Energy yield and 20 MW grid cap for a 25.2 MW wind farm
A 25.2 MW onshore wind farm is planned with twelve 2.1 MW turbines at 110 m hub height. The consultant's table of hub-height wind-speed bins with average turbine output is: 0–4 m/s, 1,200 h, 0 kW; 4–6 m/s, 2,100 h, 350 kW; 6–8 m/s, 2,400 h, 950 kW; 8–10 m/s, 1,600 h, 1,650 kW; 10–12 m/s, 900 h, 2,100 kW; 12–25 m/s, 560 h, 2,100 kW. The power curve was measured at the standard air density of 1.225 kg/m³, but the site's annual mean density at hub height is 1.10 kg/m³. Wake modelling gives an 8% energy loss and technical availability is 96%. The grid connection is limited to 20 MW export, and the evacuation line cannot be upgraded within the project's timeline. The developer's information memorandum quotes 'over 100 GWh per year net' and the lender requires a P50 estimate before sanction.
1. Compute the gross and net annual energy and the net capacity factor, and assess the 100 GWh claim.
Read the worked answer
Air-density ratio = 1.10/1.225 = 0.898. Apply it only in the partial-load bins, because a turbine at rated power is pitch-regulated and cannot exceed 2.1 MW.
Per-turbine gross energy:
- 4–6 m/s: 350 × 0.898 = 314.3 kW × 2,100 h = 0.660 GWh
- 6–8 m/s: 950 × 0.898 = 853.1 kW × 2,400 h = 2.047 GWh
- 8–10 m/s: 1,650 × 0.898 = 1,481.7 kW × 1,600 h = 2.371 GWh
- 10–12 m/s: 2,100 kW × 900 h = 1.890 GWh
- 12–25 m/s: 2,100 kW × 560 h = 1.176 GWh
Gross = 8.144 GWh per turbine; gross CF = 8.144/18.396 = 44.3% (high, so the table should be audited). Net = 8.144 × 0.92 × 0.96 = 7.193 GWh; net CF = 39.1%. Farm net = 12 × 7.193 = 86.3 GWh/yr.
The memorandum overstates net production by about 14 GWh (16%). Lenders should be given a P50 near 86 GWh, and the P90 will sit materially below it given the wake and availability assumptions.
2. Explain why the density correction is applied only to the partial-load bins and quantify the error if it were applied to every bin.
Read the worked answer
Below rated wind speed the turbine operates on a fixed Cp curve, so captured power scales with air mass flow, i.e. with density: P proportional to 0.5 rho A v³ Cp. Above rated speed the controller pitches the blades to hold 2.1 MW whatever the density, so no correction applies.
Applying 0.898 to the rated bins would wrongly delete 10.2% of 1.890 + 1.176 = 3.066 GWh, i.e. 0.313 GWh per turbine per year (about 3.8% of gross). Over the farm that is roughly 3.8 GWh/yr of phantom loss - enough on its own to make a marginal project look unbankable.
There is a second-order point worth flagging: low density also delays the wind speed at which rated power is first reached, by a factor of (1/0.898)^(1/3) = 1.036, i.e. about 3.6%. With coarse bins this shifts a small amount of energy from the 8–10 m/s bin into 10–12 m/s and is conservative for the developer, but it means the binned table understates production slightly rather than overstating it.
3. Quantify the curtailment loss imposed by the 20 MW export limit and advise the developer.
Read the worked answer
The farm reaches rated output only in the two highest bins, totalling 900 + 560 = 1,460 h/yr.
Nameplate in those hours is 12 × 2.1 = 25.2 MW, but the physically expected output is 25.2 × 0.92 × 0.96 = 22.26 MW. With a 20 MW cap, spill = 2.26 MW × 1,460 h = 3.30 GWh/yr, about 3.8% of the 86.3 GWh net estimate.
A naive calculation that ignores wake and availability would quote (25.2 − 20) × 1,460 = 7.6 GWh, roughly double the true loss. The 3.3 GWh figure is the one to use in the lender case.
Judgement: 3.3 GWh/yr at, say, ₹5/kWh is about ₹1.65 crore per year of foregone revenue - significant but far cheaper than upgrading a 33 kV line. The right actions are (i) a deemed-generation or curtailment-compensation clause in the PPA, (ii) an active power set-point controller that spills across all turbines rather than tripping one machine, and (iii) accepting the 20 MW connection, since the incremental 2.3 MW of expected peak output operates for only 1,460 h/yr.