1. (15 points) A PV system covers 20 m2 and has an average insolation of 280 W/m2; it is assumed to return 10% of this value in electricity. The system cost is $20,000 up front and displaces electricity at 0.10/kW-hr. There is no salvage value. If the investment lifetime is 25 years and the MARR is 6%, what is the NPV of a system (a) if the price of electricity in constant dollars remains the same, (b) if the price of electricity increases on average by 3% per year due to rising fossil fuel costs, constraints on grid electric supply, and the like?
6. A rudimentary Solar Electric Generating Station (SEGS) system consists of 2500 heliostats, each of 10 m2, focusing on a central tower. The tower-heliostat system is able to transfer 50% of the incoming solar energy to incoming water, which then boils and is transferred to the turbine. Ignore other losses between the heliostats and expansion in the turbine. The plant averages 10 h/day of operation year round, and during that time the incoming sun averages 400 W/m2. Ignore losses of insolation due to the heliostats not facing in a normal direction to the sun. Before entering the tower, the water is compressed to 20 MPa. In the tower it is then heated to 700°C. The superheated steam is then expanded through the turbine using a basic Rankine cycle, and condensed at 33°C. Assume that the actual efficiency achieved by this cycle is 85% of the ideal efficiency. The generator is 98% efficient. What is the annual electric output in kWh/year?
7. The cost of the facility in the previous problem is $15 million (assuming that mass production has brought the cost down from the current cost of such experimental facilities), and it has an expected life of 25 years with no salvage value. If the MARR is 5%, what is the levelized cost of electricity from the system in $/kWh? Ignore the portion of electricity used onsite (also known as parasitic loads), and ignore maintenance and other costs.
1. The following wind measurements by bin are given for a proposed wind turbine location. Assume the air has a density of 1.15 kg/ m3.
2.
|
Wind Speed(m/s)
|
|
|
Bin
|
Minimum
|
Maximum
|
Hours/year
|
|
1
|
0.0
|
0.0
|
|
|
2
|
0.0
|
1.0
|
200
|
|
3
|
1.0
|
2.0
|
501
|
|
4
|
2.0
|
3.1
|
850
|
|
5
|
3.1
|
4.1
|
1300
|
|
6
|
4.1
|
5.2
|
1407
|
|
7
|
5.2
|
6.2
|
1351
|
|
8
|
6.2
|
7.2
|
990
|
|
9
|
7.2
|
8.2
|
641
|
|
10
|
8.2
|
9.3
|
480
|
|
11
|
9.3
|
10.3
|
375
|
|
12
|
10.3
|
11.3
|
291
|
|
13
|
11.3
|
12.3
|
180
|
|
14
|
12.3
|
13.4
|
78
|
|
15
|
13.4
|
14.4
|
32
|
|
16
|
14.4
|
And above
|
4
|
a. Calculate the total estimated energy available in the wind from the bin data, in kWh/m2. For bin 16, assume an average wind speed of 16 m/s.
b. Calculate the estimated energy available in the wind using the average wind speed and the Rayleigh function. For bin 16, assume an average wind speed of 16 m/s.
c. Calculate the estimated energy using the method of FAT (13-10) in the chapter.
d. Calculate the error between the actual value from (a) and the estimated values from (b) and from (c).
e. Plot both estimated and actual curves on a single graph, with hours per year as a function of bin number.
11. Suppose the 10-kW turbine from Problem 4 is installed in a remote location to provide off¬the-grid power. Including battery and thermal storage system, the cost is $70,000. If the system lasts for 25 years and the MARR is 6%, what is the levelized cost per kWh? You can assume all electricity produced is equally valuable, whether it is consumed in electrical applications or goes into battery or thermal storage.