Single-Phase Power Analysis
Analyze residential and light commercial power loads. Calculate the total energy profile beyond simple wattage.
System Inputs
The actual work performed by the equipment.
Total power supplied to the circuit.
The Power Triangle Formulas
Single-phase AC power has three components — real, reactive, and apparent — that form the power triangle.
Real Power (kW)
P = V × I × PF The power that actually does work — measured in kilowatts. This is what your electricity bill charges you for.
Reactive Power (kVAR)
Q = V × I × sin(θ) Power stored and released by inductive and capacitive loads. It causes current without doing useful work, increasing cable losses.
Apparent Power (kVA)
S = V × I = √(P² + Q²) The total power the supply must deliver — the vector sum of real and reactive power. Used for sizing generators and transformers.
Understanding Single-Phase AC Power
Single-phase AC power is the standard supply for residential buildings and light commercial facilities. Unlike DC, AC voltage reverses direction periodically (50 or 60 times per second), which enables efficient voltage transformation but introduces the concept of power factor — the relationship between the voltage and current waveforms.
The Power Triangle
Real power (kW), reactive power (kVAR), and apparent power (kVA) form a right triangle. The angle θ between the apparent and real power vectors is the phase angle — and the cosine of this angle is the power factor. A PF of 1.0 means the triangle collapses to a straight line: all apparent power is real power.
What Causes Low Power Factor?
- Induction Motors: The most common cause. Motors use reactive power to build rotating magnetic fields. Lightly loaded motors have worse PF than fully loaded ones.
- Transformers at Light Load: The magnetizing current drawn by transformer cores is largely reactive.
- Fluorescent Lighting (older ballasts): Magnetic ballasts introduce significant reactive current. Electronic ballasts largely solve this.
- Variable Speed Drives: Can improve motor PF but introduce harmonic distortion which has its own effects on the supply.
Power Factor Correction
Low power factor can be corrected by adding capacitor banks in parallel with inductive loads. Capacitors supply reactive power locally, reducing the reactive current that must flow from the utility. This reduces cable losses, improves voltage regulation, and avoids utility penalties for industrial customers with PF below 0.9.