Power system transient stability design using reachability based stability-region computation

This paper presents a reachability based method to compute the stability region of a stable equilibrium point and uses it to design controls for transient stability of power systems. First, a Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDF) is obtained for the propagation of the backward reachability set of a nonlinear system. This computation when used to obtain the backward reachable set of a stable equilibrium point yields its stability region. Using the stability regions of various discrete controls (also called modes) transient stability design is performed. For example the effectiveness of a control can be verified by checking whether a post-fault initial state is in the stability region of the system with that control switched on. We illustrate our method by applying it to a single-machine infinite-bus system equipped with series and shunt capacitive compensation.