Capacitor Bank Resonance on a Drive-Loaded 400 V Board
A 400 V, 50 Hz TN-S board is fed by a dedicated 500 kVA transformer with 5.5% impedance. The board supplies a 132 kW 6-pulse DC drive (current THD 28% at full load) and a 150 kVAr automatically switched capacitor bank connected to the same busbar with no series reactors. Within four months of commissioning, two capacitor fuses have blown, three capacitor cans are visibly bulging, and the capacitor contactors chatter when the second step cuts in. A clamp meter on the capacitor feeder reads 268 A rms; the bank's rated current at 400 V is 216 A. The power quality logger shows 5th and 7th voltage harmonic distortion of 6.8% and 4.1% respectively, both rising when the second capacitor step is energised. The plant electrician proposes adding a second identical 150 kVAr bank to "improve the power factor further", because the utility invoice still shows a reactive charge at light load.
1. Calculate the parallel resonance order between the bank and the transformer, and explain what the measurements indicate. Which harmonic is at risk, and why?
Read the worked answer
Short-circuit capacity of the supply. S_sc = 500 kVA / 0.055 = 9,091 kVA
Parallel resonance order. h_r = √(S_sc / Q_c) = √(9,091 / 150) = √60.6 ≈ 7.8, i.e. f_r ≈ 7.8 × 50 = 390 Hz.
What that means. The 7th harmonic (350 Hz) sits immediately below this parallel resonance peak and the 8th sits above it. Transformer impedance tolerance, capacitor tolerance (±5–10%), cable capacitance and the number of switched steps all shift h_r, so the bank cannot be assumed to sit safely away from 350 Hz. The 7th harmonic current injected by a 6-pulse drive is modest in absolute terms, but at a parallel resonance it is multiplied by the Q of the circuit, limited mainly by resistance. A 4.1% 7th voltage distortion therefore corresponds to a large 7th current circulating in the capacitor.
Evidence that matches this diagnosis:
- Capacitor current 268 A against a 216 A rated fundamental: 24% overcurrent, which is roughly 54% extra I²R heating in the dielectric, fuses and terminations.
- Bulging cans are the classic end stage of dielectric overheating and overvoltage, not a manufacturing defect.
- Fuses rupturing under a combination of high switching inrush and continuous harmonic overcurrent.
- Distortion rising when the second step is connected, because additional capacitance lowers h_r and drags the resonance towards the 5th and 7th.
Key point: the drive is the source; the bank is only the amplifier. Replacing fuses and capacitors without changing the impedance will reproduce the same failure within months.
2. Specify the detuned reactor solution: tuning order, capacitor voltage rating, effective reactive output, and the ratings that must be checked before ordering.
Read the worked answer
Detuning requirement. The reactor must move the bank's series resonance below the lowest significant harmonic present (5th, 250 Hz) with margin, so that at 250 Hz and above the branch is inductive and cannot form a parallel resonance with the transformer.
Choose p = X_L/X_C = 7%: h_s = 1/√0.07 = 3.78 → f_s = 189 Hz. This is the standard 189 Hz detuned bank. The effective resonance with the network is pulled down to about the 3.8th, well below 250 Hz, so neither the 5th nor the 7th is amplified.
Capacitor voltage rating. The series reactor raises the voltage across the capacitor above the busbar voltage: U_C = U / (1 − p) = 400 / 0.93 ≈ 430 V. A 400 V-rated capacitor would be overstressed continuously, so specify at least 440 V; many designers use 525 V for margin and life, accepting fewer kVAr per can.
Effective reactive output. Q_eff = Q_rated × (1 − p) = 150 × 0.93 ≈ 139.5 kVAr at 400 V. If 150 kVAr is genuinely required at the busbar, the capacitor must be oversized to 150 / 0.93 ≈ 161 kVAr.
Ratings to check before ordering:
- Reactor continuous current at least equal to the capacitor current including harmonic content; the 400 V, 150 kVAr capacitor already draws about 216 A fundamental.
- Reactor thermal class and temperature rise at the actual panel ambient, not at 20 °C.
- Fuse type and rating specified by the manufacturer for a detuned bank; inrush is higher than for a plain bank and a general-purpose fuse is the wrong choice.
- Discharge resistors and the step-switching interval.
Re-run the harmonic survey after commissioning. The acceptance criterion is capacitor current within rating and reduced 7th voltage distortion, not merely an improved displacement power factor on the invoice.
3. The electrician's proposal is to add a second identical 150 kVAr bank without reactors. Assess that proposal and list the commissioning checks that must be completed before any modified bank is energised.
Read the worked answer
The proposal makes the problem worse, not better. Adding capacitance lowers the resonance order: with 300 kVAr connected, h_r = √(9,091 / 300) = √30.3 ≈ 5.5, which puts the parallel resonance essentially on the 5th harmonic, the largest harmonic produced by a 6-pulse drive. Capacitor current, voltage distortion and dielectric heating all rise sharply; failure of the new bank within weeks is the likely outcome, and the drive may start tripping on DC-bus or overcurrent faults.
There is a second, subtler problem: an automatically switched bank changes h_r every time a step is added or removed, so the installation sweeps through resonance conditions as the load varies. A fixed reactor design plus a controller that switches on displacement power factor alone can still leave the plant at a leading power factor at light load, which raises voltage and can trip drives.
Commissioning checks before the modified bank is energised:
- Harmonic survey at the busbar and at the capacitor feeder with all steps in and all steps out, before and after the reactors are fitted.
- Verification of the actual transformer impedance and of any other capacitance on the same busbar (long cables, other banks, surge capacitors).
- Capacitor current and voltage THD measured at full drive load, compared with the capacitor's permissible overload per its standard.
- Reactor temperature rise after several hours at maximum load, measured at the hottest accessible point.
- Correct fuse type and rating, and correct contactor rating for capacitor switching.
- Discharge resistors and the minimum reclose interval between steps.
- Confirm the target power factor is reached at light load without going leading.
If the drive load is expected to grow, a tuned 5th/7th filter or an active filter is the correct next step, not more detuned kVAr.