for why synchronous motor is not self-starting
Do you know why Synchronous motor is not the self-starting motor, i.e. when we apply three-phase voltage to the three-phase winding of stator, the current will flow through the winding, which sets up a synchronous rotating magnetic field across the stator in air gap as shown in Figure 1.
Figure 1: Simple synchronous motor Model
This rotating magnetic field should produce torque in the stationary rotor. However, analyses of the rotating magnetic field on the rotor are shown in Figure 2.
Figure 2: Effect of the rotating magnetic field of the stator
In the first case, the Rotor Nr pole of the rotor is aligned with the stator Ns pole, while Sr pole is aligned with the Sr pole of the stator. In this case, the rotor will experience a push due to repulsion between similar poles, and torque will produce in the rotor in an anticlockwise direction as highlighted in figure with the help of case (i). At the very next moment, due to the rotating magnetic field of the stator, the stator Ss pole will be aligned with Nr pole of the rotor and Ns pole of the stator will be aligned with Sr pole of rotor. In this case, due to opposite poles attraction, again there will be a force on rotor, resulting in equal torque but this time in the opposite direction as compared to the previous case. Therefore, in case (ii) rotor will experience clockwise torque. Thus, in every half cycle, torque direction is changing and the rotor in normal condition moves back and forth according to the direction of torque. However, due to its inertia, it does not respond that fast to the changing torque resulting in zero net effect and no movement of the rotor.
In order to start it, the rotor is first started with the help of some DC motor and speed is increased until it reaches a synchronous speed of stator. Then three-phase supply is applied on the stator to produce a magnetic field across it, and external power to the rotor is removed. The rotor is already rotating at synchronous speed, due to continuous change in direction of rotor poles at a similar rate with stator magnetic field; it will always experience unidirectional torque. Due to this magnetic field locking, the rotor will continue to move at synchronous speed in one direction due to unidirectional repulsion from the stator.
I think you can understand now why synchronous motor is not self-starting