COMPLEX POWER AND POWER TRIANGLE

Complex Power and Power Triangle

Complex power S is the product of the voltage and the complex conjugate of the current.

S = VrmsIrms Cos (θv - θi) + jVrms Sin (θv - θi) 

If S is the complex power then,

S = V . I* V is the phasor representation of voltage and I* is the conjugate of current phasor.So if V is the reference phasor then V can be written as |V| ∠0.

(Usually one phasor is taken reference which makes zero degrees with real axis. It eliminates the necessity of introducing a non zero phase angle for voltage)

Let current lags voltage by an angle φ, so I = | I | ∠-φ(current phasor makes -φ degrees with real axis) I*= | I | ∠φSo,

S = |V| | I | ∠(0+φ) = |V| | I | ∠φ (For multiplication of phasors we have considered polar form to facilitate calculation)Writting the above formula for S in rectangular form we get

S = |V| | I | cos φ + j |V| | I | sin φ 

Power Triangle


POWER TRIANGLE HAS THREE SIDES:-
1-APPARENT POWER (VA)
2-REACTIVE POWER (VAR)
3-REAL POWER (W)
THE RELATIONSHIP B/W THESE CAN BE EXPRESSED BY REPRESENTING QUANTITIES AS VECTORS.
REAL POWER IS HORIZONTAL VECTOR.
REACTIVE POWER IS VERTICAL POWER.
APPARENT POWER IS HYPOTENUSE OF RT.ANGLED TRIANGLE.

(apparent power)2 = (real power)2 + (reactive power)2

RATIO OF REAL POWER TO APPARENT POWER IS CALLED POWER FACTOR.
PF=W / VA