AC Power Fundamentals

Concept

In an alternating current (AC) circuit, voltage and current vary as sine waves and can be out of phase. Because of this phase difference caused by inductive and capacitive loads, power is divided into three components:

1. Real Power / Active Power: The time-average power that actually does work or is lost as heat.
2. Reactive Power: The power that oscillates back and forth between the source and reactive components (inductors and capacitors), doing no net work.
3. Apparent Power: The complex sum of real and reactive power, representing the total power capacity the electrical system must support.

The ratio of real power to apparent power is called the Power Factor (PF).

Formula & Method

Using the RMS values of voltage and current, and the phase angle difference $\theta = \theta_v - \theta_i$:

• Real Power: $P = V_{rms} I_{rms} \cos(\theta)$
• Reactive Power: $Q = V_{rms} I_{rms} \sin(\theta)$
• Apparent Power: $S = V_{rms} I_{rms}$
• Power Factor: $\text{PF} = \cos(\theta) = \frac{P}{S}$

This relationship can be visualized as a power triangle, where $S = \sqrt{P^2 + Q^2}$.

Variables & Units

• $P$ = Real power, in Watts (W)
• $Q$ = Reactive power, in Volt-Amperes Reactive (VAR)
• $S$ = Apparent power, in Volt-Amperes (VA)
• $V_{rms}, I_{rms}$ = RMS voltage (V) and current (A)
• $\theta$ = Phase angle difference between voltage and current
• $\text{PF}$ = Power factor, a dimensionless number between 0 and 1

Engineering Meaning

Power factor is a critical index of energy efficiency in electrical systems. A low power factor means the system must draw more current than necessary to do real work, which increases losses in transmission lines ($I^2R$) and requires larger transformers. Engineers use capacitor banks to correct and improve a low lagging power factor.

Engineering Check

Ensure that calculations use RMS values for voltage and current, not peak values. Distinguish clearly between a leading (capacitive) and lagging (inductive) power factor. By convention, the sign of $Q$ is positive for inductive loads and negative for capacitive loads.

Explicit Exclusions

This article covers single-phase AC power fundamentals. It does not cover three-phase power systems, complex power notation ($S = P + jQ$), harmonic distortion analysis, and detailed sizing calculations for power factor correction.