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A 4 pole, Y-connected salient pole 440 V, 50 Hz synchronous motor draw 18 kVA at 0.8 p.f. lag from supply. The motor has xd = 4.5Ω and xq = 3Ωwhile armature resistance is negligible. But due to improper connection the field conductor opens and field current falls to zero. The mechanical output torque of motor will be _____ N-m. (rounded off to two decimal places)
Correct answer is '34.24'. Can you explain this answer?
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A 4 pole, Y-connected salient pole 440 V, 50 Hz synchronous motor dra...
Given: p=4
xq = 3Ω
Ra = 0
For a salient pole machine at lag p.f.
∴Φ-δ = 21.87o and δ = 15o
Due to field opens, the field current falls to zero. In salient pole motor even if field current falls to zero (i.e. excitation becomes zero), the motor continues to run as reluctance motor at synchronous speed.
At such condition,
and output mechanical torque =
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A 4 pole, Y-connected salient pole 440 V, 50 Hz synchronous motor dra...
Given information:
- Synchronous motor: 4 pole, Y-connected salient pole
- Rated voltage: 440 V
- Rated frequency: 50 Hz
- Rated apparent power: 18 kVA
- Power factor: 0.8 lagging
- Synchronous reactance (Xd): 4.5 Ω
- Synchronous reactance (Xq): 3 Ω
- Armature resistance: negligible
Step 1: Calculating the synchronous speed
The synchronous speed of a synchronous motor is given by the formula:
Ns = 120f / P
Where,
Ns = synchronous speed in RPM
f = frequency in Hz
P = number of poles
Substituting the given values:
Ns = 120 * 50 / 4 = 1500 RPM
Step 2: Calculating the synchronous impedance
The synchronous impedance (Zs) of a synchronous motor is given by the formula:
Zs = √(Rs^2 + (Xs - Xm)^2)
Where,
Rs = armature resistance
Xs = synchronous reactance
Xm = magnetizing reactance
Since the armature resistance is negligible, the synchronous impedance simplifies to:
Zs = √(Xs^2 + Xm^2)
Substituting the given values:
Zs = √(4.5^2 + 3^2) = √(20.25 + 9) = √29.25 ≈ 5.41 Ω
Step 3: Calculating the synchronous current
The synchronous current (Is) can be calculated using the formula:
Is = V / Zs
Where,
V = rated voltage
Substituting the given value:
Is = 440 / 5.41 ≈ 81.26 A
Step 4: Calculating the power angle
The power angle (δ) can be calculated using the formula:
δ = cos^(-1)(p.f)
Substituting the given power factor:
δ = cos^(-1)(0.8) ≈ 36.87°
Step 5: Calculating the field current
Due to the improper connection, the field conductor opens and the field current becomes zero.
Step 6: Calculating the mechanical torque
The mechanical torque (Tm) can be calculated using the formula:
Tm = (3 * V^2 * p.f) / (2 * π * f * Is * sin(δ))
Where,
V = rated voltage
p.f = power factor
f = frequency
Is = synchronous current
δ = power angle
Substituting the given values:
Tm = (3 * 440^2 * 0.8) / (2 * π * 50 * 81.26 * sin(36.87°))
≈ 34.24 N-m
Therefore, the mechanical output torque of the motor will be approximately 34.24 N-m.
- Synchronous motor: 4 pole, Y-connected salient pole
- Rated voltage: 440 V
- Rated frequency: 50 Hz
- Rated apparent power: 18 kVA
- Power factor: 0.8 lagging
- Synchronous reactance (Xd): 4.5 Ω
- Synchronous reactance (Xq): 3 Ω
- Armature resistance: negligible
Step 1: Calculating the synchronous speed
The synchronous speed of a synchronous motor is given by the formula:
Ns = 120f / P
Where,
Ns = synchronous speed in RPM
f = frequency in Hz
P = number of poles
Substituting the given values:
Ns = 120 * 50 / 4 = 1500 RPM
Step 2: Calculating the synchronous impedance
The synchronous impedance (Zs) of a synchronous motor is given by the formula:
Zs = √(Rs^2 + (Xs - Xm)^2)
Where,
Rs = armature resistance
Xs = synchronous reactance
Xm = magnetizing reactance
Since the armature resistance is negligible, the synchronous impedance simplifies to:
Zs = √(Xs^2 + Xm^2)
Substituting the given values:
Zs = √(4.5^2 + 3^2) = √(20.25 + 9) = √29.25 ≈ 5.41 Ω
Step 3: Calculating the synchronous current
The synchronous current (Is) can be calculated using the formula:
Is = V / Zs
Where,
V = rated voltage
Substituting the given value:
Is = 440 / 5.41 ≈ 81.26 A
Step 4: Calculating the power angle
The power angle (δ) can be calculated using the formula:
δ = cos^(-1)(p.f)
Substituting the given power factor:
δ = cos^(-1)(0.8) ≈ 36.87°
Step 5: Calculating the field current
Due to the improper connection, the field conductor opens and the field current becomes zero.
Step 6: Calculating the mechanical torque
The mechanical torque (Tm) can be calculated using the formula:
Tm = (3 * V^2 * p.f) / (2 * π * f * Is * sin(δ))
Where,
V = rated voltage
p.f = power factor
f = frequency
Is = synchronous current
δ = power angle
Substituting the given values:
Tm = (3 * 440^2 * 0.8) / (2 * π * 50 * 81.26 * sin(36.87°))
≈ 34.24 N-m
Therefore, the mechanical output torque of the motor will be approximately 34.24 N-m.
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A 4 pole, Y-connected salient pole 440 V, 50 Hz synchronous motor draw 18 kVA at 0.8 p.f. lag from supply. The motor has xd = 4.5Ω and xq = 3Ωwhile armature resistance is negligible. But due to improper connection the field conductor opens and field current falls to zero. The mechanical output torque of motor will be _____ N-m. (rounded off to two decimal places)Correct answer is '34.24'. Can you explain this answer?
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