We present a nonlinear reachability framework for control of power system transients. The power system consists of synchronous generators, coupled by transmission lines and controlled HVDC links. The approach consists of characterisation of the region of attraction as a backward reachable set of a stable equilibrium point of the power system. Furthermore, the optimal HVDC control as a feedback map is synthesised. As such, the set of the generators’ disturbed states that return to a stable equilibrium point under an optimal HVDC control input are computed. The numerical examples include a two area power system with a HVDC link.