Electrical Power Systems and Motors
This domain tests power fundamentals, motor efficiency, variable-frequency drives, power-factor correction, and demand management. Questions often require a kW/kVA/kVAR calculation or an estimate of VFD savings using the affinity laws.
Power relationships
- Real power kW = kVA × power factor. Reactive power kVAR = kW × tan(θ), where θ = arccos(PF).
- Three-phase power = √3 × V × I × PF ÷ 1,000 for kW with line-to-line voltage and line current.
- Motor input power = shaft output ÷ motor efficiency. NEMA Premium motors are more efficient but may be oversized for the load.
- Centrifugal fans and pumps follow the affinity laws: flow ∝ speed, head ∝ speed², and power ∝ speed³ for variable-torque loads.
- Transformers have no-load core losses and load-dependent copper losses; oversized transformers waste energy at low load.
Worked example
A facility has a 500 kW load at 0.80 power factor and wants to correct to 0.95. tan(arccos 0.80) = 0.750; tan(arccos 0.95) = 0.329. Required reactive compensation = 500 × (0.750 − 0.329) = 500 × 0.421 = 210.5 kVAR. Adding about 210 kVAR reduces line current and losses and may avoid a power-factor penalty. The reasoning: correction supplies reactive power locally, so the utility no longer carries it. The capacitor bank must be sized in steps to avoid leading power factor at light load.
Motor and drive economics
A 100 hp motor delivers 75 kW shaft output at 93% efficiency, so input = 75 ÷ 0.93 = 80.6 kW. At 4,000 hours per year, energy = 322,400 kWh. If a VFD reduces a centrifugal load to 80% speed, power falls to about 0.80³ = 0.512 of the original, or 41.3 kW, before drive losses. The reasoning: affinity-law savings are large but apply only to variable-torque centrifugal loads, not positive-displacement or constant-torque loads.
Traps that cost marks
- Applying the cube law to constant-torque loads or to systems with static head.
- Using nameplate horsepower instead of actual shaft load.
- Ignoring motor part-load efficiency and drive losses.
- Correcting power factor above the utility threshold without checking leading-PF risk.
- Ignoring harmonics from VFDs and the need for filtering or derating.
- Confusing demand reduction with energy reduction.