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
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    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
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    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
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    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
    Star Load Voltage = 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
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    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
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    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
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    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
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    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

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

    (*) 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

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

    (*) Load
    Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
    Phase Current = Line Current = 69.28A
    Load Phase 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

    (∆)Load
    Phase Voltage = Line Voltage = 400V
    Phase Current = Line Current/√3 = 69.28/√3 = 40A
    Phase Load Current = 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

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

    (*) 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

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

    (*) Load
    Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
    Phase Current = Line Current = 69.28A
    Load Phase 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

    (∆)Load
    Phase Voltage = Line Voltage = 400V
    Phase Current = Line Current/√3 = 69.28/√3 = 40A
    Phase Load Current = 40A



    IS THIS CORRECT please someone check?...
     
  9. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    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
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    Thanks heaps for your time! Appreciated!!
     
  11. Ryza

    Thread Starter New Member

    Jun 12, 2011
    15
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    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
    Load Phase Voltage/√3 = 400/√3 = 230.94V
    Load Phase Current = 230.94/10 = 23.094A
    Load Phase Current = 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
    Load Phase Voltage = Line Voltage = 400V
    Load Phase Current = V/R = 400/10 = 40A
    Load Phase Current = 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
    Load Phase Voltage = Line voltage/√3 = 400/√3 = 230.94V
    Load Phase Current = V/R = 230.94/10 = 23.094A
    Load Phase Current = 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

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

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

    (∆)Source
    Source Phase Voltage = Line Voltage = 400V
    Source Phase Current = 69.28/√3 = 40A
    Source Phase Current = 40A


    THANKS SOOO MUCH I SORTED IT OUT - I WAS JUST GETTING ALL CONFUSED BUT YOU HELPED ME HEAPS!!! :D
     
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