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Question 6.18: A Loan to Pay for a Small Wind Turbine. Suppose that a 900-W......

A Loan to Pay for a Small Wind Turbine. Suppose that a 900-W Whisper H900 wind turbine with 7-ft diameter (2.13 m) blade costs $1600. By the time the system is installed and operational, it costs a total of $2500, which is to be paid for with a 15-yr, 7 percent loan. Assuming O&M costs of $100/yr, estimate the cost per kWhr over the 15-year period if average windspeed at hub height is 15 mph (6.7 m/s).

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The capital recovery factor for a 7%, 15-yr loan would be

CRF\left(0.07, \ 15 \ yr\right) \ = \ \frac{i\left(1 \ + \ i\right)^{n}}{\left(1 \ + \ i\right)^{n} \ – \ 1} \ = \ \frac{0.07\left(1 \ + \ 0.07\right)^{15}}{\left(1 \ + \ 0.07\right)^{15} \ – \ 1} \ = \ {0.1098}/{yr}

which agrees with Table 5.5. So, the annual payments on the loan would be

A \ = \ P \ \times \ CRF\left(0.07, \ 15\right) \ = \ \$ 2500 \ \times \ {0.1098}/{yr} \ = \ {\$ 274.49}/{yr}

The annual cost, including $100/yr of O&M, is therefore $274.49 + $100 = $374.49.

To estimate energy delivered by this machine in 6.7-m/s average wind, let us use the capacity factor approach (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} \ – \ \frac{P_{R}\left(kW\right)}{D^{2}\left(m^{2}\right)} \ = \ 0.087 \ \times \ 6.7 \ – \ \frac{0.90}{2.13^{2}} \ = \ 0.385

The annual energy delivered (6.59)

\text{Annual energy} \ \left({kWh}/{yr}\right) \ = \ P_{R} \ \left(kW\right) \ \times \ 8760 \ \left({h}/{yr}\right) \ \times \ CF (6.59)

{kWh}/{yr} \ = \ 0.90 \ kW \ \times \ 8760 \ {h}/{yr} \ \times \ 0.385 \ = \ 3035 \ {kWh}/{yr}

The average cost per kWh is therefore

\text{Average cost} \ = \ \frac{\text{Annual cost} \ \left({\$}/{yr}\right)}{\text{Annual energy} \ \left({kWh}/{yr}\right)} \ = \ \frac{{\$ 374.49}/{yr}}{3035 \ {kWh}/{yr}} \ = \ {\$ 0.123}/{kWh}

That’s a pretty good price of electricity for a small system—cheaper than grid electricity in many areas and certainly cheaper than any other off-grid, home-size generating system.

TABLE 5.5 Capital Recovery Factors as a Function of Interest Rate and Loan
Term
Years 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13%
 5 0.2184 0.2246 0.2310 0.2374 0.2439 0.2505 0.2571 0.2638 0.2706 0.2774 0.2843
10 0.1172 0.1233 0.1295 0.1359 0.1424 0.1490 0.1558 0.1627 0.1698 0.1770 0.1843
15 0.0838 0.0899 0.0963 0.1030 0.1098 0.1168 0.1241 0.1315 0.1391 0.1468 0.1547
20 0.0672 0.0736 0.0802 0.0872 0.0944 0.1019 0.1095 0.1175 0.1256 0.1339 0.1424
25 0.0574 0.0640 0.0710 0.0782 0.0858 0.0937 0.1018 0.1102 0.1187 0.1275 0.1364
30 0.0510 0.0578 0.0651 0.0726 0.0806 0.0888 0.0973 0.1061 0.1150 0.1241 0.1334

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