#### 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.

_{a}= Armature current/phase_{a}= Armature resistance/phase## Input Power to Motor :

#### Motor input power per phase is V I_{a} Cos Φ. Now, the total input power for 3-Φ star-connected motor is,
*P = √ 3 V*_{L} I_{L} Cos Φ
*P = 3 V*_{ph} I_{ph} Cos Φ
Where,- V
_{L} and I_{L} are line values. - V
_{ph} and I_{ph} are phase values.

*P = √ 3 V*

_{L}I_{L}Cos Φ*P = 3 V*

_{ph}I_{ph}Cos Φ_{L}and I_{L}are line values._{ph}and I_{ph}are phase values.## Power Developed by Motor :

#### The mechanical power developed / phase is,

= Back emf * Armature current * Cosine of the angle between E

_{b}and I_{a}= E

_{b}I_{a}Cos (α - Φ) for lagging PF= E

_{b}I_{a}Cos (α + Φ) for leading PF#### The copper loss in a synchronous motor takes place in the armature windings. Therefore,

Armature copper loss per 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 three-phase,

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.

## 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 per phase. - α = Load angle.
- θ = Internal or Impedance angle = Tan
^{-1} (X_{r} per Z_{s}). - I
_{a} = Armature current per phase = E_{r} per Z_{s}. - Z
_{s} = R_{a} + J X_{s} = Synchronous impedance.

Mechanical power developed per phase is given by,

_{b}= Back emf per phase.^{-1}(X_{r}per Z_{s})._{a}= Armature current per phase = E_{r}per Z_{s}._{s}= R_{a}+ J X_{s}= Synchronous impedance.