Three Phase Electrical

Overview

Engineering reference data for Three Phase Electrical in electrical engineering.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Power

$P = VI = I^2R = V^2/R$

Electrical power.

Energy

$E = Pt$

Energy = Power × Time.

Variables

Power Factor Reference Data

Additional Formulas

Real power calculations for three-phase systems:

Using line-to-line voltage: $W_{\text{applied}} = \sqrt{3} \, U_{ll} \, I \, \cos(\phi) = \sqrt{3} \, U_{ll} \, I \, \text{PF}$

Using line-to-neutral voltage: $W_{\text{applied}} = 3 \, U_{ln} \, I \, \cos(\phi)$

Total power in a balanced three-phase system: $W = \sqrt{3} \, U \, I$

Brake horsepower (actual shaft power): $W_{BHP} = \frac{\sqrt{3} \, U \, I \, \text{PF} \, \mu}{746}$ where $\mu$ is device efficiency (decimal).

Important Definitions and Properties

Power Factor (PF) is defined as $\cos(\phi)$, where $\phi$ is the phase angle between voltage and current. It ranges from 0 to 1:

• Pure resistive loads (e.g., incandescent lamps, resistive heaters) have $\text{PF} = 1$ (current and voltage are in phase).
• Inductive loads (e.g., motors, solenoids, relays) have $\text{PF} < 1$ (current lags voltage).

Load Type Characteristics:

• Resistive loads convert current directly into other forms of energy, primarily heat.
• Inductive loads use magnetic fields for operation (e.g., motors, solenoids, relays).

Example Calculation: For a pure resistive load ($\text{PF} = 1$) in a 400 V (line-to-line) / 230 V (line-to-neutral) system with 20 A current: $W_{\text{applied}} = \sqrt{3} \times 400 \, \text{V} \times 20 \, \text{A} \times 1 = 13,856 \, \text{W} \approx 13.9 \, \text{kW}$

References

• Original Source