Power in AC systems is not a single number — it is a triangle. Real power (kW) performs work: turning shafts, generating heat, producing light. Reactive power (kVAR) sustains the electromagnetic fields that make motors, transformers, and inductors function — it flows back and forth between source and load 120 times per second without performing work. Apparent power (kVA) is what the utility must deliver and what transformers, conductors, and switchgear must be rated for: kVA = √(kW² + kVAR²). Understanding this triangle is the key to correctly sizing every component in an electrical distribution system.

Power factor (PF) is the cosine of the angle between real and apparent power: PF = kW / kVA. A PF of 1.0 means all delivered power performs useful work (purely resistive load). Most industrial and commercial loads are inductive (motors, transformers, magnetic ballasts) with lagging power factors of 0.7–0.9. The impact on infrastructure is dramatic: a 100 kW load at PF 0.70 requires 143 kVA of transformer capacity and draws 172A at 480V 3-phase, while the same 100 kW at PF 0.95 requires only 105 kVA and draws 127A — a 26% reduction in current that directly reduces conductor sizing, transformer loading, and I²R losses.

Three-phase power calculations are essential for commercial and industrial systems. For balanced loads: P = √3 × V_LL × I_L × PF, where V_LL is line-to-line voltage and I_L is line current. Equivalently: P = 3 × V_LN × I_L × PF, using line-to-neutral voltage. The √3 factor (1.732) accounts for the 120° phase displacement between phases. For unbalanced loads (common in commercial buildings with single-phase branch circuits), each phase must be calculated individually and the neutral current determined from the vector sum of the three phase currents.

Single-phase power calculations are simpler but still require attention to power factor. For single-phase: P = V × I × PF. A 240V, 30A single-phase circuit with PF = 0.85 delivers: P = 240 × 30 × 0.85 = 6,120W of real power, while the apparent power is S = 240 × 30 = 7,200 VA. The difference (1,080 VA) is lost to reactive power that loads conductors and transformers without performing useful work. For resistive loads (water heaters, electric ovens), PF ≈ 1.0 and watts equal volt-amperes.

Power chain efficiency losses accumulate through every conversion stage. In a typical commercial building, utility power at 13.8 kV is stepped down through a medium-voltage transformer (98-99% efficient), distributed at 480V through switchgear (99.5%), stepped down again to 208/120V through dry-type transformers (96-98%), and finally delivered to loads. The compounded efficiency from utility to load is 93-96% — meaning 4-7% of all purchased energy is lost as heat in the distribution infrastructure. For data centers, UPS systems add another 3-6% loss, and power distribution units (PDUs) add 1-2%.

Accurate power measurement requires understanding the difference between direct metering and instrument transformer metering. For circuits up to 200A, direct-connected meters measure voltage and current directly. For larger services, current transformers (CTs) and potential transformers (PTs) step down the measured quantities. CT ratios (e.g., 400:5) must be applied to the meter readings: a meter reading 85A with a 400:5 CT indicates 85 × 80 = 6,800A actual current. Modern power meters measure true RMS values, total harmonic distortion, and power factor simultaneously — essential for identifying power quality issues.