Question

Problem 2. A three phase transformer rated at 5 MVA, 115/13.2 kV has a per phase series impedance of 0.007 + j0.075 per unit (shunt parameters are ignored). The low voltage side is connected to a short distribution line which modeled by a series per phase impedance of 0.02 +j0.1 per unit on the base of 10 MVA. The line supplies a balanced three phase constant impedance load at 4 MVA, 13.2 kV with power factor of 0.85 lagging

• a) Draw an equivalent circuit of the system indicating all impedances in per unit. Choose 10 MVA, 13.2 kV as the base values of load.

• b) Calculate the per unit source voltage that must be supplied to the high voltage side of transformer to supply the load ar rated voltage.

• c) Find the per unit current based on the high voltage side of the transformer.

Answer #1

For a transformer we have -

Given base values as 10 MVA and 13.2 KV

For a transfromer PU

Base current = Base KV/ Base V

I_{B} = 10M/ 1.732 *13.2 K =
437.386 A

Base impedance -

Z_{B} = KV_{B}
^{2} /MVA_{B} = 17.424 ohms

per unit system equivalent circuit -

Also Z_{PU will} be same on either side of transformer
ie, primary and secondary

Given Z = 0.007 + j0.075 then

Now Z_{pu old} =
Z_{act} / Z_{B}

= 0.007 + j0.075 / 17.424

= 0.4 + j 4.3 m ohms

now

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