Critical clearing angle

The greatest change in the load angle curve prior to clearing the fault without losing synchronism is known as the critical clearing angle. In other words, the system becomes unstable when a fault occurs because the load angle curve starts to rise. The CCA is the angle at which the fault is discovered and the system becomes stable.

There is a CCA when the initial load is applied, and the system becomes unstable if the actual clearing angle is greater than the critical clearing angle. Otherwise, the system is stable. As shown below, let’s assume curve A stands for the power angle curve in a healthy condition, curve B for a faulty condition, and curve C for the power angle curve following the isolation of the fault.

Where γ₁ is the ratio of system reactance in healthy condition to that of during the fault. And γ₂ is the ratio of steady state limit of the system after the isolation of fault and that of system under the initial condition.

For transient stability limit, two areas  A₁ = A₂ or. In other words the area under curve adec (rectangle) is equal to the area under the curve da’b’bce.

Now substituting, we have,

                                                                       or

Also from the curves

                                                                          or

Thus if γ₁, γ₂, and δ₀ are known, the critical clearing angle δc can be determined.