The generators at a hydroelectric generating station generate alternating curren

Question

The generators at a hydroelectric generating station generate alternating current (AC) as a magnetized rotor spins inside a set of stationary coils. The output voltage of a particular generator is 6600 V and the output current is 1.4 × 105 A.

1) What is the power output of this generator? (kW)

2) Before being distributed long distance to consumers, the voltage is increased from from 6600 V up to voltage between 100-750 kV (depending on the distance that the power must be delivered) using heavy-duty industrial transformers. Under ideal conditions, what is the current output from the transformers if the voltage is increased from 6600 V to 4 × 105 V? (A)

4) After travelling long distances cross-country (for instance, 2700 miles from Hoover Dam to Los Angeles!), the high voltage is decreased at power distribution sub-stations using transformers. From a sub-station, the electricity is distributed throughtout a neighborhood of a given city or town for business, residential, and industrial use. If the transformers at a certain substation take in 1.3 × 104 kW of power at 4 × 105 V and decrease the voltage to 4800 V to deliver to a residential area, what is the current output of the substation transformers? (A)

5) What is the ratio of secondary windings to primary windings in the substation transformers?

6) Before reaching a home, utility pole transformers decreases the voltage from 4800 V down to 240 V. The MAIN circuit breaker in a typical household is rated at for 200 A service. What is the maximum power input that a typical household can recieve before the main circuit breaker of the home breaks the circuit due to overloading?

7) Asuming that each household serviced has this maximum power input given by your correct answer to Part (6), how many homes can be serviced by the substation?

Explanation / Answer

(1) P = V x i = 6600 x 1.4*105 = 924*106 Watt = 924 MW

(2)By Vs/Vp =Ip/Is
=>4*105/6600 = 1.4*105/Is
=>Is = 2310 amp

(3)By Ns/Np = Vs/Vp
=>Ns/Np = 4*105/6600 = 60.60

(4)By P = Vp x Ip = Vs x Is
=>Is = P/Vs = 1.3*104*103W / 4800 = 2708.33 amp

(5)By Ns/Np = Vs/Vp = 4800/4*105 = 0.012

(6)P(max) = V x i(max)
=>P(max) = 240 x 200 = 48000 W = 48 kW

(7) n = 1.3*104kW / 48kW = 270.83

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