How Single Pole Switching of Circuit Breaker can improve the transient stability of the Power System?
The majority of faults in a grid transmission system are phase-to-ground.  So, we can clear the fault by tripping only the faulted phase.  This helps transient stability because you can still transmit power on the 2 un-faulted phases.
The easiest way to think about it is to picture a machine connected to the grid via one transmission line.  If the machine is operating at some electrical output P, and you open all three poles (phases) of the transmission line then P will go into speeding up the machine - since it can't get out over the transmission line.  Remember, at an operating equilibrium you have P mechanical input = P electrical output + losses.
But, if you only open 1 pole, a significant amount of P can still exit the generator and the increase in machine speed will be much less.
Read section II of this paper and you will see what I'm describing.