A Lur'e-type Lyapunov function for multi-machine power systems with transfer conductances

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“…SAEKIt, M. ARAKIt and B. KONDO § In our paper given in the title (Saeki et al 1985) Qian and Demarco (1990) found that the algebraic Riccati equation, which must be solved for the construction of a Lyapunov function, does not have a solution for the numerical example given, and raised the question of whether a Lyapunov function can really be constructed by our method for a multi-machine power system with transfer conductances.…”

Transient stability of multi-machine power systems with transfer conductances

“…Meanwhile, we prove that the system satisfying the conditions of [3] also satisfy our conditions. This means that our conditions are weaker than those of [3]. Hence, the Lyapunov function of Lurie type presented in [3] can be constructed by the conditions obtained in this paper as well.…”

“…This means that our conditions are weaker than those of [3]. Hence, the Lyapunov function of Lurie type presented in [3] can be constructed by the conditions obtained in this paper as well. Finally we present the algebraic conditions for the existence of a Lurie-type Lyapunov function for multi-machine power systems with transfer conductances.…”

“…Researchers have made some effective methods in dealing with the case of no transfer conductances [1, 51. However, there is the greatest difficulty in constructing of a Lyapunov function for electric power systems which contain transfer conductances, although many efforts have been made [3]. A new techique of dealing with power systems was proposed and the sufficient conditions of the power system stability was then derived in [3].…”

“…However, there is the greatest difficulty in constructing of a Lyapunov function for electric power systems which contain transfer conductances, although many efforts have been made [3]. A new techique of dealing with power systems was proposed and the sufficient conditions of the power system stability was then derived in [3]. However, these sufficient conditions are presented in form of the existence of a positive definite matrix solution for so complicated matrix equations.…”