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

TL;DR

This paper introduces a novel angle-based feedback control method for power systems using negative-imaginary systems theory, ensuring stability and optimal operation with distributed control and large-scale batteries.

Contribution

It links angle-based feedback linearization with negative-imaginary systems theory and demonstrates internal stability for distributed control in power networks.

Findings

Ensures frequency synchronization and steady-state power flow within network envelopes.

Achieves stability robustness without conservative criteria like the equal area criterion.

Enables maximum power operation of transmission lines.

Abstract

This paper considers a power transmission network characterized by interconnected nonlinear swing dynamics on generator buses. At the steady state, frequencies across different buses synchronize to a common nominal value such as $50$Hz or $60$Hz, 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. Our approach will enable transmission lines to be operated at maximum power capacity since stability robustness is ensured by the use of feedback controllers rather than conservative criteria such as the equal area criterion. By means of numerical simulations, we illustrate our results.