Constructing Lyapunov Function for Power System Including Induction Machine Dynamic Characteristics

This paper presents a systematic procedure of constructing a Lyapunov function for power system considering with induction machine dynamics characteristics by the state function method. Constructing Lyapunov function for power systems with induction machines is very difficult problem and is hoped for being settled for a long time. In the composition process of the proposed Lyapunov function, the slipping dynamic characteristic of the induction machine is implicitly expressed in the swing equation of power systems. As a result, the dynamic characteristic of an induction machine becomes equivalent to a synchronous machine with a voltage adjustment mechanism to which a dissipation function is added. Using this proposed system description, the Lyapunov function is composed by the state function method, which is based on an expanded energy function, under the condition of some approximations. The effectiveness of the proposed Lyapunov function is verified numerically for multi-machine power systems with induction machine loads.