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
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
Where,-
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.
Therefore,
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
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 :
Let
- 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.