Synchronizing power coefficient

The ratio of differential power change to differential load angle change is define as synchronizing power coefficient or electrical stiffness of asynchronous machine. It’s used as measure of system stability. The linearization of swing equation about initial operating point (δ₀, P₀) is possible for steady state analysis. Under normal state,   P_m = P_e = P₀    and  δ = δ₀. Let due to small disturbance (electrical load changes to P₀ + ΔP) load angle changes to (δ₀ + Δδ).

 

 

If S_P > 0;         Roots are pure imaginary and conjugate pair Rotor motion is                        oscillatory & undamped about δ₀

If S_P < 0;         Both roots are real with one +ve & one –ve.                         

                       System is unstable.      

If S_P = 0;         Roots are zero System is critically stable.