Phasor Diagram for Synchronous Motor

We will discuss here the simplest way of drawing the phasor diagram for synchronous motor and we will also discuss advantages of drawing the phasor diagram. Before we draw phasor diagram, let us write the various notations for each quantity at one place. Here we will use:
E_f to represent the excitation voltage V_t to represent the terminal voltage I_a to represent the armature current Θ to represent the angle between terminal voltage and armature current ᴪ to represent the angle between the excitation voltage and armature current δ to represent the angle between the excitation voltage and terminal voltage r_a to represent the armature per phase resistance.

We will take V_t as the reference phasor in order to phasor diagram for synchronous motor. In order to draw the phasor diagram one should know these two important points which are written below: (1) We know that if a machine is made to work as a asynchronous motor then direction of armature current will in phase opposition to that of the excitation emf. (2) Phasor excitation emf is always behind the phasor terminal voltage. Above two points are sufficient for drawing the phasor diagram for synchronous motor. The phasor diagram for the synchronous motor is given below,

In the phasor one the direction of the armature current is opposite in phase to that of the excitation emf. It is usually customary to omit the negative sign of the armature current in the phasor of the synchronous motor so in the phasor two we have omitted the negative sign of the armature current. Now we will draw complete phasor diagram for the synchronous motor and also derive expression for the excitation emf in each case. 

Motoring operation at lagging power factor. (b) Motoring operation at unity power factor. (c) Motoring operation at leading power factor. Given below are the phasor diagrams for all the operations.