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The per unit impedance of 98 km of 412 kV transmission line is (0.768 + 4.823i) x 10^-3 to bases of rated voltage and 115 MVA. Calculate the magnitude of the per unit impedance when the apparent power base is changed to 1,047 MVA.

For this question, I have calculated the initial per unit impedance magnitude to be 0.0444, and now I am wondering, do I multiply it by the distance in meters to get the final per unit impedance magnitude value?

Would the final answer be 0.0444 or would it be (0.0444 * 98000) = 4357.42?

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  • \$\begingroup\$ @MarcusMüller Not per-unit impedance. per-unit is a weird system of ratios (which are unitless) used in power transmission engineering. \$\endgroup\$
    – Hearth
    Dec 5, 2021 at 19:28
  • \$\begingroup\$ @Hearth aaaaah sorry! \$\endgroup\$ Dec 5, 2021 at 19:29
  • \$\begingroup\$ Check out section D of this paper. \$\endgroup\$ Dec 5, 2021 at 23:22

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There is a change of base formula for changing per unit impedance from an old base to a new base. What I show below is from the "Electrical and Computer: Power Reference Handbook Version 1.1.2" top of page 35, the supplied cheat sheet/book for the Power PE test.

The following equation may be used to change a per-unit impedance from an old base to a new base: $$ Z_{\rm new} = Z_{\rm old} \cdot \left( {\rm Base}\, kV_{\rm old} \over {\rm Base}\, kV_{\rm new} \right)^2 \cdot \left( {\rm Base}\, kV\!A_{\rm new} \over {\rm Base}\, kV\!A_{\rm old} \right). $$

You'll notice since voltage base remains constant, the first parenthesis in the change of base formula goes to 1 and can be ignored.

You've listed 98km for this problem but then list the per unit impedance. We normally use the distance to find the total line impedance, which we divide by a calculated "Base Impdance" derived from our base voltage and power to finally get our per unit impedance.

I will re-write the given per unit line impedance of the 98KM line (0.768 + 4.823i) x 10^-3 as (0.000768 + 0.004823i)

Given that the old base is 115MVA = 115,000 KVA and the new base is 1,047MVA = 1,047,000 KVA, we can solve the equation.

$$ \begin{aligned} Z_{\rm new}({\rm p.u}) &= {\rm New\ Per\ Unit\ Impedance} \\ &= (0.000768 + 0.004823\,i) \cdot 1^2 \cdot \left( 1,\!047,\!000 \over 115,\!000 \right) \\ &= 0.0073 + 0.046\,i. \end{aligned} $$

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