Design and Stability of Angle Based Feedback Control in Power Systems: A Negative-Imaginary Approach

This paper considers a power transmission network. At the steady state, frequencies across different buses synchronize to a common nominal value and power flows on transmission lines are within steady-state envelopes. We assume that fast measurements of generator rotor angles are available. Our approach to frequency and angle control centers on equipping generator buses with large-scale batteries that are controllable on a fast timescale. We link angle based feedback linearization control with negative-imaginary systems theory. Angle based feedback controllers are designed using large-scale batteries as actuators and can be implemented in a distributed manner incorporating local information. Our analysis demonstrates the internal stability of the interconnection between the power transmission network and the angle based feedback controllers. This internal stability underscores the benefits of achieving frequency synchronization and preserving steady-state power flows within network envelopes through the use of feedback controllers. Finally, we illustrate our results through numerical simulations.