Local blackout and global power system wide blackout are caused by non-linear negative damping

Local blackout occurs when the transient stability limit is exceeded after a transmission line fault. As to global blackout, a recording of the 10 August 1996-WECC blackout shows that it was accompanied negative damping. A turbine-generator swinging against an infinite bus is used to approximate the dynamics leading to the WECC blackout. There is no analytic solution when non-linearity is included. Small-signal linearisation shows that negative damping can occur but cannot produce the waveform recorded in the WECC blackout. Therefore, the graphical phase-plane method, which is easy to use, is resorted to. The study shows that the kernel of non-linearity consists of the gradients which produce limit cycles. Positive or negative damping is produced by shifting the gradients of the limit cycles to the right or left in the direction of the trajectory. The study makes a contribution by showing that phase plane can be used to study the impact of multiple independent controllers. A worked example shows when transient stability limit is exceeded, local blackout occurs. The swing equation of local blackout is applied to the WECC blackout. As proof that negative damping was due to non-linearity, a waveform having the frequency of the recorded WECC blackout is presented.