Voltage Drop and Losses on a Long 33 kV Radial Feeder
A 33 kV, 25 km radial feeder supplies a block headquarters and a cluster of tube-well pumps. At peak the feeder delivers 4.2 MW at 0.82 power factor lagging; the sending-end voltage is 33.0 kV and the receiving-end voltage falls to 30.2 kV. Energy loss on the feeder is 9.4%, against a target of 5%. The divisional engineer has three proposals: (i) install 2 × 1.5 MVAr capacitor banks at the 33/11 kV substation, (ii) reconductor the first 12 km with a higher-capacity conductor at Rs 3.1 crore, or (iii) shift 1.2 MW of pump load to a solar feeder during daytime. The feeder also has recurring 11 kV lateral fuse blowing whenever large pump motors start, and the local MLA has demanded immediate compensation. The engineer must prioritise within a Rs 2 crore annual works budget.
1. Estimate the reactive compensation required to reach 0.95 power factor and comment on the utility's proposal.
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Qc = P(tanφ1 − tanφ2). At 0.82 pf, tanφ1 = 0.698; at 0.95, tanφ2 = 0.329. With P = 4.2 MW, Qc = 4.2 × 0.369 ≈ 1.55 MVAr.
The proposal of 2 × 1.5 MVAr is nearly double the need. At light load the fixed 3 MVAr would export reactive power, raise the 33 kV voltage, and may trip the bank or overvoltage the 11 kV side. Recommend 1.5 MVAr split into two 0.75 MVAr steps with automatic power-factor control, or a 1.2 MVAr fixed bank plus one switched step. Verify with a load-flow study; do not size only on peak load.
2. Will the capacitor alone solve the voltage problem? Support your answer with an estimate and recommend a budget priority.
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Approximate line resistance 0.6 Ω/km × 25 km = 15 Ω and reactance 0.4 Ω/km × 25 km = 10 Ω. Voltage rise from 1.5 MVAr ≈ QX/V = 1.5 × 10/33 ≈ 0.45 kV. The observed drop is 2.8 kV, so the capacitive correction is only about one-sixth of the problem; the feeder is resistance-dominated and the conductor is evidently undersized.
Loss reduction from power-factor correction is roughly 1 − (0.82/0.95)² ≈ 25%, taking 9.4% to about 7%, still above target. The capacitor is justified first because it is quick and cheap, but reconductoring the first 12 km or shifting 1.2 MW of pump load is needed for the voltage target. Within Rs 2 crore, do the capacitor and load shifting this year and defer reconductoring to a DPR next year.
3. How would you investigate the recurring fuse blowing on the 11 kV laterals, and what would you recommend?
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Fuse blowing at motor start is usually a coordination problem, not a fuse-size problem. Check the fuse time-current characteristic against the motor starting current and start time, the upstream 11 kV relay, and the cable short-circuit rating. A large pump may draw 5–6 times full-load current for 8–12 s; a fuse selected only on continuous rating will fatigue.
Propose a motor-protection relay or MCCB with overload and short-circuit settings, and set the upstream relay with a 0.3 s grading margin. Do not simply increase the fuse, because that defeats protection. Collect motor data and carry out a coordination study before the next pump is connected.