Fault cleared at 30°, Pe = 2.1 sin δ

Data: $P_e = 2.1\sin\delta$ (normal and, assuming a temporary fault, also post-fault), $P_m = 1.0$ pu. The fault is at the generator bus, so $P_e = 0$ during the fault.

Step 1: Initial and maximum angles

$$\begin{aligned} \delta_0 &= \sin^{-1}\frac{1.0}{2.1} = 28.44^\circ = 0.4963\ \text{rad} \\ \delta_{max} &= 180^\circ - 28.44^\circ = 151.56^\circ \end{aligned}$$

Step 2: Stability check for clearing at $30^\circ$

$$\begin{aligned} A_1 &= P_m(\delta_c - \delta_0) = 1.0(0.5236 - 0.4963) = 0.0273\ \text{pu·rad} \\ A_{2,max} &= 2.1(\cos30^\circ - \cos151.56^\circ) - 1.0(2.6453 - 0.5236) = 1.5436\ \text{pu·rad} \end{aligned}$$

Since $A_{2,max} \gg A_1$, the system is stable. Clearing occurs only $1.56^\circ$ after the fault.

Step 3: Maximum (critical) clearing angle

With $P_{max2} = 0$ and $P_{max3} = P_{max1}$:

$$\begin{aligned} \cos\delta_{cr} &= (\pi - 2\delta_0)\sin\delta_0 - \cos\delta_0 \\ &= (3.1416 - 0.9926)(0.4762) - 0.8793 \\ &= 0.1440 \\ \delta_{cr} &= 81.72^\circ \end{aligned}$$

Answer: Stable when cleared at 30°; maximum (critical) clearing angle ≈ 81.7°.