Control Lyapunov functions for Controllable Series Devices

Controllable Series Devices (CSD), i.e., series-connected Flexible AC Transmission Systems (FACTS) devices, such as Unified Power Controller (UPFC), Controllable Series Capacitor (CSC) and Quadrature Boosting Transformer (QBT) with a suitable control scheme can improve transient stability and help to damp electromechanical oscillations. For these devices, a general model, which is referred to as injection model, is used. This model is valid for load flow and angle stability analysis and is helpful for understanding the impact of the CSD on power system stability. Also, based on Lyapunov theory a control strategy for damping of electromechanical power oscillations in a multi-machine power system Is derived. Lyapunov theory deals with dynamical systems without inputs. For this reason, it has traditionally been applied only to closed-loop control systems, that is, systems for which the input has been eliminated through the substitution of a predetermined feedback control. However, in this paper, we use Lyapunov function candidates in feedback design itself by making the l.yapunov derivative negative when choosing the control. This control strategy is called Control Lyapunov Function (CLF) for systems with control inputs.