A Wind Turbine for a School
A school considers a 10 kW rated wind turbine. Local wind data show an average wind speed of 5.5 m/s at hub height. The turbine's power curve gives 1.2 kW at 5 m/s and 2.0 kW at 6 m/s. Capacity factor at this site is estimated at 22%. The school uses 45,000 kWh per year. The turbine costs $38,000 installed with a 20-year life and $1,500/year maintenance. The grid pays $0.11/kWh for exported power, and the school buys grid power at $0.16/kWh. A neighbour objects that the turbine will be noisy and will not pay back.
1. Estimate the turbine's annual energy output and the fraction of the school's demand it meets.
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Annual output using capacity factor:
Energy = rated power × hours per year × capacity factor = 10 kW × 8,760 h × 0.22 = 19,272 kWh/year, about 19,300 kWh.
Fraction of school demand: 19,272 ÷ 45,000 = 0.428, about 43%.
Cross-check with the power curve: at 5.5 m/s the turbine sits between 1.2 kW and 2.0 kW, roughly 1.6 kW instantaneous. If the wind blew at 5.5 m/s constantly, that would give 1.6 × 8,760 = 14,016 kWh. The capacity-factor estimate is higher because wind speeds vary and output rises steeply with speed, so gusty periods contribute disproportionately. The two estimates bracket the likely output; a realistic range is roughly 14,000–19,000 kWh per year, or 31–43% of demand. The school should treat 43% as an optimistic case and 31% as conservative.
2. Assess the economics and address the neighbour's payback objection.
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Value of output. If the school self-consumes most of the power, each kWh displaces $0.16 of grid purchase. At 19,272 kWh:
- Savings: 19,272 × 0.16 = $3,083/year.
- Net of maintenance: $3,083 − $1,500 = $1,583/year.
- Simple payback: $38,000 ÷ $1,583 ≈ 24 years.
That exceeds the 20-year life, so at the optimistic output the project does not pay back. At the conservative 14,000 kWh:
- Savings: 14,000 × 0.16 = $2,240; net $740/year; payback ≈ 51 years.
Conclusion: the neighbour's payback objection is correct on these numbers. The project only becomes viable with a capital grant, a higher capacity factor, or a lower installed cost.
Noise: the neighbour's concern is legitimate and should be checked against the manufacturer's sound-power level and the distance to the property line, not dismissed. A siting setback and a noise specification should be part of any revised proposal.