Relative and Mean Motions of Multi-Machine Power Systems in Classical Model
Provides theoretical justification for a standard practice in power system stability analysis, but is incremental as it formalizes known assumptions.
This paper proves that under uniform damping, the two real eigenvalues in an m-machine power system do not affect the dynamics of the complex eigenvalues, justifying the use of relative or COI coordinates for rotor angle stability analysis.
It is well-known that in an m-machine power system where each machine is represented by a second-order differential equation, the Jacobian of the system equation contains (m-1) pairs of conjugate eigenvalues and two real eigenvalues, including at least one zero. This letter proves that under the uniform damping condition, the dynamics associated with the two real eigenvalues do not have any impact on the dynamics associated with those complex eigenvalues. This conclusion is important to justify the use of the relative motions or center-of-inertia (COI) coordinate to analyze the rotor angle stability in a multi-machine power system.