# Hamiltonian-inspired energy function for power grid stability

I'm looking at this paper which proposes an energy function for a 3-bus power system example. I'm trying to replicate the results in the paper but am uncertain about the D parameters in Sec III. In particular, the authors verify that with a certain A matrix adjusting the gradient dynamics, the model has a stable equilibrium, but I'm confused about the D parameters in this matrix.

Here is the relevant section:

EDIT1: it looks like the D terms are some sort of rotor damping.

EDIT2 (follow up question): I'm having trouble tying out the dimensions of the A3bus matrix to the Abus matrix. Specifically, the dimensions of Mg seem off. It appears that the g means both slack and generator node, but then I don't see how to fit A3bus into the Abus structure. Any advice?

EDIT3: this paper helps somewhat but is still a bit unclear on the interpretation of the Pi matrices.

Thanks!

• What page specifically were you looking at? – W5VO Oct 22 '18 at 22:37
• Sorry, just realized I uploaded a different but related link. Let me extract the pages of the paper I'm referring to – rrrrr Oct 22 '18 at 22:45

Stub of an answer right now, but the D parameters refer to machine damping values in the classical swing equations. The epsilon parameter is a singular perturbation of an algebraic constraint related to the reactive power flow.