Negative Imaginary and Passivity Properties of Synchronous Machine Systems

TL;DR

This paper proves that nonlinear synchronous machine systems exhibit passivity and negative imaginary properties, which are preserved under certain control conditions, aiding stability analysis in renewable energy power systems.

Contribution

It establishes fundamental dissipativity properties of nonlinear synchronous machines and shows their preservation under passive control interconnections, advancing stability assessment methods.

Findings

Synchronous machines are passive from current to voltage.

They exhibit a nonlinear negative imaginary property from torque to rotor angle.

Interconnection with passive controllers preserves these properties, ensuring stability.

Abstract

The recent rapid proliferation of renewable energy is fundamentally changing the dynamic operations of power systems, necessitating new approaches to assess stability for these highly nonlinear systems. In this paper, we prove that synchronous machine systems, modeled in the nonlinear dq-frame, possess fundamental dissipativity properties. Specifically, we show passivity from current input to voltage output and a nonlinear negative imaginary property from torque input to rotor angle output. For the nonlinear system shifted around an equilibrium point, we derive explicit conditions for both passivity and the NI property to hold. Finally, we demonstrate that interconnection with passive droop controllers preserves these dissipativity properties with identical supply rates, thereby ensuring closed-loop stability.