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page 75

Next, consider the partial derivative for the reactance,

 

 

 

PL

= ----------------------------------------------------------------

 

Vs22RL( XL + Xs)

= 0

 

 

 

 

 

 

 

 

 

XL

( (

RL + Rs)

2

+ (

2

2

 

 

 

 

 

 

XL + Xs) )

 

 

 

 

 

 

 

 

 

 

 

 

 

XL = Xs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.3 3-PHASE CIRCUITS

3-phase circuits are common in large scale power generators and delivery systems.

These systems carry 3 phases of voltage, each 120 degrees out of phase, on three separate conductors. If these three wires are connected through a balanced load the sum of currents is zero. Most systems provide a fourth wire as a neutral.

generator

V1( t)

V2( t)

V3( t)

phase 1

load

neutral

phase 2

phase 3

= Vpeak sin ( ω

t) = Vrms 0°

 

 

 

 

2π

 

 

 

= Vpeak sin ω

t +

-----

= Vrms

120°

3

 

 

4π

 

 

 

= Vpeak sin ω

t +

-----

= Vrms

240°

3