Three Phase Power

Analysis
Back Note

Load Connected in Star

Phase Voltages

V_{an} = Dummy Text ∠0 °  V

V_{bn} = Dummy Text ∠240 °  V

V_{cn} = Dummy Text ∠120 °  V

Phase Currents

I_{a} = \frac{V_{an}}{Z}

I_{a} = Dummy Text ∠ °  A

I_{b} = \frac{V_{bn}}{Z}

I_{b} = Dummy Text ∠ °  A

I_{c} = \frac{V_{cn}}{Z}

I_{c} = Dummy Text ∠ °  A

dummy text dummy text

Load Connected in Delta

Phase Voltages

V_{ab} = Dummy Text ∠30 °  V

V_{bc} = Dummy Text ∠270 °  V

V_{ca} = Dummy Text ∠150 °  V

Phase Currents

I_{ab} = \frac{V_{ab}}{Z}

I_{ab} = Dummy Text ∠ °  A

I_{bc} = \frac{V_{bc}}{Z}

I_{bc} = Dummy Text ∠ °  A

I_{ca} = \frac{V_{ca}}{Z}

I_{ca} = Dummy Text ∠ °  A

Line Currents

I_{a} = I_{ab} - I_{ca}

I_{a} = Dummy Text ∠ °  A

I_{b} = I_{bc} - I_{ab}

I_{b} = Dummy Text ∠ °  A

I_{c} = I_{ca} - I_{bc}

I_{c} = Dummy Text ∠ °  A

dummy text dummy text

In three phase circuit the source as well as load can both be connected either in star or delta. Here the source is star connected. The delta connected source is rarely used in practice.

In star connected load the voltage across the impedance Z is phase voltage and the current flowing through Z is the line current.

In delta connected load the voltage across the impedance Z is line voltage and the line current is √3 times the load current through Z. The load current in delta load leads the line current by 30°.

Whether the load or source are Star or Delta connected

P = \sqrt{3} V_{l} I_{l} cos(φ)

V_l and I_l are values of line voltage and current

Q = \sqrt{3} V_{l} I_{l} sin(φ)

Electrical Systems

Three Phase Power