# Power Engineering Help (Star-Delta)

#### mksa

Joined May 6, 2006
2
1) An unbalanced delta-connected load on a 400 V (line-line) 50 Hz system has
impedances of:
Za = 40 ohm; Zb = j 40 ohm; Zc = 20  j 20 ohm.
Calculate the phase and line currents.

2) A star-connected 400 V resistive load is connected to a 3-wire system. The
Za = 20 ohm; Zb = 40 ohm; Zc = 40 ohm.
Calculate the voltage of the neutral point.

3) An unbalanced star-connected load on a 220 V 60Hz 4-wire system. The legs of the load have impedances of:
Za = 5 ohm; Zb = 5 +j 5 ohm; Zc = 5 j 5ohm.
To insure correct phase voltage the star is connected to the neutral line
Calculate the phase and neutral currents.

4) An 400 V (line-line) star-connected unbalanced load has an earthed start point.
The load on phase 1 is 10 ohm, the load on phase 2 is 10 + j5 ohm and the load on
phase 3 is 10  j5 ohm. Calculate the phase currents and the star to earth current
and sketch the current phasor diagram.

I can do the balance system but the unbalanced I can't. and I would like to ask what is the diffrenece between xxx V (line-line) and xxxV xxHz and the difference between the 4-wire system and 3-wire system.

thank you.

#### mksa

Joined May 6, 2006
2
1) An unbalanced delta-connected load on a 400 V (line-line) 50 Hz system has
impedances of:
Za = 40 ohm; Zb = j 40 ohm; Zc = 20  j 20 ohm.
Calculate the phase and line currents.
the phase currnts
for Iab=Vab/Za=400/40=10A
for Ibc =Vbc/Zb=400 phase-120/40 phase90 = 10 phase -210 A
for Ica=Vca/zc=400 phase 120 / 28.28 phase -45 = 14.144 phase 165 A
the line currents
for IAa = Iab-Ica=10 phase 0 - 14.144 phase 165 = 23.94 phase -8.79 A
for IBb = Ibc-Iab=10 phase -210 - 10 phase 0 = 218.43 phase -23.55 A
for ICc = Ica - Ibc = 14.144 phase 165 - 10 phase -210 = 191.793 phase 24.69 A

2) A star-connected 400 V resistive load is connected to a 3-wire system. The
Za = 20 ohm; Zb = 40 ohm; Zc = 40 ohm.
Calculate the voltage of the neutral point.
Vsn=Ya*Van+Yb*Vbn+Yc*Vcn/Ya+Yb+Yc
Vsn=1/20 * (400/ √ 3 phase 0) + 1/40 * 230.94 phase -120 + 1/40 * 230.94 phase 120 / (1/20 + 1/40 + 1/40) = 95.6751 phase 180.013 V

3) An unbalanced star-connected load on a 220 V 60Hz 4-wire system. The legs of the load have impedances of:
Za = 5 ohm; Zb = 5 +j 5 ohm; Zc = 5 j 5ohm.
To insure correct phase voltage the star is connected to the neutral line
Calculate the phase and neutral currents.
first we find Van , Vbn and Vcn which 220/ √ 3
Van=127 phase 0 V
Vbn= 127 phase -120 V
Vcn=127 phase 120 V
Ian = Van/Za = 127 phase 0 / 5 = 25.4 A
Ibn=Vbn/Zb = 127 phase -120 / 7.07 phase 45 = 17.96 phase 165 A
Icn=Vcn/Zc = 127 phase 120 / 7.07 phase -45 = 17.96 phase 165 A
In = Ian + Ibn + Icn = 25.4 phase 0 + 17.96 phase 165 + 17.96 phase 165
In = 13.15 phase 134.998 A
4) An 400 V (line-line) star-connected unbalanced load has an earthed start point.
The load on phase 1 is 10 ohm, the load on phase 2 is 10 + j5 ohm and the load on
phase 3 is 10  j5 ohm. Calculate the phase currents and the star to earth current
and sketch the current phasor diagram.
first we find Van , Vbn and Vcn which 400/ √ 3
Van=231 phase 0 V
Vbn= 231phase -120 V
Vcn=231phase 120 V
Ian = Van/Za = 231phase 0 / 10 = 23.1 A
Ibn=Vbn/Zb = 231phase -120 / 11.18 phase 26.565 = 20.66 phase 146.565 A
Icn=Vcn/Zc = 231 phase 120 / 11.18 phase -26.565 = 20.66 phase 146.565 A
In = Ian + Ibn + Icn = 23.1 phase 0 + 20.66 phase 146.565 A+ 20.66 phase 146.565 A
In = 25.45 phase 116.56 A

#### mksa

Joined May 6, 2006
2
1) An unbalanced delta-connected load on a 400 V (line-line) 50 Hz system has
impedances of:
Za = 40 ohm; Zb = j 40 ohm; Zc = 20  j 20 ohm.
Calculate the phase and line currents.
the phase currnts
for Iab=Vab/Za=400/40=10A
for Ibc =Vbc/Zb=400 phase-120/40 phase90 = 10 phase -210 A
for Ica=Vca/zc=400 phase 120 / 28.28 phase -45 = 14.144 phase 165 A
the line currents
for IAa = Iab-Ica=10 phase 0 - 14.144 phase 165 = 23.94 phase -8.79 A
for IBb = Ibc-Iab=10 phase -210 - 10 phase 0 = 218.43 phase -23.55 A
for ICc = Ica - Ibc = 14.144 phase 165 - 10 phase -210 = 191.793 phase 24.69 A

2) A star-connected 400 V resistive load is connected to a 3-wire system. The
Za = 20 ohm; Zb = 40 ohm; Zc = 40 ohm.
Calculate the voltage of the neutral point.
Vsn=Ya*Van+Yb*Vbn+Yc*Vcn/Ya+Yb+Yc
Vsn=1/20 * (400/ √ 3 phase 0) + 1/40 * 230.94 phase -120 + 1/40 * 230.94 phase 120 / (1/20 + 1/40 + 1/40) = 95.6751 phase 180.013 V

3) An unbalanced star-connected load on a 220 V 60Hz 4-wire system. The legs of the load have impedances of:
Za = 5 ohm; Zb = 5 +j 5 ohm; Zc = 5 j 5ohm.
To insure correct phase voltage the star is connected to the neutral line
Calculate the phase and neutral currents.
first we find Van , Vbn and Vcn which 220/ √ 3
Van=127 phase 0 V
Vbn= 127 phase -120 V
Vcn=127 phase 120 V
Ian = Van/Za = 127 phase 0 / 5 = 25.4 A
Ibn=Vbn/Zb = 127 phase -120 / 7.07 phase 45 = 17.96 phase 165 A
Icn=Vcn/Zc = 127 phase 120 / 7.07 phase -45 = 17.96 phase 165 A
In = Ian + Ibn + Icn = 25.4 phase 0 + 17.96 phase 165 + 17.96 phase 165
In = 13.15 phase 134.998 A
4) An 400 V (line-line) star-connected unbalanced load has an earthed start point.
The load on phase 1 is 10 ohm, the load on phase 2 is 10 + j5 ohm and the load on
phase 3 is 10  j5 ohm. Calculate the phase currents and the star to earth current
and sketch the current phasor diagram.
first we find Van , Vbn and Vcn which 400/ √ 3
Van=231 phase 0 V
Vbn= 231phase -120 V
Vcn=231phase 120 V
Ian = Van/Za = 231phase 0 / 10 = 23.1 A
Ibn=Vbn/Zb = 231phase -120 / 11.18 phase 26.565 = 20.66 phase 146.565 A
Icn=Vcn/Zc = 231 phase 120 / 11.18 phase -26.565 = 20.66 phase 146.565 A
In = Ian + Ibn + Icn = 23.1 phase 0 + 20.66 phase 146.565 A+ 20.66 phase 146.565 A
In = 25.45 phase 116.56 A