Q1. Wind Turbine
As a consultancy you have been asked to compare the performance of a wind turbine power plant of 12 MW name plate capacity and a combined cycle gas turbine of the same size for the local energy mix in Victoria at a given location. Both power plants are used to provide power to the grid at times of peak demand.
In the following the turbines specifications and wind resources are given, together with financial parameters and CO2 emission considerations.
Wind turbine: rated power output 2MW (6 turbines are installed), Specific rated capacity 0.31438kW/m2, annual capacity factor estimated 36% at 80m hub height. The power curve is the following:
wind Power output speed m/s (kW) 0 0 1 0 2 0 3 21 4 85 5 197 6 364 7 595 8 901 9 1275 10 1649 11 1899 12 1971 13 1991 14 1998 15 2000 16 2000 17 2000 18 2000 19 2000 20 2000 21 2000 22 1906 23 1681 24 1455 25 1230 26 0
Wind resources: wind site average wind power density estimated over one year is 800 W/m2 at 50 m. Terrain roughness length z0=0.02 m. Use density of air =1.225 kg/m3.
Gas turbine: rated power 12 MW, annual capacity factor of 60%, efficiency 50%.
Cost of gas is 2.6 $/MMBTU (1BTU=1055 J, 1MMBTU=106 BTU).
Greenhouse emission factor for gas is 57.2 kg CO2-e / GJ.
Capital cost of the wind turbine is $ 1470/kW, Annual O&M is 5% of the capital cost, while the salvage value at the end of the project is 10% of the capital cost.
Capital cost of the gas turbine $1010/kW, Annual O&M is 5% of the capital cost, while the salvage value at the end of the project is 10% of the capital cost.
Assume that both plants life is of 20 years life. The discount rate is assumed to be 5%. The electricity is sold at 20 c/kWh.
Performance questions on both plants.
1. Determine the annual energy produced by the two plants in MWh.
2. Determine the two power plants average power in MW.
3. Determine the two plants full load hours.
Performance questions on the wind turbine.
4. Determine the proportion of wind energy captured by a single wind turbine %
5. Determine the coefficient of performance of the turbine at wind speed 9 m/s %
6. Determine the rated wind speed velocity of the turbine, m/s
Financial and emission questions.
7. Determine the annual amount of cost of fuel for the gas turbine plant in $.
8. Determine the annual income from selling the electricity of both plants.
9. Determine the simple payback period for the wind farm (consider the annual income).
10. Determined the discounted payback period for the wind farm.
11 Determine the present worth of the wind farm.
12. Determine the annual worth of the wind farm.
13. Determine the cost of electricity for wind farm (answer in cents/kWh)
14. Determine the cost of electricity for gas turbine (answer in cents/kWh)
15. Determine the saving in CO2 emission in tons when replacing the gas turbine power plant by the wind farm.
Q2: Solar Energy
An energy company hires an engineer to size a solar PV roof top system off-grid in Adelaide (34.9285° S, 138.6007° E, GMT+9.30) to supply a household daily average energy demand of 15 kWh/day, assumed constant during the year. The sun irradiations at summer solstice, winter solstice and at the equinoxes and the average temperatures during the year are given in Table 1.
Additionally, a solar water heater needs to be designed to keep a pool of 7 (length)x4(width) x1(depth)m not below 25 ◦C all year around (recall that 1 m3=1000 L).
Table. 1 Summary of irradiation in Adelaide and temperature obtained from 20 years data average.
The following systems specifications are chosen.
Modules of rated power in standard conditions (1 kW/m2, 25◦C operating temperature, AM1.5) of 250W each are chosen. The width of each module is 992 mm and length 1650 mm.
The temperature power reduction of the modules is –0.47%/ºC of difference from the module temperature
(consider Tmodule = Tambient + 25ºC), while other causes of power derating in the final PV system provide a total power derating factor of 0.72.
The solar water heater specifications efficiency is =0.77-0.6×(Ti-Tamb)/G. The inlet temperature Ti in winter is assumed 19◦ C.
Determine:
1. The design month/day of both PV and water heater systems and the PSH, choose if tilted at latitude angle or on horizontal plane, justify the choice.
2. The length of the day of the design month (either Summer solstice, winter solstice or Equinox)
3. The altitude of the Sun at solar noon at design day
4. The standard time at solar noon of the design day (neglect EoT and day light savings)
5. The average irradiance from the sun on the design month/day as in 2.
PV system
6. The total capacity of the PV system (number of modules) as per power installed given the energy
demand.
7. The annual capacity factor of the PV system (consider the Annual energy production based on annual average PSH and total derating factor as calculated in 6. )
8. The efficiency of the PV system at operating conditions for the design month/day as above. (tip: efficiency=rated power/power from the sun, consider the rated power reduced by the temperature derating factor and as power from the sun the average irradiance).
9. Assume the PV system costs $1.4/W, the annual maintenance cost is 5% of the capital cost, the discount rate is 5% and 20 years life, determine the cost of the electricity produced by the PV system
(consider the annual costs including the capital recovery cost)
10. Assume that you have 7 PV panels each of 4 modules for a total length of each panel of L=1.65 m. The panels are titled at latitude angle and facing north. Which is the minimum distance (Y in the figure 1) from one panel to another you need to avoid shading during all year? (Consider sun position at winter solstice at 10 am, read altitude and azimuth on the Sun Chart.
Figure 1 Lay out of 2 exemplary panels.
11. Calculate the altitude and azimuth angles of the point A and B on the panel with respect to point
O.
Point
Altitude
Azimuth (from North)
A
B
12. Draw the altitude and azimuth angles of the points A and B on the panel with respect to point O
on the Sun chart of Adelaide below at design day at solar noon.
Solar water heater System
13. What is the efficiency of the solar water system at the design day? (tip: determine the average irradiance from irradiation at design day and the length of the day and consider the ambient temperature the mean)
14. What is the total area of the collectors required to satisfy the need of having the swimming pool always at least at 25◦ C? Given that each collector is about 3 m2, how many collectors are needed?
