A note on the equal-area stability criterion

In the application of the equal-area stability criterion to the case of a synchronous machine connected via a transmission line to either an infinite busbar or another synchronous machine, the limiting load angle θ1 is related to the initial load-angle θ0 by the equation(π−θ1−θ0)sinθ1=cosθ0+cosθ1if resistances are neglected.This equation is not soluble analytically, and it is usual to employ empirical solutions.By advancing the origin of the displacement angle by π/2 and writing (π/2−θ0=α and (π/2−θ0=γ, the equation becomes(α + γ) cos α = sin α + sin γa very good approximate solution of which is α=γ/2.The paper applies this simple approximation, both graphically and algebraically, to the two problems considered, and shows that over the normal practical range the errors introduced are not likely to exceed about 1%.