Application of NMI to the Design of FACTS Damping Control with Multiple Operating Points

This paper discusses the design of the damping control of FACTS with multiple operating points. The problem of such a damping control design is actually the problem of designing optimal output-feedback controllers for a multi-model system, of which control requirements can be described by nonlinear matrix inequalities (NMI). The design approach can transfer the original NMI into linear matrix inequalities (LMI) through suitable parameterization and transformation. This can be applicable to the design of FACTS damping control that can guarantee the satisfactory performance over a wide range of operating conditions rather than one operating condition. There are two control design strategies that can be applied in applying the LMI approach. The first control design strategy is that a single damping controller is determined and used for all operating points. The second control strategy is that instead of using a single damping controller for all operating points, multiple damping controllers are designed and utilized. Each of the multiple damping controllers is corresponding to a few operating points. The advantage of the second control design strategy is that the LMI design problem is relatively small and easy to solve, and the corresponding damping controllers may provide better control performance in comparison to the single damping controller of the first design strategy. The LMI approach along with the two design strategies are demonstrated on a 4-machine 2-area system. Numerical results show that the damping controller designed by the two multiple operating point based approaches can ensure simultaneous stability and adequate damping for the multiple operating points.