Tail-End Voltage on a Loaded 11 kV Agricultural Feeder
An 11 kV rural feeder leaves a 33/11 kV substation and runs 7 km on 55 mm² ACSR (Rabbit) conductor, with R = 0.545 Ω/km and X = 0.40 Ω/km per phase. Peak load is 2.0 MW at 0.78 power factor lagging, dominated by agricultural pump sets running between 18:00 and 24:00. The tail-end voltage logged at peak is 9.9 kV. The licence permits ±6% at the consumer terminal, so the lower limit is 10.34 kV. The 33/11 kV transformer has an off-load tap changer; the substation engineer has already raised it one step so the 11 kV bus sits at 11.3 kV, and the utility will not raise it further because the upstream 33 kV feeder is itself heavily loaded. Feeder load is growing about 8% a year. Two proposals are on the table: an 800 kVAr shunt capacitor bank at the tail end, or reconductoring with 100 mm² ACSR (Dog), R = 0.273 Ω/km and X = 0.35 Ω/km. The budget covers only one measure this year.
1. Calculate the line-to-line voltage drop at peak load on the existing conductor and compare it with the logged tail-end voltage. What does the comparison establish about the cause of the problem?
Read the worked answer
Load current: S = 2.0/0.78 = 2.564 MVA, so I = 2.564×10⁶/(√3×11000) = 134.6 A.
Per-phase drop = I(R cosφ + X sinφ)L, with cosφ = 0.78 and sinφ = 0.626:
= 134.6 × (0.545×0.78 + 0.40×0.626) × 7 = 134.6 × (0.425 + 0.250) × 7 = 636 V per phase.
Line-to-line drop = √3 × 636 = 1102 V ≈ 10.0% of 11 kV.
With the bus at 11.3 kV, the predicted tail voltage is about 11.3 × 0.90 = 10.17 kV; the logged 9.9 kV is slightly worse, which is consistent with the true peak being a little above the recorded 2.0 MW and with unbalance across the three phases.
The calculation confirms the cause is resistive plus reactive drop along a long, lightly-sized conductor, not a metering error and not a substation bus-voltage problem. The bus is already at 11.3 kV and cannot be raised further, so the whole 10% loss must be removed downstream. Note also that at 0.78 power factor, reactive drop contributes about 37% of the total, which is why a capacitor is worth evaluating.
2. Evaluate each proposal on its own: calculate the tail-end voltage with the 800 kVAr capacitor alone and with reconductoring alone. Does either measure meet the 10.34 kV limit?
Read the worked answer
Capacitor alone. Load reactive power = 2.0 × tan(acos 0.78) = 2.0 × 0.802 = 1.604 MVAr. With 0.80 MVAr compensation, net Q = 0.804 MVAr, so S = √(2.0² + 0.804²) = 2.156 MVA, I = 2.156×10⁶/(√3×11000) = 113.2 A, cosφ = 0.928, sinφ = 0.373.
Drop = 113.2 × (0.545×0.928 + 0.40×0.373) × 7 = 113.2 × 0.655 × 7 = 519 V per phase; line-to-line = 899 V = 8.2%. Tail voltage ≈ 11.0 × 0.918 ≈ 10.1 kV (using the 11.3 kV bus gives roughly 10.37 kV under light loading, but at the design peak with bus at 11.0 kV it fails). Marginal at best and fails the 10.34 kV limit at peak.
Reconductoring alone. I stays 134.6 A; drop = 134.6 × (0.273×0.78 + 0.35×0.626) × 7 = 134.6 × 0.432 × 7 = 407 V per phase; line-to-line = 705 V = 6.4%. Tail ≈ 11.3 × 0.936 = 10.58 kV, but with the bus restored to 11.0 kV it is 10.30 kV - still just below 10.34 kV.
Conclusion: neither measure alone gives dependable compliance. The capacitor is cheaper but fixes only the reactive component; reconductoring fixes the resistive component but leaves the feeder at the limit with zero margin for 8% annual growth.
3. Recommend a course of action for this year and justify it, including how you would handle the tap changer and the projected load growth.
Read the worked answer
Recommendation: reconductor to 100 mm² ACSR and install the 800 kVAr bank at the tail, phased so that reconductoring happens first (it removes the resistive drop and increases capacity) and the capacitor follows within the same financial year.
Combined check: I = 113.2 A, cosφ = 0.928, using Dog data: Drop = 113.2 × (0.273×0.928 + 0.35×0.373) × 7 = 113.2 × 0.384 × 7 = 304 V per phase; line-to-line = 527 V = 4.8%. Tail ≈ 11.3 × 0.952 = 10.76 kV, and even with the bus at 11.0 kV it is 10.47 kV - comfortably above 10.34 kV.
Why not rely on the tap changer: it is already one step up and the 11 kV bus at 11.3 kV leaves only 0.36 kV before the upper +6% limit (11.66 kV) is breached for consumers near the substation. Pushing it further transfers the problem upstream and can over-voltage pump-set motors and capacitor banks on adjacent feeders.
Growth: at 8% a year the combined scheme's 0.4 kV margin is consumed in roughly two to three years. Flag the feeder in the capital plan for bifurcation or conversion to a 33 kV spur, and record the pre-monsoon capacitor health check and tail-end voltage logger as routine O&M so the evidence for the next investment is already collected.