The impact of load placement on grid resonances during grid restoration

Adolfo Anta, Diego Cifelli

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper states and sketches a proof that, for small load changes, placing the load at the center maximizes the damping of the first resonance and that the sensitivity improves monotonically as the load approaches the center, using a linearization of its characteristic equations (its equations (12)–(17)) and Chebyshev-based formulas, though the crucial monotonicity step is deferred to ‘lengthy computations’ rather than shown . The candidate model derives an explicit sensitivity formula via the implicit function theorem applied directly to the exact characteristic polynomial, isolates the j-dependence as a Chebyshev product, and proves strict monotonicity and the center optimum (with the even-n tie) cleanly. Conclusion: both reach the same result; the model provides a more rigorous derivation while the paper offers a correct but sketch-level argument corroborated by its analytics and examples .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper addresses a practically relevant and analytically tractable question, deriving closed-form spectral relations for a loaded 2-Toeplitz RLC ladder and establishing the center as the locally optimal load placement for damping the first resonance. The core formulas and conclusions are correct, but the monotonicity proof is asserted rather than shown, and a few assumptions (simplicity, spectral gap, small-load regime) are implicit. Clarifying these points and tightening the sensitivity argument would elevate the work.