Determining optimal allocation of flow controllers based on system stability and controllability

A hierarchical screened method for determining the optimal allocation of flow controllers are proposed in this paper. Since the allocation patterns are found basing on the concept of tree/co-tree in graph theory, all line flows of the system are controllable only by the minimum number of flow controllers. In order to prevent from system instability resulting from flow control, the eigen analysis of the sensitive matrices characterized the corresponding allocations are taken. It is helpful to screen out the invalid allocations where flow controllers may cause instability in the system. Finally, by comparison with the flow controllability of each allocation, the optimal one hit the target of flow control can be found. A three-machine four-bus two-loop model system is given as an example to confirm the effectiveness of the proposed method.