Equations & Concepts

Core Metaphor: The Particle Flow

The 3D animation uses particles to represent power flow. Not all power does useful work.

Active Power (P): These blue particles move directly from source to load, representing the "true" power that performs useful work.
Inductive Reactive Power (Q): This orange, turbulent flow represents energy used to create magnetic fields (e.g., in motors). It "sloshes" back and forth, doing no net work.
Capacitive Reactive Power (Q): This purple turbulence represents energy stored in electric fields. Like its inductive counterpart, it also does no net work.

The Power Triangle

The relationship between power types is described by a right triangle, where φ is the phase angle between voltage and current.

Apparent Power: S = V_rms I_rms (VA)

Active Power: P = S cos(φ) (Watts)

Reactive Power: Q = S sin(φ) (VAR)

Relationship: S² = P² + Q²

Instantaneous Power

The power at any instant, p(t), has two components:

p(t) = P(1+ cos(2ωt)) + Q sin(2ωt)

The Active component is always positive (delivering power), while the Reactive component averages to zero over a full cycle.

Reactive Power: The Particle Flow

Power Triangle

Waveforms

Active Power (green) always delivers energy. Reactive Power (orange/purple) averages to zero, doing no net work.

Power Factor

Inductive Capacitive

Additional Information

Reactive power is essential for maintaining voltage levels in AC systems, but it does not contribute to useful work.

Explore how the power factor affects efficiency by adjusting the slider in the dashboard. A lower power factor indicates higher reactive power, which can strain electrical infrastructure.

Understanding reactive power is crucial for engineers designing efficient power systems, as it impacts the sizing of transformers, cables, and other components.