Three single-phase 50kVA, 2300/230V, 50Hz transformers are connected t...
Problem Statement
Three single-phase 50kVA, 2300/230V, 50Hz transformers are connected to form a three-phase star-delta transformer. The equivalent impedance of each transformer referred to HV side is (1.2 j1.6)Ω. The three-phase transformer thus formed supplies a three-phase load of 120kVA at 230V with 0.85 power factor (lag). Determine the voltage regulation of the transformer.
Solution
Given:
- Three single-phase transformers of rating 50kVA, 2300/230V, 50Hz
- Transformers are connected to form a three-phase star-delta transformer
- Equivalent impedance of each transformer referred to HV side is (1.2 j1.6)Ω
- Three-phase transformer supplies a load of 120kVA at 230V with 0.85 power factor (lag)
Step 1: Calculate the line current
Line current = 120kVA / (√3 * 230V * 0.85) = 345.59A
Step 2: Calculate the HV current
HV current = Line current / √3 = 200A
Step 3: Calculate the equivalent impedance referred to LV side
Equivalent impedance referred to LV side = (1/3) * (1.2 + j1.6)Ω = 0.4 + j0.533Ω
Step 4: Calculate the voltage drop in the transformer
Voltage drop in the transformer = HV current * equivalent impedance referred to LV side
Voltage drop in the transformer = 200A * (0.4 + j0.533)Ω = 80 + j106.6V
Step 5: Calculate the secondary voltage
Secondary voltage = 230V - voltage drop in the transformer = 230V - (80 + j106.6)V = 149.2 - j106.6V
Step 6: Calculate the voltage regulation
Voltage regulation = ((230V - secondary voltage) / secondary voltage) * 100%
Voltage regulation = ((230V - 149.2V) / 149.2V) * 100% = 54.04%
Conclusion
The voltage regulation of the transformer is 54.04%.