Clock 12:00Sun 0°Cloud over array 0 %GHI 0 W/m²PV AC 0 kWGrid 0 kWBattery 0 kW · SOC 50 %Ramp 1 min 0 kWFPS 0

Drag to orbit, wheel or pinch to zoom. Dark patches on the ground and on the panels are cloud shadows; yellow dots show sunlight and current, green dots the power sent to the grid. Illustrative 2 MWp plant.

Cloud Passage Lab: PV Power Ramps and Battery Smoothing

When a cloud edge crosses a solar field, output can fall by more than half in a minute. How big is that ramp, and how much battery does it take to hide it from the grid?

Clouds

Site and panels

Battery

Time

Live readouts

Irradiance: clear sky, array, single sensor

PV, grid and battery power

Experiments

Each button simulates whole days headless (04:00 to 22:00) with the current settings and tabulates the result.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; five camera presets (Module layers shows the exploded cell stack).
Sliders act at once. "Time of day" jumps the clock; the cloud pattern is advected by the wind, so the same day can be replayed with different speeds.
Battery ON: the grid ramp is limited to the chosen percent of inverter rating per minute; the battery absorbs or supplies the difference until its power or energy limit is hit.
Time scale = simulated seconds per real second.

The science

Sun and clear sky. Declination δ = 23.45° sin(360(284+n)/365), hour angle ω = 15°(h − 12), cos θ_z = sin φ sin δ + cos φ cos δ cos ω. Clear-sky global horizontal irradiance (Haurwitz): GHI_cs = 1098 cos θ_z exp(−0.057 / cos θ_z) W/m².

Clouds. A moving value-noise field gives a local cloud fraction N (0 to 1) for each of ten 30 m wide sections; the whole pattern is advected at wind speed u. Clear-sky index (Kasten–Czeplak form, kt = 1 − 0.75 N^3.4) gives GHI = kt · GHI_cs; the diffuse fraction follows the Erbs correlation. Both are empirical fits [перевірити за джерелом]. Shadow edges are shifted by the cloud height over tan(elevation), the same offset used to draw the clouds.

Plane of array and power. POA = beam · R_b + diffuse · (1 + cos β)/2 + albedo · GHI · (1 − cos β)/2 with the Duffie–Beckman incidence angle. Cell temperature T_c = T_amb + (NOCT − 20)/800 · G (NOCT = 45 °C), DC power P = P_STC (G/1000)(1 + γ(T_c − 25)), γ = −0.35 %/K, inverter efficiency 0.97 and AC limit P_STC/1.25 (clipping).

Battery ramp limiter. Grid power follows PV but may change by at most R per minute: P_g ← clamp(P_pv, P_g − R dt, P_g + R dt); the battery takes P_b = P_pv − P_g within its power rating and 10–95 % state of charge, with one-way efficiency √0.9. Ledger: E_pv − E_grid = ΔE_stored + E_loss.

Simplifications: a single plane-of-array model per section, no spectral or angle-of-incidence losses, no soiling or wiring loss, cloud field is a texture-like noise, not real cloud physics, ambient temperature is a fixed daily cosine, no battery degradation, and the grid-code ramp value is illustrative. Assets built with Blender; scene by Three.js.