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
• 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 3-φ star-connected 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_a² R_a

Total copper loss = 3 I_a² 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_a² 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.