Presets
Playback
Lamp, module and load
Turn the load from a short circuit to an open circuit and the operating point slides along the curve; the maximum power sits at the knee.
Load sweep
Model checks
The science
What is modelled
A photovoltaic module is modelled as a current source (photocurrent proportional to light) in parallel with a diode and a shunt resistance, followed by a series resistance. A resistive load fixes the operating point where the load line V = I R crosses the module curve; the maximum power point is the knee of that curve.
Equations
- One-diode model
I = Iph - I0 (e(V + I Rs)/a - 1) - (V + I Rs)/Rsh,a = n N k T / q. - Photocurrent
Iph ∝ G cosθ (1 + α(T - Tref)); saturation currentI0 ∝ T3 exp(-q Eg/(n k T))relative to 25 C. - Fill factor
FF = Pmax / (Isc Voc), efficiencyη = Pmax / (G A). - Temperature drift
dVoc/dT ≈ (Voc - 3a - N Eg/q) / T.
Checks run in the page
- The diode equation solved by library bisection and by an independent Newton iteration.
- Open-circuit voltage satisfies its own closed form.
- Golden-section maximum power point against a brute-force scan.
- dVoc/dT against the analytic estimate.
Honest simplifications
A single-diode, lumped model with illustrative parameters: no second diode, no reverse breakdown, no partial shading or bypass diodes, no spectral response, and the cell temperature is set by hand instead of from a heat balance. Tilt only reduces irradiance by the cosine, without reflection losses at large angles.
What to try
- Press Sweep the load and watch the orange points trace the whole curve from Isc to Voc.
- Choose Hot module: the current barely changes but the voltage and the power fall.
- Choose Poor module: the knee rounds off and the fill factor drops.