“…For the purpose of WAC, we consider P mi to be constant, and design controller using only the excitation voltage u i . I qi , I di , V i , and θ i are algebraic variables that can be eliminated from (1)(2)(3)(4) by expressing them in terms of (E qi , δ i ), i = 1, .., n, using power balance equations through a process called Kron-reduction [8]. The resulting 4n nonlinear equations can, thereafter, be used to determine the steady-state equilibrium (δ i0 , Ω i0 , E ′ qi0 , E f di0 ), i = 1, ..., n. Considering a small-signal perturbation around 1 For ease of notation, we will omit the augment t from all variables.…”