3 phase induction motor

Discussion in 'Homework Help' started by Jess_88, Oct 29, 2011.

  1. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    Hey guys. :)
    Just studying for my exam and I'm a little stuck on this question. mainly part b)

    A three phase, four pole, 60Hz motor is rated at 10hp, 208V and 1755rpm. The approximate equivalent circuit referred to the stator is as follows;
    R1 = 0.15, R2 = 0.15, X1 = 0.4, X2 = 0.25, Xm = 30
    The combined rotational losses(including frictional, winding and core losses) are 500W. The motor operates at rated speed when connected to a 208V 60Hz source. Assuming the shunt component (Xm) is connected at the front of the equivalent circuit, calculate
    a)Synchronous speed and slip. draw the equivalent circuit.
    b)Line current and input power factor
    c)induced (airgap) power and torque
    d)Output horsepower and torque
    e)Efficiency of the motor


    Solutions.
    S = 0.025, ILine = 20.25A, PF = 0.95 lagging, Pg = 6787W, Tg = 36Nm, Hp = 8.2Hp, Tout = 33.28Nm, efficiency = 88%


    my attempt
    a) Nsyc = (120*60)/4 = 1800
    s = (1800 - 1755)/1800 = 0.025

    b)This is where I'm a bit lost for what formula to use
    is IL = (Vphase/(R1 + (R2/s)) ?
    = (208/(√3))/(0.15 + (0.15/0.025)) = 19.52A.... Not quite right :(



    Thanks guys :)
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    You must include the inductive reactances [both series and shunt] in the analysis - not just the resistive elements.
     
    Jess_88 likes this.
  3. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    It works! Thanks!

    Zeq = Zm||(R1 + X1 + R2/s + X2)
     
  4. Jess_88

    Thread Starter Member

    Apr 29, 2011
    174
    1
    should I be using
    PF = Pin/[(√3)*VL*IL] ?
    And Pin = Pag + Pscl + Pfwc
    Pag= 6960W
    Pscl = 3(I1^2)*R1
    Pfwc = 500W
     
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