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TUTORIAL

THREE-PHASE CIRCUITS

4.1 Balanced Three-Phase Voltages

1. If Vab= 400 V in a balanced Y-connected three-phase generator, find the phase voltages,assuming the phase sequence is

(a) abc(b) acb

!. "ssuming the abcsequence, if Vca= !0# !0V in a balanced three-phase circuit, find

Vab, Vbc, Van, and Vbn.

$. %iven that the line voltages of a three-phase circuit are

Vab= 4!0 0,Vbc= 4!0 -1!0

Vac= 4!0 1!0V

find the phase voltages Van, Vbn, and Vcn.

4.2 Balanced Connections : -

4. &btain the line currents in the three-phase circuit of 'igure 1.

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'igure 1

(. " balanced Y-Y four-)ire s*stem has phase voltages

Van= 1!0 0, Vbn= 1!0 -1!0

Vcn= 1!0 1!0V

+he load impedance per phase is 1 1$ , and the line impedance per phase is 1 !

. /olve for the line currents and neutral current.

. +he magnitude of the phase voltage of an ideal balanced three-phase Y-connected source

is 4000 V. +he source is connected to a balanced Y-connected load b* a distribution line

that has an impedance of #1 + j . +he load impedance is !211, + j . +he phase

sequence of the source is abc. 3se the a-phase voltage of the source as the reference.

i5 6onstruct a single-phase equivalent circuit of the s*stem.

ii5 6alculate the magnitude and phase angle of T!R"" #$%phase voltages at the

load.

iii5 6alculate the magnitude and phase angle of T!R"" #$%line voltages at the load.

4.$ Balanced Connections :-&

2. /olve for the line currents in the - circuit of 'igure !. +a7e '

= 04(.

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'igure !

#. " balanced delta-connected load has a phase current IAC= 10-$0".

a5 8etermine the three line currents assuming that the circuit operates in the positivephase sequence.

(b) 6alculate the load impedance if the line voltage is VAB= 110 0V.

. In a )*e-delta three-phase circuit, the source is a balanced, positive phase sequence )ith

Van= 1!0 0V. It feeds a balanced load )ith '

= 1!

per phase through a balanced line )ith 'l= 1 0.(per phase. 6alculate the phase

voltages and currents in the load.

4.4 Balanced Connections :- &-&

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10. +hree !$0-V generators form a delta-connected source that is connected to a balanced

delta-connected load of 9:= 10 # ; per phase as sho)n in 'igure $ belo).

a5 8etermine the value of I"6.b5

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1$. " balanced three-phase Y-@ s*stem has Van= 1!0 0 > Vrmsand 9@= (1 4( ;. If the

line impedance per phase is 0.4 1.! ;, find the total compleA po)er delivered to the

load.

14. +hree equal impedances, 0 $0 ; each, are delta-connected to a !$0-V rms, three-phase circuit. "nother three equal impedances, 40 10 ; each, are )*e-connectedacross the same circuit at the same points. 8etermine

a5 the line currentb5 the total compleA po)er supplied to the t)o loads

c5 the po)er factor of the t)o loads combined

1(. " three-phase source delivers 4#00 V" to a )*e-connected load )ith a phase voltage of

!0# V and a po)er factor of 0. lagging. 6alculate the source line current and the source

line voltage.