Presets
Playback
Wind, sun, equipment
Independent checks
The science
Wind speed distribution
Hourly hub-height wind follows a Weibull law, f(v) = (k/c)(v/c)k-1 exp(-(v/c)k), with mean c Γ(1 + 1/k). The series is a correlated Gaussian process (hour-to-hour correlation ρ) mapped through the Weibull inverse CDF, so the histogram is right and the gusts persist like weather does.
Power curve and capacity factor
Below cut-in (3 m/s) a turbine gives nothing; between cut-in and rated speed (12 m/s) the cubic law P ∝ v3 applies, normalised to rated power; above that pitch control holds the power flat until cut-out at 25 m/s. Rated power is ½ ρ (π D2/4) vr3 Cp with Cp = 0.45, below the Betz limit 16/27. The capacity factor CF = ∫ P(v)/Pr f(v) dv is integrated with Simpson's rule and compared with a 20-year hourly sample.
Sun, demand and battery
Solar declination δ = 23.44° sin(2π(284+n)/365), elevation sin β = sin φ sin δ + cos φ cos δ cos h, clear-sky irradiance (Haurwitz) G = 1098 sinβ exp(-0.059/sinβ) scaled by a random clearness index, and PV output = peak power x G/1000 x 0.82. Demand has a daily double peak, a weekend dip and persistent noise. Surplus charges the battery (limited by power and free space), a deficit discharges it, the rest is served by gas; surplus beyond that is curtailed. The round-trip efficiency is split equally between charging and discharging.
Honest simplifications: a synthetic weather week, not measured data; one hub-height wind speed for all turbines (no wake losses); no grid transmission limits, forecast errors, ramp rates, battery ageing or prices; the gas plant is unlimited; the 'long run' capacity factor assumes the Weibull parameters you set stay fixed. Educational model, not a planning tool.