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A small town with a demand of 1 MW at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of two line wires carrying is `0.5 Omega` per km. Two step down transformers are available : 4000 V - 220 V and 100000 V - 220 V at a substationin the town for supply of power. Which one will you prefer and why? |
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Answer» Here, power required `= 1 MW = 10^(6) W = 10^(3) kW` Total resistance of two line wires `R = 2xx 20 xx 0.5 = 20 ohm`. (a) If power is supplied throuhg `4000 V - 220 V` transformer `E_(v) = 4000 V, I_(v) = (P)/(E_(v)) = (10^(6)W)/(4000 V) = 250 A` Line power loss `=I_(v)^(2) = (250)^(2) xx 20 = 1250000 W = 1250 kW` If there is no other power loss, then the essential plant supply `= (1000 + 1250) kW = 2250 kW` voltage drop on the line `= I_(v) xx R = 250 xx 20 = 5000 V :.` voltage for transmission `= 4000 + 5000 = 9000 V` As power is generated at 440 V, the step up transformer needed at the plant is 440 V - 9000 V Power loss in the process `= (1250)/(2250) xx100% = 55.5%` (b) If is supplied through 100,000 V - 220 V transformer `E_(v) = 1000,000 V` `I_(v) = (P)/(E_(v)) = (10^(6)W)/(100,000 V) = 10 A` Line power loss `= I_(v)^(2) = 10^(2) xx 20 = 2000 W = 2 kW` If there is no other power loss, then the essential plant supply `= (100 + 2 ) kW = 1002 kW` voltage drop on the line `= I_(v) xx R = 10 xx 20 = 200 V` `:.` Voltage for transmission `= (100000 + 200) V = 100200 V` As power is generated at 440 V, the step up transformer needed at the plant is `440 V - 100200 V` |
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