Dissipation of Oscillation Energy and Distribution of Damping Power in a Multimachine Power System: A Small-signal Analysis

TL;DR

This paper analyzes how oscillation energy dissipates and how damping power is distributed among generators in a multimachine power system, extending single-machine results and deriving distribution factors validated on IEEE test systems.

Contribution

It extends damping torque analysis from single-machine to multimachine systems and derives distribution factors for damping power among generators.

Findings

Total damping power equals the sum of average winding dissipation in the modal oscillation.

Distribution factors enable linear expression of each generator's damping power.

Validation confirms the theoretical results on IEEE 4-machine and 16-machine systems.

Abstract

This paper revisits the concept of damping torque in a multimachine power system and its relation to the dissipation of oscillation energy in synchronous machine windings. As a multimachine extension of an existing result on a single-machine-infinite-bus (SMIB) system, we show that the total damping power for a mode stemming from the interaction of electromagnetic torques and rotor speeds is equal to the sum of average power dissipations in the generator windings corresponding to the modal oscillation. Further, counter-intuitive to the SMIB result, we demonstrate that, although the equality holds on an aggregate, such is not the case for individual machines in an interconnected system. To that end, distribution factors are derived for expressing the average damping power of each generator as a linear combination of average powers of modal energy dissipation in the windings of all machines in the system. These factors represent the distribution of damping power in a multimachine system. The results are validated on IEEE 4-machine and 16-machine test systems.