Power Flow Diagram & Power Developed by Synchronous Motor

April 28, 2020
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 / phase = V I_{a} Cos φ
Total input power for 3φ star connected motor,
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,
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_{a}^{2 }R_{a }
Total copper loss = 3 I_{a}^{2 }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_{a}^{2} 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 an Synchronous Motor
The power developed in a synchronous motor as follows.
Motor Input Power, P
1. Stator ( Armature ) copper loss P_{cu}
2. Mechanical power developed, P_{m}
a. Iron, friction and excitation losses
b. Output power, P_{out}
Net Power Developed by a Synchronous Motor :
The expression for power developed by an synchronous motor interns of α, θ, V, E_{b} and Z_{s} is 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}
Mechanical power developed / phase,
Armature resistance is neglected
If R_{a} is neglected, then Z_{s} ≈ X_{s} and θ = 90°. substituting these values in the above equation
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