Power Factor, Harmonics, and Motor Replacement Trade-off
A plastics extruder plant has a 1,200 kVA transformer at 85% loading, a billed power factor of 0.82, and $9/kVA-month demand charges with a 0.90 PF penalty threshold. The plant added 40 VFDs over three years. A power quality survey shows 5th and 7th harmonic current distortion of 18% THD-i at the service, and capacitor banks installed in 2005 have failed twice. The plant also runs 30 old 50-hp standard-efficiency motors at 70% load, 6,000 h/yr. Options: (A) add a 300 kVAr detuned capacitor bank, $48,000; (B) replace 30 motors with NEMA Premium units, $135,000; (C) install an active harmonic filter, $160,000.
1. Evaluate the capacitor bank option given the harmonic environment, and quantify the PF correction benefit.
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The 18% THD-i with 5th/7th dominance and repeated capacitor failures is a classic resonance warning. Plain capacitors can resonate with transformer and source impedance near the 5th harmonic, amplifying voltage distortion and destroying capacitors. A detuned bank with 7% reactors shifts resonance below the 5th and is the correct choice - so option A is viable only as a detuned design, not a standard bank.
Quantify: at 85% of 1,200 kVA = 1,020 kVA apparent, PF 0.82 gives 836 kW real and 585 kVAr reactive. Correcting to 0.95 requires kVAr = 836 x (tan acos 0.82 - tan acos 0.95) = 836 x (0.698 - 0.329) = 308 kVAr. A 300 kVAr bank brings PF near 0.95. Billed kVA falls from 1,020 to about 880, saving 140 kVA x $9 x 12 = $15,100/yr, plus penalty avoidance. Payback ~3.2 yr. Verify with a harmonic study that the detuned bank does not create a new resonance with the VFDs.
2. Should the plant prioritize motor replacement or harmonic mitigation? Frame the decision.
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Motor replacement: 30 x 50 hp at 70% load. Standard efficiency ~91%, premium ~94.5% at that load. Input kW standard = 30 x 50 x 0.746 x 0.70 / 0.91 = 861 kW; premium = 829 kW; savings 32 kW x 6,000 h = 192,000 kWh = $19,200/yr, plus ~25 kW demand = $2,700. Payback 135,000/21,900 = 6.2 yr. Solid, low-risk, and improves reliability.
Harmonic filter: $160,000 with no direct energy savings; justified only if distortion causes failures, nuisance tripping, or utility penalties. The failed capacitors suggest a real problem, but the detuned bank plus a harmonic study may resolve much of it at lower cost.
Recommendation: do the detuned capacitor bank first (cheapest, addresses PF penalty and partially the resonance), commission a harmonic study, then replace motors on a failure-or-planned basis. Reserve the active filter for equipment that still misbehaves after detuning, or if the utility enforces IEEE 519 limits.