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Three-Phase Power Equations

Electrical 3-phase equations

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Most AC power today is produced and distributed as three-phase power where three sinusoidal voltages are generated out of phase with each other. With single-phase AC power there is only one single sinusoidal voltage.

Real Power

Line to line voltage:

Wapplied = 31/2 Ull I cos Φ

             = 31/2 Ull I PF                      (1)

where

Wapplied = real power (W, watts)

Ull = line to line voltage (V, volts)

I = current (A, amps)

PF = cos Φ = power factor (0.7 - 0.95) 

Line to neutral voltage:

Wapplied = 3 Uln I cos Φ                    (2)

where

Uln = line to neutral voltage (V, volts)

For pure resistive load: PF = cos Φ = 1 

  • resistive loads converts current into other forms of energy, such as heat
  • inductive loads use magnetic fields like motors, solenoids, and relays

Power Factor

Typical power factors:

DevicePower Factor
Lamp, fluorecent uncompensated 0.5
Lamp, fluorecent compensated 0.93
Lamp, incandescent 1
Motor, induction 100% load 0.85
Motor, induction 50% load 0.73
Motor, induction 0% load 0.17
Motor, synchronous 0.9
Oven, resistive heating element 1
Oven, induction compensated 0.85
Pure resistive load 1

Example - Pure Resistive Load

For pure resistive load and power factor = 1 the real power in a 400/230 voltage (line to line / line to neutral) 20 amps circuit can be calculated as

  Wapplied = 31/2 (400 V) (20 A) 1

         = 13856 W

         = 13.9 kW

Total Power

W = 31/2 U I                       (2)

Brake Horsepower

WBHP = 31/2 U I PF μ / 746                       (3)

where

WBHP = brake horse power (hp)

μ = device efficiency

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