Domain of stability of ac/dc power systems

The domain of stability (DOS) of a dynamic system is the sub-state space within which the system converges to a stable equilibrium state if the operating point varies because of a disturbance. The cell mapping technique has been widely used to find the DOS of second-order systems. However, there is no generic method reported in the literature for finding the DOS of any system of order greater than two, other than for ac power systems or for ac/dc power systems with dc dynamics omitted. For these two systems, the DOS can be found using the transient energy function (TEF) because a TEF has been available only for ac-dynamics-only systems. The DOS for ac/dc systems with dc dynamics has not been found because a TEF for dc systems with dc dynamics was not available until the authors recently derived one. In this paper, the existing cell mapping technique is improved to find the DOS of systems of order greater than two. This improved cell mapping technique and the recently developed TEF for dc systems have been used to find the domains of stability of ac/dc systems.