Negative Imaginary and Passivity Properties of Synchronous Machine Systems

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.