Power Flow Diagram & Power Developed by Synchronous Motor

The phasor diagram of a synchronous motor is shown below. From the phasor diagram,


    V = Supply voltage / phase

    Ia  = Armature current / phase

    Ra  = Armature resistance / phase

    α = Load angle

    φ  = Power factor angle

Power Flow Diagram & Power Developed by Synchronous Motor

Input Power to Motor :

Motor input power / phase  =  V Ia Cos φ

Total input power for 3-φ star connected motor,

P  =  √ 3 VL IL Cos φ 

    =  3 Vph Iph Cos φ


   VL and  IL  are line values

   Vph and  Iph are phase values

Power Developed by Motor :

The mechanical power developed / phase,

Pm  =  Back emf * Armature current * Cosine of the angle between Eb and Ia

=   EIa Cos ( α - φ )   for lagging p.f

=   EIa Cos ( α + φ )   for leading p.f

     The copper loss in a synchronous motor takes place in the armature windings.


Armature copper loss / phase  =  Ia2 R

Total copper loss  =  3 Ia2 R

     By subtracting the copper loss from the power input, we obtain the mechanical power developed by a synchronous motor as

Pm  =  P - Pcu

For three phase,

Pm  =  √  3 IIL Cos φ – 3 Ia2 Ra

Power Output of the Motor :

      To obtain the power output we subtract the iron, friction and excitation losses from the power developed.


Net output power, Pout  =  Pm  -  iron, friction and excitation losses.

     The above two stages can be shown diagrammatically called as Power Flow Diagram of an Synchronous Motor

Power Flow Diagram & Power Developed by Synchronous Motor

The power developed in a synchronous motor as follows.

Motor Input Power, P

  1. Stator ( Armature ) copper loss Pcu

  2. Mechanical power developed, Pm

         a. Iron, friction and excitation losses

         b. Output power, Pout

Net Power Developed by a Synchronous Motor :

     The expression for power developed by an synchronous motor interns of  α, θ, V, Eb and Zs is as follows :


   V  =  Supply voltage

   Eb  =  Back emf / phase

   α  =  Load angle

   θ  =  Internal or Impedance angle  =  Tan-1 ( Xr / Zs )

   Ia  =  Armature current / phase  =  Er / Zs

   Zs  =  Ra + J Xs  =  Synchronous impedance

Mechanical power developed / phase,

Armature resistance is neglected

     If Ra is neglected, then Zs   Xs and θ = 90°. substituting these values in the above equation

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