Power-Factor Correction and Harmonic Resonance in a VFD Plant
A factory is supplied by a 1,000 kVA, 11 kV/400 V transformer. Monthly maximum demand is 650 kW at 0.78 power factor. The main LV board feeds 12 variable-frequency drives and a 250 kVAr automatic capacitor bank. The capacitor bank has failed twice in six months; the last failure burnt contacts in one step. Power quality monitoring shows voltage THD 6.8%, current THD 22%, and 5th and 7th harmonic currents of 85 A and 48 A. Neutral current on the main incoming feeder is 180 A while phase currents are 420 A, 405 A and 415 A. The capacitor bank is connected to the same bus as the VFDs. The utility charges a power-factor penalty below 0.95. The plant wants to replace the failed capacitors with a larger 350 kVAr bank to avoid the penalty. The transformer impedance is 5.5% and the LV fault level is 28 kA.
1. Calculate the capacitor kVAr needed to correct 650 kW from 0.78 to 0.95 power factor. Is the proposed 350 kVAr bank appropriate?
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P = 650 kW. At pf1 = 0.78, tan phi1 = tan(acos 0.78). cos phi1 = 0.78, sin phi1 = 0.626, tan phi1 = 0.626/0.78 = 0.802. At pf2 = 0.95, tan phi2 = tan(acos 0.95) = 0.329. Required Qc = P(tan phi1 - tan phi2) = 650(0.802 - 0.329) = 650 x 0.473 = 307 kVAr. So about 310 kVAr is needed at the load, not 350. A 350 kVAr plain bank would slightly overcorrect at full load and, more importantly, would shift the resonance. With 350 kVAr and 18.18 MVA short-circuit, h = sqrt(Ssc/Qc) = sqrt(18.18/0.35) = 7.2, close to the 7th harmonic. A 250 kVAr bank gives h about 8.5. So the proposed larger bank is not appropriate; a detuned bank rated for the harmonic environment is needed, with staged steps around 300-325 kVAr.
2. Explain why the capacitor bank failed and why neutral current is 180 A despite phase currents near 410 A.
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The bank is on a bus with 12 VFDs. A 6-pulse VFD draws 5th and 7th harmonics; the measured 85 A fifth and 48 A seventh are significant. Capacitors have low impedance at higher frequencies, so they attract harmonic current and can overheat. The resonance calculation shows the 350 kVAr (or even the 250 kVAr) bank is close to a harmonic order; if the resonance is near the 5th or 7th, capacitor current and voltage distortion rise. Burnt contacts in one step indicate switching overcurrent or harmonic heating. The neutral current of 180 A with phase currents 420/405/415 A is not explained by fundamental unbalance (small); it indicates triplen harmonics, likely from single-phase loads or VFD control and EMC filters. Triplen currents add in the neutral. Need a harmonic spectrum for the neutral and a check for 3rd/9th harmonics.
3. Recommend a power-factor correction and harmonic mitigation design. Include switching, protection, and verification.
Read the worked answer
Do not replace with a larger plain capacitor bank. Install a detuned automatic bank with reactors (typically 7% for 5th/7th-dominated systems), rated for the actual voltage and harmonic current, in steps sized to avoid resonance and to follow load. Size real power factor to about 300-325 kVAr at 400 V, but check the detuned bank's effective output at 400 V and its reactor voltage rating. Use capacitor-duty contactors or thyristor switching with detuning; add harmonic filters if voltage THD remains above limits. Protect with HRC fuses, overcurrent, overvoltage, and temperature monitoring. Separate the sensitive capacitor bus from the VFD bus if possible. Verify with a post-installation power-quality survey: pf, voltage and current THD, neutral current, and capacitor current. Recalculate resonance with actual bank steps and transformer impedance.