Figure 32.9 shows the power transfer characteristics (Pδ × δ) of a transmission line, which is first assumed to be transmitting power PS0 at phase angle δ0. If a problem happens in the line (a fault, for example) the turbine that drives the generator cannot change its mechanical power input immediately even if there is no power transmission for a short time. This situation accelerates the generator, increasing its frequency and leading to an increase of the phase angle δ to δ1. If the line restarts operation at the instant corresponding to this phase angle δ1, the transmitted power will be P1, which is larger than P0 and decelerates the turbine or generator. The area A1 corresponds to the energy that accelerated the turbine. As the frequency gets higher than the rated frequency at (PS1, δ1), the phase angle will increase up to δ2, where the area A2 is equal to the area A1. If the area given by the A2 plus A3 is larger than A1, the system is said to be dynamically stable. On the contrary, if it is not possible to have an area A2 equal to A1, the system is said to be unstable. An unstable situation is shown in Fig. 32.10 in which the system is the same as in Fig. 32.9 but assuming a longer interval with no power transmission. In this case, the turbine or generator accelerates more than that in Fig. 32.9 and the phase angle δ increases above its critical value δc, which is slightly less than 90◦ reaching δ1. Therefore, the area below the Pδ curve to decelerate the system is not enough leading to an unstable system because A2 is smaller than A1.