String partitions, PVsyst application

Method

Each table of the scene is cut into its strings, stacked across its width or side by side along its length as its type gives them. The placements that name one string form that string, whatever their orientation. A string that a shadow of a neighbouring table or an object touches stops producing from the direct light. A shadow on the bottom or the top row of cells of a string takes only the shaded share of that row of cells. A shadow on the cells between those two rows takes the whole string. A string named by its placements loses what its most shaded placement loses. The partition fraction is the share of the field's strings lost, weighted by modules, over every table of the orientation. With the shading-factor table it is tabulated on the same grid of sun heights and azimuths and read bilinearly. Its row at the horizon is its 2° row extrapolated with its 10° row and kept within 0 and 1.0001. With the direct projection it is projected at every step. With row-to-row shading off, as on a roof, the tables do not shade one another: the objects' shadows projected on every table at every step form the partition fraction, and the objects' masks form the beam shaded fraction. The electrical loss is the partition fraction beyond the beam shaded fraction, times the fraction for electrical effect. It applies to the direct light on the plane after the horizon, the incidence-angle loss and soiling. It counts only on steps with at least 5 W/m² of direct light on the plane, where it or the beam shaded fraction reaches 0.01. One cell's height is the racking section's cell height over its collector band width, applied to each type's width.

The math

$$F_p = \frac{\sum_t m_t\,\ell_t}{\sum_t m_t},\qquad \ell_t = \frac{1}{n_t}\sum_{k=1}^{n_t} \lambda_{t,k} \tag{1}$$ $$\lambda_{t,k} = \begin{cases} 1 & \text{the shadow touches the central cells} \\ \max(s_B, s_C) & \text{otherwise} \end{cases} \tag{2}$$ $$f_{elec} = \begin{cases} f_{frac}\,(F_p - F_b) & G_b \ge 5\ \text{W/m}^2 \text{ and } \max(F_p - F_b,\ F_b) \ge 0.01 \\ 0 & \text{otherwise} \end{cases} \tag{3}$$ $$F_p(0^\circ) = \min\!\left(1.0001,\ \max\!\left(0,\ F_p(2^\circ) + \tfrac{2}{8}\left(F_p(2^\circ) - F_p(10^\circ)\right)\right)\right) \tag{4}$$ $$h_c = \frac{c}{W}\,W_t \tag{5}$$

where

Symbol	Meaning	Unit
$F_p$	the partition fraction of the orientation	—
$m_t$	the modules of table $t$	—
$\ell_t$	the share of table $t$'s strings lost	—
$n_t$	the strings of table $t$, one for a placement that names its string	—
$\lambda_{t,k}$	the loss of string $k$ of table $t$	—
$s_B, s_C$	the shaded shares of the string's bottom and top rows of cells	—
$f_{elec}$	the share of the direct light lost to the electrical effect	—
$f_{frac}$	the fraction for electrical effect	—
$F_b$	the beam shaded fraction of the step	—
$G_b$	the direct light on the plane after the horizon	W/m²
$F_p(h)$	the tabulated partition fraction at sun height $h$	—
$h_c$	the height of one row of cells on table $t$	the scene's unit
$c$	the cell height along the slope of the racking section	m
$W$	the collector band width of the racking section	m
$W_t$	the width of table $t$	the scene's unit

Note

Compared with PVsyst 8.1.5's electrical effect according to module strings on a field of 100 fixed racks read through its shading-factor table, the table of the partition fraction equals PVsyst's at every sun height from 10°, and the annual energy agrees within 0.01 %.

References

1. PVsyst 8 help, Electrical effect according to module strings

API

array.shade_mode = strings_partition

Symbols follow the symbol registry.