Question 6.19: Price of Electricity from a Wind Farm. A wind farm project h......
Price of Electricity from a Wind Farm. A wind farm project has 40 1500-kW turbines with 64-m blades. Capital costs are $60 million and the levelized O&M cost is $1.8 million/yr. The project will be financed with a $45 million, 20-yr loan at 7% plus an equity investment of $15 million that needs a 15% return. Turbines are exposed to Rayleigh winds averaging 8.5 m/s. What levelized price would the electricity have to sell for to make the project viable?
We can estimate the annual energy that will be delivered by starting with the capacity factor, (6.65):
CF \ = \ 0.087 \bar{V} \ – \ \frac{P_{R}}{D^{2}} \quad \left(\text{Rayleigh winds}\right) (6.65)
CF \ = \ 0.087 \bar{V} \ \left({m}/{s}\right) \ – \ \frac{P_{R}\left(kW\right)}{\left[D\left(m\right)\right]^{2}} \ = \ 0.087 \ \times \ 8.5 \ – \ \frac{1500}{64^{2}} \ = \ 0.373For 40 such turbines, the annual electrical production will be
The debt payments will be
The annual return on equity needs to be
\text{Equity} \ = \ {0.15}/{yr} \ \times \ \$ 15,000,000 \ = \ \$ 2.25 \ \times \ {10^{6}}/{yr}The levelized O&M cost is $1.8 million, so the total for O&M, debt, and equity is
\text{Annual cost} \ = \ \$\left(4.24 \ + \ 2.25 \ + \ 1.8\right) \ \times \ 10^{6} \ = \ \$ 8.29 \ \times \ {10^{6}}/{yr}The levelized price at which electricity needs to be sold is therefore
\text{Selling price} \ = \ \frac{\$ 8.29 \ \times \ {10^{6}}/{yr}}{196 \ \times \ 10^{6} \ {kWh}/{yr}} \ = \ \$ 0.0423 \ = \ {4.23\cancel{c}}/{kWh}