A 120/208 V distribution transformer bank of three single phase transformers is connected as a four wire {D pri. – YN sec.} with Neutral wire at the secondary side to service different load demand of 120/208 Vac. The transformer turn ratio is 100:1. The load in the system consists of ONE 72KW , 3 phase motor with PF =1 operating at Vt of 208V; THREE 12KW, 1 phase lighting circuits with a terminal voltage of 120V; and THREE 1 phase 10 KVA motors, PF=0.8 lagging with the terminal voltage of 208 V. Calculate
- The total KVA load of the circuit
*The KVA rating of the individual transformers (KVA/Transformer bank) to be used knowing that 50KVA, 100KVA and 150KVA is available in the market
*The full line currents (in AMPS) on the high voltage side of the transformer using a transformer rating of 150KVA
- The secondary line current in AMPs;
*The Vline at the primary side of transformer in KV
*The KVA of the transformer bank if ratings of 100KVA, 112.5 KVA and 150KVA & 200KVA are only available in the market!
*The primary line current in AMPS
*The Vline in KV at the secondary side of transformer
The correct answer and explanation is :
Solution: Distribution Transformer Bank Calculations
Step 1: Calculate the Total Load in kVA
- Three-phase motor load
[
S_{3\phi} = \frac{P}{PF} = \frac{72}{1} = 72 \text{ kVA}
] - Three single-phase lighting loads (120V circuits)
[
S_{\text{lights}} = 3 \times 12 = 36 \text{ kVA}
] - Three single-phase motors (208V, PF = 0.8 lagging)
[
S_{\text{1ϕ motors}} = 3 \times 10 = 30 \text{ kVA}
]
Total kVA load:
[
S_{\text{total}} = 72 + 36 + 30 = 138 \text{ kVA}
]
Step 2: Determine kVA per Transformer
The system uses a Δ-Y connection, so the total kVA is divided equally among the three transformers.
[
S_{\text{per transformer}} = \frac{S_{\text{total}}}{3} = \frac{138}{3} = 46 \text{ kVA}
]
The closest available transformer rating is 50 kVA, so we select three 50 kVA transformers.
Step 3: Full Line Current on the High Voltage (HV) Side
The HV side is delta-connected with a primary voltage of 12 kV (assuming 12 kV primary for 120/208 V secondary).
Total bank rating: 150 kVA (since we chose 50 kVA per transformer).
HV line voltage: 12 kV
Delta connection formula for HV line current:
[
I_{\text{HV}} = \frac{S_{\text{total}}}{\sqrt{3} V_{\text{line HV}}}
]
[
I_{\text{HV}} = \frac{150}{\sqrt{3} \times 12} = \frac{150}{20.78} = 7.22 \text{ A}
]
Step 4: Secondary Line Current
The secondary side voltage is 208 V (line-to-line).
[
I_{\text{secondary}} = \frac{S_{\text{total}}}{\sqrt{3} V_{\text{line secondary}}}
]
[
I_{\text{secondary}} = \frac{138}{\sqrt{3} \times 208} = \frac{138}{360.13} = 383.3 \text{ A}
]
Step 5: Primary Line Voltage
Given the transformer ratio 100:1, the primary line voltage:
[
V_{\text{line primary}} = \frac{208}{100} = 12 \text{ kV}
]
Step 6: Choosing kVA of Transformer Bank
Available options: 100 kVA, 112.5 kVA, 150 kVA, 200 kVA
Since we need at least 138 kVA, we select 150 kVA (3 × 50 kVA).
Step 7: Primary Line Current
[
I_{\text{primary}} = \frac{S_{\text{bank}}}{\sqrt{3} V_{\text{primary}}}
]
[
I_{\text{primary}} = \frac{150}{\sqrt{3} \times 12} = 7.22 \text{ A}
]
Step 8: Secondary Line Voltage
The secondary voltage remains:
[
V_{\text{line secondary}} = 208V = 0.208 \text{ kV}
]
Final Answers:
- Total kVA Load = 138 kVA
- kVA per Transformer = 50 kVA
- HV Line Current = 7.22 A
- Secondary Line Current = 383.3 A
- Primary Line Voltage = 12 kV
- Transformer Bank Rating = 150 kVA
- Primary Line Current = 7.22 A
- Secondary Line Voltage = 0.208 kV
This ensures that the transformer bank is adequately rated for safe and efficient operation.