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

`\Delta t = 25.957\,years`

Step-by-step explanation:

The annual energy production of the wind park is:

`W_(el) = \eta_(el) \cdot n_(turb)\cdot (1)/(2)\cdot \rho_(air)\cdot ((\pi)/(4)\cdot D^(2))\cdot \overline v_(wind)^(2) \cdot \Delta t`

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

`W_(el) = 2.219* 10^(12)\,J`

`W_(el) = (2.219* 10^(12)\,J)\cdot ((1\,kWh)/(3.6* 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\,(USD)/(kWh) )\cdot (616388.889\,kWh)`

`C_(year) = 46229.167\,USD`

The payback time is:

`\Delta t = (1200000\,USD)/(46229.167\,USD)`

`\Delta t = 25.957\,years`