Motors & Drives & Compressed Air Systems
Load factor and the cube law
Motor work starts with load factor: measured current against full-load amps, plus efficiency (NEMA Premium / IE3) and the decision between rewinding and replacing. Oversized motors run at poor load factor and low power factor. Variable frequency drives capture savings through the affinity laws - flow ∝ speed, head ∝ speed², power ∝ speed³ - but the cube law applies only to systems with negligible static head; throttled or bypass-controlled systems gain less.
Compressed air is the most expensive utility in the plant. Rules a candidate should carry: specific power of roughly 18–22 kW per 100 cfm at 100 psig for lubricated rotary screw machines; leaks typically 20–30% of production; and about 1% compressor energy saved per 2 psi of pressure reduction. Also know artificial demand, storage sizing, sequencing to avoid part-loaded trim compressors, desiccant versus refrigerated dryers, and heat recovery from the oil/air circuit.
Traps. Comparing cfm without normalizing to standard conditions (scfm at 14.7 psia, 68°F); assuming nameplate hp equals running load; applying the cube law where static head dominates; treating a VFD on a fixed-displacement compressor like a centrifugal; and forgetting that leak flow through an orifice grows sharply with pressure.
Worked example
A 1/8-inch equivalent leak at 100 psig passes roughly 26 cfm. At 20 kW per 100 cfm that is about 5.2 kW. Over 8,000 hours per year: 5.2 × 8,000 = 41,600 kWh, roughly $4,200/yr - from one leak. Ultrasonic surveying and tagging is almost always the highest-return item in a compressed-air audit.