Presets
Playback
Site and array
Latitude, date, panel tilt and size.
Weather
Clearness index and how long dull spells last.
Loads
Hours of use per day. Fixed loads are the toggle buttons.
Battery
Capacity, allowed depth of discharge and starting charge.
Playback
Layers
Model checks
The science
What this models
An off-grid power system for a small apiary: a PV array charges a battery through an MPPT controller; an inverter feeds the honey-house loads, the electric fence and the hive monitors. Every hour of the run is stepped: solar geometry, irradiance on the tilted plane, cell temperature, array output, battery state of charge, and any load that cannot be served.
Solar geometry and irradiance
Declination d = 23.45 sin(360 (284+n)/365), sunset hour angle cos ws = -tan(phi) tan(d). Extra-terrestrial energy on a horizontal plane: H0 = (24/pi) Gsc E0 (cos phi cos d sin ws + ws sin phi sin d). Daily global H = Kt H0 (Kt is the clearness index). The hourly split uses Collares-Pereira and Rabl; the diffuse share comes from the Erbs correlation; the tilted plane uses the Liu-Jordan isotropic-sky model: I_T = I_b R_b + I_d (1+cos b)/2 + I rho (1-cos b)/2, with R_b = cos(theta)/cos(theta_z).
Array and battery
Array power P = Wp (I_T / 1 kW/m2) [1 - 0.004 (Tcell - 25)] PR eta_MPPT (1 - soiling) with Tcell = Tair + (NOCT-20)/800 I_T (NOCT 45 C). Battery: usable energy C x DoD; charge and discharge each lose sqrt(eta_roundtrip); the controller disconnects the load at the DoD floor. Autonomy of a full battery with no sun: days = C DoD sqrt(eta) / (L/eta_inv). Rules of thumb shown in the readouts: panel size Wp = L / (PSH PR) for a mean-day balance and battery size C = L N_aut / (DoD sqrt(eta)).
Weather
Daily clearness index follows a clipped AR(1) series around the mean Kt: persistence makes dull days cluster, which is what empties real batteries. The seed button draws a new sequence. This is a statistical stand-in, not a measured weather record.
Honest simplifications
- Isotropic sky (underestimates circumsolar and horizon-brightening diffuse); fixed equator-facing array; no snow, no partial shading beyond the dirt/shading slider; no inverter standby loss; battery has no temperature, rate or ageing effects (a real lead-acid bank loses life when cycled deeply, which is why the default DoD is 50 %).
- Load windows are fixed times of day; real use varies. Ambient temperature is a sine around the mean you set.
- For a real installation, use measured irradiation (for example PVGIS) and manufacturer data, and have a qualified electrician certify the wiring.
Checks run in the page
(1) The closed-form H0 against a numerical integral of the sun's cosine over the day, and the hourly split against Kt H0. (2) Battery autonomy: simulated delivered energy and cut-off hour against the closed form. (3) Energy balance of the battery over the whole run.
What to try
- Choose UK December: low sun, then Flat panel: tilt matters most when the sun is low. Press Set best tilt and watch the yield curve and the unmet load.
- Choose Dull spell, small battery. Raise the spell persistence and see the charge fall to the red cut-off line; then double the battery in the design chart (graph 4) versus adding panels.
- Press Size panels for 99 % and compare the result with the rule-of-thumb readout "Wp for mean-day balance".
- Turn the fence and monitors off and see how much of the daily load they are (about 240 Wh) compared with one hour of the extractor.