Question

An investor is to install a total of 40 identical wind turbines in a location with an average wind speed of 7.2 m/s. The blade diameter of each turbine is 18 m and the average overall wind turbine 5-28 efficiency is 33 percent. The turbines are expected to operate under these average conditions 6000 h per year and the electricity is to be sold to local utility at a price of $0.075/kWh. If the total cost of this installation is $1,200,000, determine how long it will take for these turbines to pay for themselves. Take the density of air to be 1.18 kg/m

Answer 1

Answer:

$\Delta t = 25.957\,years$

Explanation:

The annual energy production of the wind park is:

$W_{el} = \eta_{el} \cdot n_{turb}\cdot \frac{1}{2}\cdot \rho_{air}\cdot (\frac{\pi}{4}\cdot D^{2})\cdot \overline v_{wind}^{2} \cdot \Delta t$

$W_{el} = (0.33)\cdot (40) \cdot \frac{1}{2} \cdot (1.18\,\frac{kg}{m^{3}})\cdot [\frac{\pi}{4}\cdot (18\,m)^{2}}] \cdot (7.2\,\frac{m}{s} )^{2}\cdot (6000\,h)\cdot (\frac{3600\,s}{1\,h} )$

$W_{el} = 2.219\times 10^{12}\,J$

$W_{el} = (2.219\times 10^{12}\,J)\cdot (\frac{1\,kWh}{3.6\times 10^{6}\,J} )$

$W_{el} = 616388.889\,kWh$

Amount of money derived of the sell of the electricity to local utility is:

$C_{year} = c\cdot W_{el}$

$C_{year} = (0.075\,\frac{USD}{kWh} )\cdot (616388.889\,kWh)$

$C_{year} = 46229.167\,USD$

The payback time is:

$\Delta t = \frac{1200000\,USD}{46229.167\,USD}$

$\Delta t = 25.957\,years$