Integrated System Models for Networks with Generators & Inverters

The paper derives ω_ss by first asserting Σ_n P_n = 0 under a lossless network, but justifies this by “using the property of sin() being an even function” and without explicitly invoking reciprocity/symmetry of B; sin is odd, and Σ_n P_n = 0 actually follows from G ≡ 0 together with B = B^T (reciprocity) so that pairwise terms cancel in (52a) or, equivalently, from S = 3 E ∘ (Y(ω_ss)^* E^*) with Y = jB and B symmetric (Y + Y^H = jB − jB^T = 0). The paper then sums the device equations (53) to obtain the closed-form ω_ss in (55), which matches the model’s result. The model corrects the missing hypothesis and the misstatement about sin, and also states clear existence/uniqueness conditions. See the paper’s equations (51)–(53) and the steady-state frequency result (55) for context and claims .