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    Electrical Power Systems Problems

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    Electrical Power Systems Problems

    1. A three-phase line serves a 54MW load with a .9 lagging power factor at a line voltage of 138KV. The line constants are:
    A = D = 1 at 0 degrees
    B = 85 ohms At 70 degrees
    C = 950 x 10^4 siemens at 90 degrees

    Find the line and phase values of voltage and current at the sending end.

    2. For the system shown attached:

    G1: 20KV, 250MVA, X = J10%
    TI: 20/138KV, 200MVA, X=J15%
    T2: A Bank of 3, 1-Phase Devices, each is rated at 15/79.77KV, 250MVA, X=J10%

    Draw the per-unit diagram using the generator bases.

    © BrainMass Inc. brainmass.com October 9, 2019, 4:13 pm ad1c9bdddf
    https://brainmass.com/engineering/power-engineering/electrical-power-systems-problems-25695

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    See the attached file for the full solution.
    1. Load = 54 MW @0.9 p.g. lagging @138 kV (L-L)
    Load angle = arccos(0.9) = 25.84 deg (Lag) = -25.84
    Vr = 138,000 @ 0 deg
    Now P = sqrt(3)*Vr*Ir*(p.f.) = 54E06

    sqrt(3)*138000*Ir*0.9 = 54E06
    Ir = 251.022 A @ (-25.84 deg.)

    ABCD Constants
    --------------

    A = D = 1 @ 0 deg.
    B = 85 Ohms @ 70 deg.
    C = 950E-06 @ 90 deg.= j9.5E-04 Siemens

    Sending end Quantities:
    ----------------------

    Voltage = Vs = A*Vr + B*Ir
    Vs = 138,000 + ...

    Solution Summary

    Solution is found incorporating formulas including (1) Voltage = Vs = A*Vr + B*Ir and (2) Current = Is = C*Vr + D*Ir.

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