Loading, energy and power factor on a small workshop distribution board
A fabrication shop is fed from a 415 V, 3-phase, 50 Hz supply through one distribution board. The loads are: a lathe motor rated 7.5 kW output, η 88%, pf 0.82; an air compressor rated 2.2 kW output, η 80%, pf 0.78, running about 40% of the shift; and 1.2 kW of single-phase lighting and fans spread evenly over the three phases (240 V phase-neutral). The lathe runs 6 h a day, 25 days a month, at an average of 70% of its rated output. The board has a 20 A three-phase MCB and 2.5 mm² copper PVC-insulated cable in conduit, tabulated rating 21 A. Tariff ₹8.40/kWh with a power-factor penalty below 0.90. The owner wants to know whether the existing MCB and cable are adequate, what the monthly bill is, and whether a capacitor bank would pay.
1. Calculate the full-load and running currents and judge whether the 20 A MCB and 2.5 mm² cable are adequate.
Read the worked answer
Lathe motor. Input = 7.5/0.88 = 8.52 kW. I = P/(√3 × V × pf) = 8522/(1.732 × 415 × 0.82) = 8522/589.4 = 14.45 A.
Compressor. Input = 2.2/0.80 = 2.75 kW. I = 2750/(1.732 × 415 × 0.78) = 2750/560.7 = 4.90 A.
Lighting. Per phase 1200/3 = 400 W at 240 V → 1.67 A.
Worst phase (assuming the lighting is not perfectly balanced) = 14.45 + 4.90 + 1.67 ≈ 21.0 A.
Judgement. 21 A against a 21 A cable rating and a 20 A MCB is a 100% loaded circuit with no margin - and no allowance for 34 °C ambient derating, grouping, or the motor's starting current. The MCB is already at its nominal value continuously, so nuisance tripping and cable over-heating are likely.
Recommendation: re-cable the sub-main in 4 mm² (≈ 28 A in conduit), fit a 25 A or 32 A MCB, set the motor overload relay to 14.5 A, and give the lighting its own single-phase circuit with 6 A protection so it can be isolated independently.
2. Compute the monthly energy consumption and bill, and the saving from a VFD claimed to save 12% on the lathe motor.
Read the worked answer
Lathe motor at 70% load. Output = 7.5 × 0.70 = 5.25 kW; input = 5.25/0.88 = 5.97 kW. Hours = 6 × 25 = 150 h → 5.97 × 150 = 895 kWh.
Compressor. Input when running = 2.75 kW; hours = 150 × 0.40 = 60 h → 2.75 × 60 = 165 kWh.
Lighting and fans. 1.2 × 150 = 180 kWh.
Total ≈ 1 240 kWh/month → ₹8.40 × 1 240 = ₹10 416/month (plus fixed charges).
VFD saving. 12% of 895 kWh = 107 kWh/month = ₹902/month, about ₹10 800 a year.
Judgement point: the 12% figure only holds if the lathe really spends its time at part load and the VFD is used to reduce speed, not just to start the motor. Compare ₹10 800/year against the installed cost of the drive and its harmonics/filter requirement; if the drive costs ₹45 000 the payback is about four years, which is a marginal case - and the 12% must be verified by a week of metering before purchase.
3. Size a capacitor bank to raise the power factor to 0.95 and explain the practical precautions.
Read the worked answer
Use Q = P(tan φ₁ − tan φ₂).
- Lathe average input P = 5.97 kW; cos φ₁ = 0.82 → tan φ₁ = 0.698; target cos φ₂ = 0.95 → tan φ₂ = 0.329
- Q = 5.97 × (0.698 − 0.329) = 5.97 × 0.369 = 2.20 kVAr
- Adding the compressor's average contribution (2.75 × 0.40 = 1.1 kW × 0.369 = 0.41 kVAr) gives ≈ 2.6 kVAr at the board.
Practical choice: a standard 2.5 kVAr three-phase bank, or better two switched steps of 1.25 kVAr with a pf controller.
Precautions.
- Do not over-correct: at light load (only the compressor running) a fixed 2.5 kVAr would push the pf to leading and attract the same penalty as a lagging one, so switch in steps on the measured pf.
- Contactors and fuses for capacitors must be rated for the switching in-rush; use capacitor-duty contactors and discharge resistors.
- If a VFD is fitted to the lathe, never connect the capacitor on the drive output - correct at the supply side or on the motor only when it runs direct-on-line.
- Ventilate the panel; capacitor life falls sharply above about 45 °C.