A framework for actuator placement in large scale power systems: Minimal strong structural controllability

This paper addresses the problem of minimal placement of actuators in large-scale linear time invariant (LTI) systems, such as large-scale power systems, for dynamic controller design. A novel sufficient and necessary condition to ensure a strong structurally controllable (SSC) system is proposed. Specifically, the paper addresses the problem of obtaining the minimal number of dedicated inputs, i.e., inputs which actuate only a single state variable, and the respective state variables they should be assigned to, such that the LTI system is SSC. In addition, an efficient and scalable algorithm, with polynomial implementation complexity, to achieve such minimal placement of dedicated inputs is proposed. An illustration of the proposed design methodology is provided on the IEEE 5-bus test system, thereby identifying the minimal number of physical state variables to be actuated for ensuring strong structural controllability.