Electrical Power Systems and Motors
The four relationships to write from memory
Real power (kW) does work, apparent power (kVA) loads conductors and transformers, and reactive power (kVAR) is the gap between them: kW = kVA x PF. Three-phase real power = 1.732 x V(line-line) x I x PF. Demand (kW) drives the monthly demand charge while consumption (kWh) drives the energy charge; load factor = average kW / peak kW, and low load factor signals a spiky, expensive profile. Capacitor correction reduces kVA and demand but never reduces kWh, which is why power factor correction is a demand-charge strategy, not an energy strategy.
Motors, drives, and the affinity laws
Motor efficiency peaks near 75% load, so oversized motors run inefficiently with poor power factor. NEMA Premium (IE3) motors cut losses several points versus standard efficiency. Variable speed drives save energy on centrifugal fans and pumps because power scales with the cube of speed: at 80% speed, ideal power is 51% (0.8 cubed). Traps: applying the cube law to a static-head-dominated system where savings are far smaller; confusing motor efficiency (shaft output divided by electrical input) with drive efficiency; and forgetting that part-load motor efficiency drops sharply below about 40% load.
Worked example
Input kW = hp x 0.746 x load fraction / efficiency. A 100 hp motor at 75% load and 93% efficiency draws 100 x 0.746 x 0.75 / 0.93 = 60.2 kW. At 2,000 hours per year that is 120,400 kWh, about $9,630 at $0.08/kWh. Capacitor sizing: kVAR = kW x (tan theta1 - tan theta2).