Question

A 3 phase, 60 hz, 138 kv transmission line is 250 miles long and delivers power to a 50 mw load at 132 kv and at 0.92 la...


A 3 phase, 60 hz, 138 kv transmission line is 250 miles long and delivers power to a 50 mw load at 132 kv and at 0.92 lagging power factor. The line resistance is 0.175 ohm/mile, the line inductance is 0.302mH/mile and the line capacitance is 0.0245 uf/mile.

Calculate sending end voltage

Answer

Given:r=0.175ohm/mile=43.75ohmL=0.302mH/mileXL=jWL=j28.46ohmC=0.0245μf/mileY=j2.30×10-3cosϕ=0.92lagP=50Mwf=60HZVR=132Kv 

                                           Electrical Engineering homework question answer, step 2, image 1

P=3VRIRcosϕIR=50×1063×132×103×0.92IR=237.7AIY=VR×Y2IY=j87.64AApplying KCLIz=IR+IYIz=218.75-1.45°A

Now Consider π model:Vs=VR+IzZVs=1323×103+218.75-1.4543.75+j28.46Vs=76.210K+9.570K+j6.223K-j0.2419K+0.157KVs=85.937+j5.981Vs=86.143.98°KV(Answer)

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