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A single-phase transformer is rated 220/440 V,5 kVA, leakage reactance measured from the low-tension side is 0.05Ω . The per unit leakage reactance will be _______.
(Give up to four decimal places).
Correct answer is '0.0051'. Can you explain this answer?
Most Upvoted Answer
A single-phase transformer is rated 220/440 V,5 kVA, leakage reactanc...
Understanding Per Unit System
In electrical engineering, the per unit system is a method used to normalize system quantities. This allows for easier comparison and calculation across different systems.
Given Data
- Transformer ratings: 220/440 V
- Power rating: 5 kVA
- Leakage reactance (low-tension side): 0.05 Ω
Calculating Base Values
1. Base Voltage on Low-Tension Side (V_base):
- V_base = 220 V
2. Base Power (S_base):
- S_base = 5 kVA = 5000 VA
3. Base Reactance (X_base):
- X_base = V_base^2 / S_base
- X_base = (220 V)² / (5000 VA)
- X_base = 48400 / 5000
- X_base = 9.68 Ω
Calculating Per Unit Leakage Reactance
To find the per unit (pu) leakage reactance:
- Per Unit Reactance (X_pu):
- X_pu = Actual Reactance / Base Reactance
- X_pu = 0.05 Ω / 9.68 Ω
- X_pu = 0.005171
Rounding to Four Decimal Places
- Rounding 0.005171 to four decimal places gives:
- X_pu = 0.0051
Conclusion
The per unit leakage reactance of the transformer is 0.0051. This normalized value simplifies analysis in power systems, allowing engineers to easily compare different transformers and their reactances.
In electrical engineering, the per unit system is a method used to normalize system quantities. This allows for easier comparison and calculation across different systems.
Given Data
- Transformer ratings: 220/440 V
- Power rating: 5 kVA
- Leakage reactance (low-tension side): 0.05 Ω
Calculating Base Values
1. Base Voltage on Low-Tension Side (V_base):
- V_base = 220 V
2. Base Power (S_base):
- S_base = 5 kVA = 5000 VA
3. Base Reactance (X_base):
- X_base = V_base^2 / S_base
- X_base = (220 V)² / (5000 VA)
- X_base = 48400 / 5000
- X_base = 9.68 Ω
Calculating Per Unit Leakage Reactance
To find the per unit (pu) leakage reactance:
- Per Unit Reactance (X_pu):
- X_pu = Actual Reactance / Base Reactance
- X_pu = 0.05 Ω / 9.68 Ω
- X_pu = 0.005171
Rounding to Four Decimal Places
- Rounding 0.005171 to four decimal places gives:
- X_pu = 0.0051
Conclusion
The per unit leakage reactance of the transformer is 0.0051. This normalized value simplifies analysis in power systems, allowing engineers to easily compare different transformers and their reactances.
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