Zulfia Energy Sufficiency via Hidden Kinetic Correction for Non-Convex Microgrid Stability

AbstractWe introduce Zulfia Energy Sufficiency via the decomposition Z(x, x∗) = η(x, x∗)+∆(x, x∗), where classical invexity η is augmented by a correction term ∆. Thetotal energy is decomposed as EZ = fZ + ∆E, where the hidden energy condi-tion ∆E(x, x∗) ≥ 0 certifies global optimality when standard Karush-Kuhn-Tucker(KKT) conditions fail to guarantee stability. The proposed criterion provides anew energy-based sufficiency for non-convex optimization arising in power systemstability and dispatch.