The phasor diagram of a synchronous motor is shown below. From the phasor diagram,
let, V = Supply voltage / phase
 I_{a} = Armature current / phase
 R_{a} = Armature resistance / phase
 α = Load angle
 φ = Power factor angle
Input Power to Motor :
Motor input power per phase is V I_{a} Cos φ.
Now, the total input power for 3φ starconnected motor is,
P = √ 3 V_{L} I_{L}
Cos φ
= 3 V_{ph} I_{ph}
Cos φ
Where,
V_{L} and I_{L} are line values.

V_{ph} and I_{ph} are phase values.
Power Developed by Motor :
The mechanical power developed / phase is,
P_{m} = Back emf * Armature current * Cosine of the angle between E_{b} and I_{a}
= E_{b} I_{a} Cos ( α  φ ) for lagging p.f
= E_{b} I_{a} Cos ( α + φ ) for leading p.f
The copper loss in a synchronous motor takes place in the armature windings.
Therefore,
Armature copper loss / phase = I_{a}^{2} R_{a}
Total copper loss = 3 I_{a}^{2} R_{a}
By subtracting the copper loss from the power input, we obtain the mechanical power developed by a synchronous motor as,
P_{m} = P 
P_{cu}
For threephase,
P_{m} = √3
I_{L} I_{L} Cos φ – 3 I_{a}^{2} R_{a}
Power Output of the Motor :
To obtain the power output we subtract the iron, friction, and excitation losses from the power developed.
Therefore, Net output power, P_{out} = P_{m}  iron, friction, and excitation losses.
The above two stages can be shown diagrammatically called as Power Flow Diagram of a Synchronous Motor
The power developed in a synchronous motor as follows.
Motor Input Power, P
 Stator ( Armature ) copper loss P_{cu}
 Mechanical power developed, P_{m}
 Iron, friction, and excitation losses
 Output power, P_{out}
Net Power Developed by a Synchronous Motor :
The expression for power developed by the synchronous motor in terms of α, θ, V, E_{b,} and Z_{s} are as follows :
Let
 V = Supply voltage
 E_{b} = Back emf / phase

α = Load angle

θ = Internal or Impedance angle = Tan^{1} ( X_{r} / Z_{s}
)

I_{a} = Armature current / phase = E_{r} / Z_{s}

Z_{s} = R_{a} + J X_{s} = Synchronous impedance
Mechanical power developed / phase,
The armature resistance is neglected
If R_{a} is neglected, then Z_{s} ≈ X_{s} and θ = 90°. substituting these values in the above equation.