Time 12:00Sun 0°Sunlight 0 W/m²Array 0 kWBattery 0 %

Solar Panel to Home Battery — 2D Cross-Section and I-V Plane

The flat companion of the 3D cut-away. Cross-section: photons, electron-hole pairs and energy bands. I-V plane: the curves with the maximum power point. Same physics module as the 3D version.

Switch to 3D

Time and place

Panel and weather

House and battery

Live readouts (one module unless noted)

The day: power in kW

Battery state of charge, %

Experiments

Each button simulates whole days or a measured curve with the current settings and compares it with theory.

Independent numerical checks

What the picture shows

Cross-section (top or left): layer thickness is exaggerated about 10 times. Coloured dots are photons; those with wavelength above about 1100 nm cannot lift an electron across the silicon gap and pass out of the back as heat. Short wavelengths are absorbed near the top, long ones deeper.
Blue dots are electrons, orange are holes; the junction field sweeps electrons up into the n layer and holes down into the p layer. Their rate follows the real photocurrent.
Band strip: conduction and valence band edges across the junction. The built-in potential (about 0.7 V per cell) is illustrative; the operating voltage lowers the barrier, which is why current falls as voltage rises.
I-V plane: blue = current, orange = power, dashed = the module at standard test conditions. White dot = maximum power point, green dot = where the inverter holds the array now.
Sliders act at once. "Tracker: MPPT" lets the inverter find the maximum power point; switch it off to hold a fixed fraction of Voc.

The science

Photon to electron. A photon has energy E = hc/λ. Above the silicon band gap (1.12 eV, wavelength below about 1100 nm) it lifts an electron across the gap and leaves a hole; the excess energy becomes heat. The p-n junction field separates the pair, so the cell is a current source with photocurrent I_ph ∝ G.

Single-diode model. I = I_ph − I₀(e^{(V+I R_s)/a} − 1) − (V+I R_s)/R_sh, a = n N_s kT/q (n = 1.1, 60 cells). It is solved in closed form with the Lambert W function and checked against bisection below. I₀ is fixed from datasheet-style STC values (I_sc 9.8 A, V_oc 38.4 V; illustrative numbers, not a specific product) and scales with temperature through the band gap; V_oc drops about 0.1 V per 10 K.

Sun and sky. Declination δ = 23.45° sin(360(284+n)/365), cos θ_z = sin φ sin δ + cos φ cos δ cos ω; clear-sky global irradiance by Haurwitz 1098 cos θ_z e^{−0.057/cos θ_z}, cloud factor 1 − 0.75 c^3.4, beam/diffuse split by the Erbs correlation, isotropic sky plus 20 % ground reflection on the tilted plane. Cell temperature T_c = T_a + (NOCT − 20)/800 · G.

System. Inverter 96 % efficient, clipping at 1/1.15 of the array rating; surplus charges the battery (92 % round trip, 10 to 100 % window, power limit), then the grid; a deficit comes from the battery, then the grid. The energy ledger closes to machine precision (check below).

Simplifications. Identical modules, no mismatch or wiring loss, no spectral or angle-of-incidence effects, no ageing; the dirt slider is a uniform photocurrent loss (real partial shade is non-linear). The band strip and photon paths are schematic diagrams, not simulations of carrier transport. Spot-check: Haurwitz, Erbs and Kasten-Czeplak coefficients, NOCT formula, the Voc temperature slope against a datasheet.