Voltage and current modeshapes for damping measures with PSS or FACTS devices

The commonly known rotor angle modeshapes describe the participation of generators in inter-area oscillations and provide an indication of favorable PSS sitings to increase the system damping. However, the utilization of shunt and series FACTS devices for damping measures requires additional indicators for the sensitivity of voltages and currents to the oscillations. This work intends to discuss the derivation of voltage and current observability modeshapes as well as controllability mode-shapes relevant for shunt and series controllers at any location in the power system. The basic distribution patterns of these mode-shapes are presented within a simple and vivid example. In addition to a linear modeshape derivation based on the eigenvalue analysis, the direct extraction from the nonlinear time functions is presented for both observability and controllability indicators. The comparison with the linear correspondences provides extensive assessment capability regarding the accuracy of linearization based methods. The examination of voltage and current modeshapes in a model of the European transmission system and the combination of these indicators for several modes and load-flow scenarios provides favorable sitings, type requirements and control values for PSS and shunt or series FACTS devices.