of electric power system with dc transmission 2. Differential-algebraic equation system Figure 1 shows the system model of an electric power system with dc transmission [8]. In [6] we derive the following DAE system as a mathematical model for the transient stability analysis: T ′ d0 L d - L ′ d dv ′ q dt = - ∂ U ac ∂v ′ q (v ′ q , δ, θ r ,V r ), dδ dt = Δω, 2H dΔω dt = -DΔω - ∂ U ac ∂δ (v ′ q , δ, θ r ,V r ), L dc dI dc dt = -R dc I dc +K V (e Vr cos α(I dc ) - V i cos γ ), 0 = - ∂ U ac ∂θ r (v ′ q , δ, θ r ,V r ) -K I e Vr I dc cos ϕ r , 0 = - ∂ U ac ∂V r (v ′ q , δ, θ r ,V r ) -K I e Vr I dc sin ϕ r , 0 = K I e Vr I dc cos ϕ r - K V e Vr cos α(I dc ) - 3 π X c I dc I dc , 2004 International Symposium on Nonlinear Theory and its Applications (NOLTA2004) Fukuoka, Japan, Nov. 29 - Dec. 3, 2004 423