41 voltages and a parabola

Method

The power is read at 41 voltages from 0 V to the open-circuit voltage, 40 equal steps apart (1). The voltage of the largest power and its two neighbours give a parabola (2, 3). The maximum-power point is the curve's point at the voltage of the parabola's vertex (4). Its power lies up to 0.01 % below the curve's maximum. A module rated 540 W with the datasheet point 31.2 V and 17.33 A has 540.67 W at standard test conditions, where the curve's maximum is 540.70 W.

The math

1. The voltages
2. The voltage of the largest power
3. The parabola's vertex
4. The maximum-power point

$$V_{m,k} = k\,\frac{V_{oc}}{40},\qquad P_k = V_{m,k}\,I_m(V_{m,k}),\qquad k = 0, 1, \ldots, 40 \tag{1}$$ $$k^* = \arg\max_{1 \le k \le 39} P_k \tag{2}$$ $$V_m^* = V_{m,k^*} + \frac{V_{oc}}{80}\,\frac{P_{k^*+1} - P_{k^*-1}}{2P_{k^*} - P_{k^*-1} - P_{k^*+1}} \tag{3}$$ $$P_{mpp} = V_m^*\,I_m(V_m^*) \tag{4}$$

where

Symbol	Meaning	Unit
$V_{oc}$	the open-circuit voltage of the timestep's curve	V
$V_{m,k}$	the voltage $k$	V
$P_k$	the module power at voltage $k$	W
$I_m(V_m)$	the module current. At voltage $V_m$ on the timestep's curve	A
$k^*$	the index of the voltage of the largest power	—
$V_m^*$	the voltage of the vertex of the parabola through voltages $k^*-1$, $k^*$ and $k^*+1$	V
$P_{mpp}$	the module power at the maximum-power point	W

References

1. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

options.module_mpp_point = sampled_41

Symbols follow the symbol registry.