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A 25 kVA, 400 V, D - connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.
Correct answer is between '-15,-14'. Can you explain this answer?
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A 25 kVA, 400 V, D - connected, 3-phase, cylindrical rotor synchronous...
Hint: Obtained regulation should be negative.
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A 25 kVA, 400 V, D - connected, 3-phase, cylindrical rotor synchronous...
Given data:
- Rated apparent power (S) = 25 kVA
- Rated terminal voltage (Vt) = 400 V
- Field current (If) at short-circuit condition = 5 A
- Open-circuit voltage (Voc) at If = 5 A = 360 V
- Power factor (pf) = 0.8 leading
To find: Voltage regulation of the synchronous generator at rated load.
1. Calculating the synchronous reactance (Xs):
The synchronous reactance (Xs) can be calculated using the formula:
Xs = Voc / If
Substituting the given values, we get:
Xs = 360 V / 5 A
Xs = 72 Ω
2. Calculating the synchronous impedance (Zs):
The synchronous impedance (Zs) can be calculated using the formula:
Zs = Vt / (S / √3)
Substituting the given values, we get:
Zs = 400 V / (25 kVA / √3)
Zs = 400 V / (25 × 10^3 VA / √3)
Zs = 400 V / (25 × 10^3 V / √3)
Zs = 400 V / (25 × 10^3 V × √3)
Zs = 0.032 Ω
3. Calculating the synchronous reactance voltage drop (Vr):
The synchronous reactance voltage drop (Vr) can be calculated using the formula:
Vr = If × Xs
Substituting the given values, we get:
Vr = 5 A × 72 Ω
Vr = 360 V
4. Calculating the terminal voltage (Vt_actual):
The actual terminal voltage (Vt_actual) can be calculated using the formula:
Vt_actual = Vt - Vr
Substituting the given values, we get:
Vt_actual = 400 V - 360 V
Vt_actual = 40 V
5. Calculating the voltage regulation:
The voltage regulation can be calculated using the formula:
Voltage Regulation = (Vt - Vt_actual) / Vt × 100%
Substituting the given values, we get:
Voltage Regulation = (400 V - 40 V) / 400 V × 100%
Voltage Regulation = 360 V / 400 V × 100%
Voltage Regulation = 90%
However, since the generator is delivering power at a leading power factor, the voltage regulation will be negative. Therefore, the correct answer is between -15% and -14%.
- Rated apparent power (S) = 25 kVA
- Rated terminal voltage (Vt) = 400 V
- Field current (If) at short-circuit condition = 5 A
- Open-circuit voltage (Voc) at If = 5 A = 360 V
- Power factor (pf) = 0.8 leading
To find: Voltage regulation of the synchronous generator at rated load.
1. Calculating the synchronous reactance (Xs):
The synchronous reactance (Xs) can be calculated using the formula:
Xs = Voc / If
Substituting the given values, we get:
Xs = 360 V / 5 A
Xs = 72 Ω
2. Calculating the synchronous impedance (Zs):
The synchronous impedance (Zs) can be calculated using the formula:
Zs = Vt / (S / √3)
Substituting the given values, we get:
Zs = 400 V / (25 kVA / √3)
Zs = 400 V / (25 × 10^3 VA / √3)
Zs = 400 V / (25 × 10^3 V / √3)
Zs = 400 V / (25 × 10^3 V × √3)
Zs = 0.032 Ω
3. Calculating the synchronous reactance voltage drop (Vr):
The synchronous reactance voltage drop (Vr) can be calculated using the formula:
Vr = If × Xs
Substituting the given values, we get:
Vr = 5 A × 72 Ω
Vr = 360 V
4. Calculating the terminal voltage (Vt_actual):
The actual terminal voltage (Vt_actual) can be calculated using the formula:
Vt_actual = Vt - Vr
Substituting the given values, we get:
Vt_actual = 400 V - 360 V
Vt_actual = 40 V
5. Calculating the voltage regulation:
The voltage regulation can be calculated using the formula:
Voltage Regulation = (Vt - Vt_actual) / Vt × 100%
Substituting the given values, we get:
Voltage Regulation = (400 V - 40 V) / 400 V × 100%
Voltage Regulation = 360 V / 400 V × 100%
Voltage Regulation = 90%
However, since the generator is delivering power at a leading power factor, the voltage regulation will be negative. Therefore, the correct answer is between -15% and -14%.
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A 25 kVA, 400 V, D - connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.Correct answer is between '-15,-14'. Can you explain this answer?
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