A wind-turbine powers a direct-current generator in order to recharge an electri

Question

A wind-turbine powers a direct-current generator in order to recharge an electrical storage battery.

The generator operates at steady-state with input shaft torque of 270 N-m at 180 RPM (18.85 rad/s). The

generator and battery surfaces are both hot due to internal electrical resistance and/or mechanical friction.

The heat transfer rate from the battery to the surroundings is 600 Watts while the generator steadily supplies

a constant electrical current of 100 amps at 48 volts to charge the battery. After 120 minutes of steady-state

operation the generator is shut off. Treat the generator and battery as different systems.

Find the generator shaft power input, W SHAFT (kW) and the generator heat transfer rate, Q GEN (kJ/s).

Find the total electrical work input to the battery in the 120 minute period, WELEC (kJ) and the change

in battery energy, (E BATTERY,FINAL - E BATTERY,INITIAL) (kJ)

Sketch the battery energy over time using units of E BATTERY (kWhr) vs time (hr).

NOTE: Electrical energy is typical priced in units of kilowatt-hours (kWhr).

Ans: |Q | ? 0.3 kW,

W ELEC ? 35,000 kJ

Explanation / Answer

Power input, P =torque*angular velocity

P1 = T*w = 270*18.85 = 5.09 KW

power delivered to the battery,P2 = V*I = 48*100 = 4800 = 4.8 KW


QGEN = P1 - P2 = 5.09 - 4.8 = 0.29 kW


Energy delivered to the battery in 120 min = V*I*t

WELE = 48*100*120*60 = 34560 KJ

E_Battery,Final - E_Battery,initial = 34560*10^3 - 600*120*60

                                    =30240 KJ

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