# Need Help to solve these three phase balanced load questions

Discussion in 'Homework Help' started by Ryza, Jun 12, 2011.

1. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
A 3 phase 3 wire ac circuit is fed from a 50 HZ system with line voltage of 400 V. A balanced load is connected to it. Calculate for the 4 cases given below the current in the lines connecting the source and the load, the source phase currents and the load phase currents.

Case 1: The source is star connected and the load is a balanced star connected impedance of 10 Ohms in each arm
Case 2: The source is star connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm
Case 3: The source is Delta connected and the load is a balanced star connected impedance of 10 Ohms in each arm
Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm.

2. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Ive worked it out but I think it might be slightly incorrect and confusing so want to make sure its right

3. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Case 1: The source is star connected and the load is a balanced star connected impedance of 10 Ohms in each arm
Line Voltage = 400V
Star Source Phase Voltage = Line Voltage/√3
Star Source Phase Voltage = 400/√3 = 230.94V
Star Source Phase Voltage = 230.94V
Star Load Phase Voltage = 230.94V
Line Current = V/R = 400/10 = 40amps
Line Current = 40amps
Both Star Source and Load Phase Currents = Line Current
Star Source Phase Current = 40amps
Star Load Phase Current = 40amps

Case 2: The source is star connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm
Line Voltage = 400V
Star Source Phase Voltage = Line Voltage/√3 = 400/√3 = 230.94V
Star Source Phase Voltage = 230.94V
Delta Load Phase Voltage = Line Voltage =400V
Delta Load Phase Voltage = 400V
Line Current = V/R = 400/10 = 40amps
Line Current = 40amps
Star Source Phase Current = Line Current = 40amps
Star Source Phase Current = 40amps
Delta Load Phase Current = Line Current/√3 = 40/√3 = 23.094amps
Delta Load Phase Current = 23.094amps

Case 3: The source is Delta connected and the load is a balanced star connected impedance of 10 Ohms in each arm
Line Voltage = 400V
Delta Source Phase Voltage = Line Voltage = 400V
Delta Source Phase Voltage = 400V
Star Load Voltage = Line Voltage/√3=230.94V
Line Current =V/R = 400/10 = 40amps
Line Current = 40amps
Delta Source Phase Current = Line Current/√3 = 40/√3 = 23.094amps
Delta Source Phase Current = 23.094amps
Star Load Phase Current = Line Current = 40amps
Star Load Phase Current = 40amps

Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm
Line Voltage = 400V
Delta Source and load Phase Voltages = Line Voltage = 400V
Delta Source Phase Voltage = 400V
Delta Load Phase Voltage = 400V
Line Current = V/R = 400/10 = 40amps
Line Current = 40amps
Delta Source and Load Phase Currents = Line Current/√3 = 40/√3 = 23.094amps
Delta Source Phase Current = 23.094amps
Delta Load Phase Current = 23.094amps

Is this incorrect?... dosnt seem right

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
If the line voltage is 400V with a 10Ω per arm balanced delta load, then the current in any delta arm is 40A - since there's 400V across any 10Ω arm. The line current would then be √3x40A=69.28A.

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5. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

E LINE = 400V
I LINE = Phase I x √3 = 40 x 3 = 69.282A
∆(SOURCE)PHASE VOLTAGE = E = 400V
∆PHASE (SOURCE) CURRENT I = V/R = 400/10 = 40A
∆ PHASE (LOAD) VOLTAGE E = 400V
∆ PHASE (LOAD) CURRENT I = V/R =400/10 = 40A

6. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
now I just need to suss out case 1, 2 and 3 hope my workings r correct

7. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Case 1: The source is star connected and the load is a balanced star connected impedance of 10 Ohms in each arm
Resistance = 10 Ohms
Line Voltage = 400V

(*) Source
E = 400/√3 = 230.94V
I = V/R = 230.94/10 = 23.094A
Source Phase Current = 23.094A

Line Current = Phase Current = 23.094A
Line Current = 23.094A

V = Line Voltage/√3 = 400/√3 = 230.94V
(Y) Phase Current = Line Current = 23.094A

Case 2: The source is star connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(*) Source
Phase Voltage = 400V/√3 = 230.94V
Phase Current = V/R = 230.94/10 = 23.094A
Source Phase Current = 23.094A

Line current = (Y) Phase current = 23.094A
Line Current = 23.094A

Phase Voltage = Line Voltage = 400V
Phase Current = Line Current/√3 = 23.094/√3 = 13.33A

Case 3: The source is Delta connected and the load is a balanced star connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(∆) Source
Phase Voltage = Line Voltage = 400V
Phase Voltage = 400V
Source Phase Current = V/R = 400/10 = 40A
Source Phase Current = 40A

Line Current = (∆) Phase Current x √3 = 40 x √3 =69.28A
Line Current = 69.28A

Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
Phase Current = Line Current = 69.28A

Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(∆)Source
Phase Voltage = Line Voltage = 400V
Phase Current = V/R = 400/10 = 40A
Source Phase Current = 40A

Line Current = (∆) Phase Current x √3 = 69.28A
Line Current = 69.28A

Phase Voltage = Line Voltage = 400V
Phase Current = Line Current/√3 = 69.28/√3 = 40A

IS THIS CORRECT please someone check?...

8. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
A 3 phase 3 wire ac circuit is fed from a 50 HZ system with line voltage of 400 V. A balanced load is connected to it. Calculate for the 4 cases given below the current in the lines connecting the source and the load, the source phase currents and the load phase currents.

Case 1: The source is star connected and the load is a balanced star connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(*) Source
E = 400/√3 = 230.94V
I = V/R = 230.94/10 = 23.094A
Source Phase Current = 23.094A

Line Current = Phase Current = 23.094A
Line Current = 23.094A

V = Line Voltage/√3 = 400/√3 = 230.94V
(Y) Phase Current = Line Current = 23.094A

Case 2: The source is star connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(*) Source
Phase Voltage = 400V/√3 = 230.94V
Phase Current = V/R = 230.94/10 = 23.094A
Source Phase Current = 23.094A

Line current = (Y) Phase current = 23.094A
Line Current = 23.094A

Phase Voltage = Line Voltage = 400V
Phase Current = Line Current/√3 = 23.094/√3 = 13.33A

Case 3: The source is Delta connected and the load is a balanced star connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(∆) Source
Phase Voltage = Line Voltage = 400V
Phase Voltage = 400V
Source Phase Current = V/R = 400/10 = 40A
Source Phase Current = 40A

Line Current = (∆) Phase Current x √3 = 40 x √3 =69.28A
Line Current = 69.28A

Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
Phase Current = Line Current = 69.28A

Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

(∆)Source
Phase Voltage = Line Voltage = 400V
Phase Current = V/R = 400/10 = 40A
Source Phase Current = 40A

Line Current = (∆) Phase Current x √3 = 69.28A
Line Current = 69.28A

Phase Voltage = Line Voltage = 400V
Phase Current = Line Current/√3 = 69.28/√3 = 40A

IS THIS CORRECT please someone check?...

9. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
As I said a balanced delta load with 10Ω in each leg will draw 69.28A line current with 400V line voltage.
So in Cases 2 & 4 the line current must be 69.28A.

In case 2 the source is star connected so the phase current is the same as the line current or 69.28A.

In case 4 the source is delta connected so the source phase leg current is Iline/√3=40A.

In cases 1 & 3 with star connected loads the line currents will be 23.09A as will the load star leg currents.

In case 1 with a star connected source the phase leg currents will be same as the line currents or 23.09A

In case 3 with a delta connected source the phase leg currents will be Iline/√3=13.33A.

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10. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Thanks heaps for your time! Appreciated!!

11. ### Ryza Thread Starter New Member

Jun 12, 2011
15
0
Case 1: The source is star connected and the load is a balanced star connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

Load Phase Voltage/√3 = 400/√3 = 230.94V
Load Phase Current = 230.94/10 = 23.094A

Line Current = Phase Current = 23.094A
Line Current = 23.094A

(*) Source
Source Phase Voltage = 400/√3 = 230.94V
Source Phase Current = Line Current
Source Phase Current = 23.094A

Case 2: The source is star connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

Load Phase Voltage = Line Voltage = 400V
Load Phase Current = V/R = 400/10 = 40A

Line Current = (∆) Phase current/√3 = 40 x √3 = 69.28A
Line Current = 69.28A

(*) Source
Source Phase Voltage = 400V/√3 = 230.94V
Source Phase Current = 69.28A

Case 3: The source is Delta connected and the load is a balanced star connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

Load Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
Load Phase Current = V/R = 230.94/10 = 23.094A

Line Current = (*) Phase Current = 23.094A
Line Current = 23.094A

(∆) Source
Source Phase Voltage = Line Voltage = 400V
Source Phase Current = Line Current /√3 = 23.094 /√3 =
Source Phase Current = 13.33A

Case 4: The source is Delta connected and the load is a balanced Delta connected impedance of 10 Ohms in each arm

Resistance = 10 Ohms
Line Voltage = 400V

Phase Voltage = Line Voltage = 400V
Phase Current = V/R =400/10 =40A