Harmonic Resonance from Capacitor Bank Expansion
A 480 V plant is fed by a 1,500 kVA transformer with 5.75% impedance. The plant has 400 hp of 6-pulse PWM variable-frequency drives, a 600 kvar capacitor bank switched in four 150 kvar steps, and linear motor loads. The capacitor bank has had two fuse failures and one bulged capacitor can in six months. Power monitoring shows a 5th-harmonic current of 180 A, a 7th-harmonic current of 120 A, and a voltage THD of 11.8%. The capacitor bank is connected at the 480 V bus with 3% reactors in each phase. The plant wants to add another 200 kvar of capacitance to improve displacement power factor from 0.86 to 0.95.
1. Calculate the parallel resonance order for the existing and proposed capacitor banks, and explain why the existing bank is failing.
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The transformer short-circuit capacity is Ssc = 1,500 kVA / 0.0575 = 26,087 kVA. The parallel resonance order is approximately h = sqrt(Ssc / Qc). For the existing 600 kvar bank, h = sqrt(26,087 / 600) = sqrt(43.48) = 6.6. That places the parallel resonance between the 5th and 7th harmonics, where the 6-pulse drives inject substantial current. The 3% reactors have a series tuning order of 1 / sqrt(0.03) = 5.77, which is also close to the 5th harmonic. The capacitor bank is therefore not safely detuned; it can amplify 5th and 7th harmonic currents, causing overcurrent, fuse failures, and capacitor overheating. Adding 200 kvar would make the resonance worse: h = sqrt(26,087 / 800) = sqrt(32.61) = 5.71, almost exactly at the 5th harmonic. The proposed expansion would increase harmonic amplification and should not be implemented without a harmonic study and redesigned filtering.
2. Evaluate the 3% reactors and recommend a reactor specification or alternative mitigation.
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A 3% reactor tunes the capacitor branch near 5.77 times fundamental, which is too close to the 5th harmonic for a drive-rich bus. A 7% reactor tunes the branch at 1 / sqrt(0.07) = 3.78 times fundamental, below the 5th harmonic, so the capacitor branch becomes inductive at the 5th and 7th harmonic frequencies and will not amplify those currents. The reactor must be rated for the fundamental capacitor current plus the harmonic current, and the capacitor voltage rating must be increased because the reactor raises the voltage across the capacitor. For a 480 V bank with a 7% reactor, use capacitors rated at least 525 V and verify the reactor thermal current rating. Also reduce or stage the bank so that the resonance does not sit near a characteristic harmonic under any switching step. Alternatives include an active harmonic filter, a tuned 5th-harmonic filter, or replacing the capacitor bank with a detuned bank sized by a harmonic study. The selected design should be verified by a harmonic analysis that includes the drive spectrum and all capacitor switching steps.
3. What additional operating and protection measures should be included before energizing the revised bank?
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The revised bank should be protected against overvoltage, overcurrent, and capacitor case rupture. Use capacitor-rated fuses or breakers with adequate interrupting rating, and set overcurrent protection above the expected harmonic current but below the capacitor withstand. Add overvoltage protection because harmonic resonance and switching transients can raise peak voltage. If the bank is contactor-switched, use capacitors with discharge resistors and consider pre-insertion resistors or solid-state switching to limit inrush. Measure voltage and current THD at the bus after energizing, and verify that the 5th and 7th harmonic currents in the capacitor branch are below the reactor and capacitor ratings. Confirm that the displacement power factor target is met without overcorrection during light load, because leading power factor can cause overvoltage. Document the final switching steps and train operators not to energize all steps simultaneously if the study shows a resonant condition at a particular step.