A 100 kVA, 11 kV/400 V, 3-phase transformer has its maximum possible e...
Efficiency and Voltage Regulation of a Transformer
Given Data:
- Transformer rating: 100 kVA
- Input voltage: 11 kV
- Output voltage: 400 V
- Efficiency at 80 kVA, unity pf and rated voltage: 98%
- Maximum possible voltage regulation: 4%
Efficiency Calculation:
Efficiency of a transformer is given by:
Efficiency = (Output Power / Input Power) x 100%
At maximum efficiency, the output power is 80 kVA.
Input Power = Output Power / Efficiency
Input Power = 80 kVA / 0.98 = 81.63 kVA
Hence, the input current is:
Input Current = Input Power / (sqrt(3) x Input Voltage)
Input Current = 81.63 kVA / (sqrt(3) x 11 kV) = 4.62 A
Therefore, the efficiency of the transformer at rated kVA output and 0.8 pf lagging can be calculated as follows:
Output Power = 100 kVA x 0.8 = 80 kVA
Input Power = Output Power / pf
Input Power = 80 kVA / 0.8 = 100 kVA
Hence, the input current is:
Input Current = Input Power / (sqrt(3) x Input Voltage)
Input Current = 100 kVA / (sqrt(3) x 11 kV) = 5.69 A
The input voltage drop due to the transformer's internal impedance is:
Voltage Drop = Input Current x Transformer Impedance
Let's assume the voltage drop is V.
Then, the output voltage can be calculated as:
Output Voltage = Input Voltage - V
Maximum possible voltage regulation is 4%, which means:
Voltage Regulation = (V / Input Voltage) x 100% = 4%
Hence, V = 0.04 x 11 kV = 440 V
Output Voltage = 11 kV - 440 V = 10.56 kV
Therefore, the efficiency of the transformer at rated kVA output and 0.8 pf lagging is:
Efficiency = (Output Power / Input Power) x 100%
Efficiency = (80 kVA / 100 kVA) x 100% = 80%
Voltage Regulation Calculation:
Voltage Regulation = (V / Input Voltage) x 100%
From the above calculations, we know that V = 440 V and Input Voltage = 11 kV.
Voltage Regulation = (440 V / 11 kV) x 100% = 4%
Conclusion