Electronic Engineering homework help. 1.Suppose the probability density function (PDF) for wind speed is given

as

a) Find the value of for this to be a legitimate PDF.

b) Find the cumulative distribution function (CDF) for the wind speed.

2.A homeowner considers purchasing a rooftop PV system that costs

$11,000. Assume the only costs for those PVs are the annual loan

payments on a $11,000, rate 4.5%, 10-year loan.

a)Find the levelized cost of electricity (LCOE, $/kWh) of this system.

b)Suppose the PV system generates constant power and delivers 6,000

kWh of electricity per year. It works 6 hours a day and 200 days a year.

The PV system is used to power a

50-gallon electric water heater. If the efficiency of the tank is 90% (i.e.,

10% of heat loss), how long would the PV system take to heat the full tank

of water from 10∘

� to 50∘

� ? (Recall that 3412 Btu = 1kWh and 1 gallon

of water weighs 8.35 lbs)

c)By using the LCOE, find the cost of a 12-gallon, 110∘

� shower if the

cold-water supply temperature is 55∘

�.

3. Consider a 0.015 solar cell with the equivalent circuit shown below,

where the parallel resistance of �� = 5 �. The reverse saturation current is

and at an insolation of 1-sun the short-circuit is At 20∘

�, with an output

voltage of 0.5V, find the following:

a)The load current and the power consumed by the load.

b)The efficiency of the solar cell.

4.Consider a wind turbine with a cut-in wind speed of 4 m/s, a rated wind

speed of 14 m/s, and a cut-out wind speed of 26 m/s. If the wind speed

satisfies a Weibull distribution with the shape parameter k=2, and an

average speed of 10 m/s.

a)For how many hours per year will the turbine be shut down because of

excessively high- speed winds?

b) For how many hours per year the turbine has no power output because

the wind speed is lower than the cut-in speed?

c)If this is a 1.5-MW turbine, how much energy (kWh/yr) would be

produced for winds blowing above the rated wind speed?

d)This wind turbine is used for a pumped storage system; i.e., pumping

water from a lake to a pond at an elevation of 200m above. Assume the

pump has 75% efficiency and the pond is 5000 big. Find the change in

height of the water level in the pond if the turbine keeps working at its rate

power for one day.

5. A small-scale wind turbine with the rotor diameter 1.5m uses a 500-Watt

DC motor as a generator.

a) Find the capacity factor for the machine if it delivers 100 kWh in a 30-

day month.

b) Under the standard condition of 15∘

� temperature and 1 atm pressure,

how fast

would the wind have to blow for the turbine to generate half of its rate

power if the

machine is 30% efficient at that point?

c) If the tip-speed-ratio (TSR) is 6, find the gear ratio if the generator

needs to turn at

1110 rpm to deliver 0.25kW at the wind speed obtained in question (b).

d) Suppose the turbine is deployed in a new environment of 70∘

� and 1.5

atm. Repeat

(b) and (c).