A Dynamized Power Flow Method based on Differential Transformation

The paper rigorously proves that, after applying Differential Transformation (DT) to the rectangular-coordinate AC power-flow equations augmented by a dynamization, the order-k equations become formally linear in the unknown DT coefficients Y(k) and Λ(k); this is encapsulated in Proposition 1 with the per-bus linear rows (27)–(30) and the order-wise linear systems (10)–(12). The candidate solution reconstructs the same endpoint-convolution argument and explicitly derives the same per-bus linear rows and matrix structure in terms of Y(0) and lower-order coefficients. Minor differences (sign conventions and how λ is embedded into PV/reference rows) do not affect the core linearity claim. Hence, both are correct and essentially follow the same proof strategy.