A 100 kVA, 11 kV/400 V, 3-phase transformer has its maximum possible efficiency of 98%, when it delivers 80 kVA at unity pf and rated voltage. The maximum possible voltage regulation of the transformer is 4%. Find the efficiency and voltage regulation of the transformer for rated kVA output at 0.8 pf lagging?

Question

Answer

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

Similar Electrical Engineering (EE) Doubts

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