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Electrical Power Systems Problems

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.

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Solution Preview

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 + (85@70)*(251.022@-25.84)
= 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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