THREE-PHASE POWER ANALYSIS

There are three kinds of power- real (P) , reactive (Q) and apparent(S).

REAL POWER :

P = VpIpcos(θv – θi)

it is measured in Watts(W)

where p is the phase voltage and phase current in the system.

if the system is in line voltage and line current:

P= (VoIocos(θv-θi))/sqr(3)   

 

REACTIVE POWER:

 

Q =  VpIpsinθ

 

or 

Q = VoIosinθ

 

APPARENT POWER:

 

S= VpIp

S = sqr(P^2 + Q^2)

or 

S = VoIo/sqr(3)

 

 

 

            POWER TRIANGLE

 

pf( power factor) = cosθ

 

 

Example:

 

Y-Y connected

 

z= 0.4 + j0.3 ohms / phase

Zy = 24 + j19 ohms / phase

Zo = 0.6 + j0.7 ohms / phase

pf= 0.8 lagging

Van = 120< 30° 

Find 

S ,P, Q

Solution:

 

Using ohm’s law

V= IZ

I=V/Z

I= (120< 30° )/(0.4 + j0.3 + 24 + j19 + 0.6 + j0.7)

 

I = 3.75<-8.66°  A

 

P= (120)(3.75)cos(30+8.66) 

P= 351.39 W

 

Q= Ptanθ

 

θ=arcos(pf)

θ= arccos(0.8)

θ= 36.87

 

Q=  351.39tan36.87

Q – 263.54 VAR

 

S= sqr( 263.54 ^2 + 351.39^2)

S= 439.24 VA