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 per phase is V Ia Cos φ. Now, the total input power for 3-φ star-connected motor is,
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 is,

Pm = Back emf * Armature current * Cosine of the angle between Eb and Ia
= Eb Ia Cos ( α - φ ) for lagging p.f
= Eb Ia 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 Ra

Total copper loss = 3 Ia2 Ra

     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 IL IL 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.

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

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

Power Flow Diagram & Power Developed by Synchronous Motor

The power developed in a synchronous motor as follows.

Motor Input Power, P
  • Stator ( Armature ) copper loss Pcu
  • Mechanical power developed, Pm
    • Iron, friction, and excitation losses
    • Output power, Pout

Net Power Developed by a Synchronous Motor :

     The expression for power developed by the synchronous motor in terms of α, θ, V, Eb, and Zs are 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,

The 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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