Power Flow Diagram & Power Developed by Synchronous Motor

The phasor diagram of a synchronous motor is shown below. From the phasor diagram, let,
  • 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
P = 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,

= Back emf * Armature current * Cosine of the angle between Eb and Ia
= Eb Ia Cos (α - Φ) for lagging PF
= Eb Ia 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 = 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

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. Let,
  • V = Supply voltage.
  • Eb = Back emf per phase.
  • α = Load angle.
  • θ = Internal or Impedance angle = Tan-1 (Xr per Zs).
  • Ia = Armature current per phase = Er per Zs.
  • Zs = Ra + J Xs = Synchronous impedance.
Mechanical power developed per phase is given by,

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

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