33 kV Feeder with Poor Tail-End Voltage, a Harmonic-Rich Load and a Capacitor Bank That Keeps Blowing Fuses
A 132/33 kV substation in Telangana feeds a 22 km radial 33 kV feeder supplying an industrial cluster. Conductor data are R = 0.35 ohm/km and X = 0.45 ohm/km per phase. At the evening peak the feeder carries 9.0 MW at 0.86 power factor lagging, with the 33 kV bus held at 33.9 kV; the tail-end recorder shows 30.2 kV. At 03:00 h the load falls to 2.2 MW and the tail-end voltage climbs to 35.6 kV. Two 2 MVAr capacitor banks sit at the substation 33 kV bus and are left switched in around the clock. About 11 km out, a rolling mill runs a 3 MW 6-pulse DC drive that injects a 5th-harmonic current of roughly 8% of fundamental; the capacitor bank fuses have blown twice this year. The 33 kV bus short-circuit level is 180 MVA. The licence condition is +/-6% at the consumer terminal, and the 132/33 kV transformer has an off-circuit-cum-on-load tap changer with nine steps of 1.25%.
1. Verify the tail-end voltage by calculation, then compare the voltage benefit of 2 MVAr placed at the source bus against 2 MVAr placed at the tail end. Which do you recommend, and does either alone meet the +/-6% limit?
Read the worked answer
Load current. I = 9000 / (sqrt3 x 33 x 0.86) = 183 A; cos(phi) = 0.86, sin(phi) = 0.51.
Line constants. R = 0.35 x 22 = 7.7 ohm, X = 0.45 x 22 = 9.9 ohm.
Drop. dV = sqrt3 x I x (R cos(phi) + X sin(phi)) = 1.732 x 183 x (6.62 + 5.05) = 1.732 x 183 x 11.67 = 3.70 kV. 33.9 - 3.70 = 30.2 kV, which reproduces the recorder value, so the model is trustworthy.
2 MVAr at the source bus. Source reactance Xsc = 33^2/180 = 6.05 ohm. Rise at the 33 kV bus = Q x Xsc / V = 2 x 6.05 / 33 = 0.37 kV, and almost all of that reaches the tail end because the line drop changes only marginally.
2 MVAr at the tail end. Capacitor current = 2000/(sqrt3 x 33) = 35 A. The reactive component no longer flows over 9.9 ohm of line reactance, so the tail-end rise is about sqrt3 x 35 x 9.9 = 0.60 kV.
Judgement. Tail-end placement gives roughly 1.6 times the benefit per MVAr. The limit needs 31.02 kV; 2 MVAr at the tail reaches about 30.8 kV, still short, so recommend shifting one 2 MVAr bank to about 18 km and keeping the other at the source as a switched bank, with the OLTC used for the light-load condition. Two banks at the tail would overshoot at 03:00 h unless both are switched out.
2. Is the existing 4 MVAr at the source bus safe with 8% fifth-harmonic injection? Show the check and specify the remedy, including the effect on capacitor rating.
Read the worked answer
Resonance order. For a shunt capacitor bank, the parallel resonance is h = sqrt(Ssc / Qc) = sqrt(180/4) = sqrt(45) = 6.7. That is uncomfortably close to the 5th harmonic and only just below the 7th, and the resonance band is broad because the source impedance is resistive-plus-inductive. With 8% fifth-harmonic current the bank current and voltage can be amplified several times, which explains the repeated fuse failures far better than a manufacturing defect.
Remedy. Fit a series detuned reactor with 7% reactance: tuning order = sqrt(1/0.07) = 3.78, i.e. about 189 Hz at 50 Hz, safely below the 5th. Note two consequences. First, the capacitor terminal voltage rises to V/(1 - p) = 33/0.93 = 35.5 kV, so the capacitor units must be rated at least 1.075 times system voltage; a standard 11 kV unit set will be under-rated and will fail thermally. Second, the fundamental reactive output at the bus changes only slightly, so the voltage benefit calculated earlier still holds.
Supplementary. Ask the mill to add a DC-link choke or convert to a 12-pulse front end, which removes the 5th and 7th almost entirely. Do not simply enlarge the bank: with 6 MVAr the resonance moves to h = 5.5, which is worse.
3. At 03:00 h the tail end reads 35.6 kV. Give a sequence of operating and design actions, and state which measurement you would take first to decide between them.
Read the worked answer
First measurement. Read the 03:00 h source-bus voltage and the capacitor bank status together. 35.6/33 = +7.9%, so the limit is already breached at light load; without knowing whether the 4 MVAr is in, you cannot separate the capacitor effect (about 0.4 kV at the source and more if any bank were at the tail) from a genuinely high source voltage.
If the source bus itself is high (say above 34.3 kV), the cause is upstream: move the 132/33 kV tap changer down one or two steps, and check whether the 132 kV bus is being held high for the downstream 132 kV network.
If the source bus is normal but the tail is high, the cause is the capacitor banks plus the Ferranti/charging effect of the 22 km line at light current. Sequence: (1) trip one bank at 03:00 h; (2) if still above 33.6 kV, trip the second; (3) if the daily swing still exceeds 6%, install a switched 2 MVAr shunt reactor at the tail or a small SVC/STATCOM, which is justified when the swing is a daily cycle rather than a seasonal one.
Also check the tail-end voltage transformer calibration and whether any consumer has switched in their own power-factor-correction capacitors; captive capacitors at the load end can create exactly this night-time rise and are commonly overlooked.