Power Triangle

          In AC circuits, current and voltage are normally out of phase and, as a result, not all the powerproduced by the generator can be used to accomplish work.   By the same token, power cannotbe calculated in AC circuits in the same manner as in DC circuits.   

The power triangle,  equates  AC  power  to  DC  power  by  showing  the  relationship  between  generatoroutput (apparent power - S) in volt-amperes (VA), usable power (true power - P) in watts, andwasted or stored power (reactive power - Q) in volt-amperes-reactive (VAR).   The phase angle(q) represents the inefficiency of the AC circuit and corresponds to the total reactive impedance(Z) to the current flow in the circuit.

The power triangle represents comparable values that can be used directly to find the efficiencylevel  of  generated  power  to  usable  power,  which  is  expressed  as  the  power  factor  (discussedlater).    Apparent  power,  reactive  power,  and  true  power  can  be  calculated  by  using  the  DC equivalent (RMS value) of the AC voltage and current components along with the power factor.

APPARENT POWER

Apparent  Power  (S)  is  the  power  delivered  to  an  electrical  circuit. Equation  is  a mathematical representation of apparent power.   The measurement of apparent power is in volt-amperes (VA).S = I2Z = ITwhereS   = apparent power (VA)I    = RMS current (A)E   = RMS voltage (V)Z   = impedance (W)

TRUE POWER

True power (P) is the power consumed by the resistive loads in an electrical circuit.  The measurement of true power is in watts.P = I2R = EI cosq, whereP   = true power (watts)I    = RMS current (A)E  = RMS voltage (V)R  = resistance (W) q= angle between E and I sine waves.

REACTIVE POWER

Reactive  power  (Q)  is  the  power  consumed  in  an  AC  circuit  because  of  the  expansion  and collapse of magnetic (inductive) and electrostatic (capacitive) fields.  Reactive power is expressed in volt-amperes-reactive (VAR). 

POWER FACTOR

Power factor (pf) is the ratio between true power and apparent power.  True power is the power consumed  by  an  AC  circuit,  and  reactive  power  is  the  power  that  is  stored  in  an  AC  circuit. Cos theta is called the power factor (pf) of an AC circuit.   It is the ratio of true power to apparent power, where q is the phase angle between the applied voltage and current sine waves and also between P and S on a power triangle shown on the figure above.

By: Kirk Macaraeg