DC-DC Converters Optimization in Case of Large Variation in the Load

From the uploaded paper, the arithmetic balancing law is stated as Di = (1 − Îmeani/Isum)·D0·N/(N−1) with Îmeani = Imeani − minj Imeanj and Isum = ∑Îmeani. The paper motivates the factor N/(N−1) because one relative current is zero, but does not claim ∑Di = D0; it simply says D0 is the duty cycle from the controller and N is the number of phases. Under this definition, the model correctly shows that ∑i Di = N·D0, i.e., the average per-phase duty equals D0, and it identifies the tie case Isum = 0 and nonnegativity conditions (which the paper does not discuss) . In contrast, the paper’s stability section derives the quadratic characteristic polynomial for the 2×2 linear subsystem as λ^2 + (B1 + G)λ + (B1G + c g1) = 0 and asserts via the Routh–Hurwitz test that stability holds if (B1 + G) > 0 and (B1G + c g1) > 0, further claiming these are “fulfilled automatically” given B1 = −RL/Lj and G = −[…], i.e., both negative by construction. This is inconsistent: with B1 < 0 and G < 0, (B1 + G) > 0 does not hold, and the sign of the linear term also conflicts with the standard characteristic polynomial det(λI − A) = λ^2 − (B1 + G)λ + (B1G + c g1). The model’s Phase B answer correctly applies Routh–Hurwitz to the polynomial as given, obtaining the conditions listed, but the paper’s claim that these are automatically satisfied is false as printed; it appears to be a sign error in the characteristic polynomial/criterion statement . Overall: Part A aligns (model adds necessary caveats the paper omits); Part B contains a substantive sign/correctness error in the paper, while the model’s Routh–Hurwitz application to the stated polynomial is correct.