How Do Line and Phase Currents Relate in a Three-Phase Delta-Connected Load?

[ric115]

Hi There

I have attempted the following question can anyone confirm what i have done and help with the rest of the question. Thanks

Question

Derive the numerical relationship between the line and phase currents for a balanced three-phase delta-connected load.

Three coils are connected in delta to a three-phase, three-wire, 400V, 50Hz supply and take a line current of 5A 0.8 power factor lagging. Calculate the resistance and inductance of the coils.

If the coils are star-connected to the same supply, calculate the line current and the total power.

Calculate the line currents if one coil becomes open-circuited when the coils are connected in star.

This is what i have;

EL = 400V
IL = 5 A
P.F cos0 = 0.8 lagging

Iph = IL/√3 = 5/√3 = 2.887 A

Impedance of each phase, Zph = Eph/Iph = 400/2.887 = 138.6 Ohms

Resistance of each phase, Rph = Zph cos0 = 138.6 x 0.8 = 110.8 Ohms

Reactance of each phase, Xph = Zph cos0 = 138.6 √1 - (o.8)^2 = 83.2 Ohms

Therefore inductance = Xph/2πf = .265 H

Coils connected in star;

Eph = EL/√3 = 231

Iph = Eph/Zph = 231/138.6 = 1.667 A ( Iph = IL )

Using P = √3 x EL x IL cos o.8
P = √3 x 400 x 1.667 x 0.8
P = 923.9 W

one coil becomes open-circuited; ?

Thanks

 

[jbsteele]

When one coil becomes open circuited when the coils are connected in star, then the line current will be equal to the phase current. This means that the line current will be 1.667A.