2205.10984
A mode-in-state contribution factor based on Koopman operator and its application to power system analysis
Kenji Takamichi, Yoshihiko Susuki, Marcos Netto, Atsushi Ishigame
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper defines the KMD-based mode-in-state contribution factor ωk,j := (∂φj/∂xk)(x(0)) Vj,k, and in the linear DAE case with det(A4) ≠ 0 reduces the DAE to ẋ = (A1 − A2 A4^{-1}A3)x. Under distinct eigenvalues, φj(x) = u_j^T x and Vj = v_j, so ωk,j = u_{j,k} v_{j,k} (matching classical participation factors). These steps and conclusions align exactly with the candidate solution’s elimination of y, spectral expansion e^{At} = Σ e^{λj t} v_j u_j^T, identification of φj and Vj, and the resulting ωk,j formula. See the paper’s derivation and linear-case specialization in eqs. (5)–(6) and eqs. (11)–(12) respectively .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The linear-case derivation of Koopman eigenfunctions/modes and the resulting contribution factor matches established results and the candidate model’s proof. The nonlinear framing is useful and coherent. Minor clarifications on assumptions (diagonalizability, normalization, handling complex conjugate pairs) would further improve rigor and applicability.