The characteristic impedances of an overhead line and underground cable connected in series (Fig. 7.15(a)) are 400 Ω and 50 Ω respectively. The incident surge voltage of 800 kV rms is traveling on the overhead line toward the junction. Determine: (a) the surge voltage transmitted into the cable;

Question

The characteristic impedances of an overhead line and underground cable connected in series (Fig. 7.15(a)) are 400 Ω and 50 Ω respectively. The incident surge voltage of 800 kV rms is traveling on the overhead line toward the junction. Determine: (a) the surge voltage transmitted into the cable; (b) the surge current transmitted into the cable; (c) the surge voltage reflected back along the overhead line; (d) the power in the forward wave arriving at the junction and the transmitted wave power.

Accepted Answer

(a) [latex]\upsilon _{f2}=\rho _{ref}\upsilon _{f1}=\frac{2Z_{c2}}{Z_{c2}+Z_{c1}}\upsilon _{f1}=\frac{2\cdot 50}{50+400}800=178 kV(rms) [/latex]

(b) [latex]i_{f2}=\frac{\upsilon _{f2}}{Z_{c2}}=\frac{178}{50} [/latex]=3.56 kA(rms).

(c) [latex]\upsilon _{b1}=\upsilon _{f2}-\upsilon _{f1} =178−800=−622 kV(rms).[/latex]

(d) [latex]P_{f1}=\frac{\upsilon ^2_f1}{Z_{c1}}=\frac{800^{2}}{400} =1600 MW [/latex]

[latex]P_{f2}=\frac{\upsilon ^2_{f2}}{Z_{c2}}=\frac{178^2}{50} =634 MW[/latex].

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