Agrivoltaic PV plant with dual land use

Guards every division whose denominator is provably positive, and every strictly-positive comparison.

Market range Not applicable (numerical parameter).

Neutral element used to build ratios, the CRF and the discount factors without any inline literal.

Market range Exact.

Divisor used to take the midpoint of a published cost band (site preparation, Leitfaden 2024).

Market range Exact.

Comparison floor for the input guards and for the regulatory compliance flag.

Market range Exact.

Converts between the percent convention (0-100) carried by every percent-labelled input and output and the ratios used inside the model.

Market range Exact.

kW to MW and kWh to MWh conversions.

Market range Exact.

365 x 24. Turns a capacity factor into full load hours, the Fraunhofer ISE convention for specific yield.

Market range Exact (non-leap year).

1 ha = 10 000 m2. Combined with the 1 kW/m2 STC convention it gives kWp/ha = 10000 x GCR x module efficiency.

Market range Exact.

Rounds the capacity density to the micro-kWp/ha. Purely numerical: it removes the binary floating-point drift that would otherwise put the density a 1e-14 outside its declared bound at the exact corners of the input box.

Market range Not applicable.

Below 50% light transmission (i.e. above 50% radiation reduction) the linear shade-response fitted at 40% RSR is no longer defensible: Laub et al. show every crop class turns sensitive beyond that point. The calculator refuses the region rather than extrapolating into it.

Market range Radiation reduction 0-50% is the fitted domain.

Annual output decay of the modules. Drives the gap between year-one yield and the lifetime-average yield that the LCOE actually levelizes.

Average substructure cost of a high-mounted (over 4 m) agri-PV array. It is the poste that separates agri-PV from ground-mounted PV, and the default of the corresponding input.

Low end of site preparation and installation for a high-mounted array.

High end of site preparation and installation for a high-mounted array.

Substructure cost of a conventional ground-mounted plant (PV-FFA). It is the counterfactual against which the elevated structure premium is measured.

Market range Single published figure for PV-FFA racking.

Low end of site preparation and installation for a ground-mounted plant.

High end of site preparation and installation for a ground-mounted plant.

Module poste assumed by the Leitfaden for agri-PV. Identical on both sides of the elevated-versus-ground comparison, so it never enters the structural premium - it is the default of the module input.

Midpoint of the Fraunhofer ISE all-in installed cost band for agri-PV. The model uses it once, to back out the residual poste (electrical balance of system, inverters, grid connection, planning) that the Leitfaden decomposition does not name.

Low end of the ISE agri-PV installed cost band. Used to place the built-up CAPEX inside the published band rather than asserting it.

High end of the ISE agri-PV installed cost band.

Low end of the ISE utility-scale ground-mounted PV cost band. The reconstructed ground-mount reference is placed against it as a cross-source consistency check.

High end of the ISE utility-scale ground-mounted PV cost band.

Fixed O&M of a conventional ground-mounted plant. Used only in the counterfactual LCOE, so the agri-PV premium is measured against a like-for-like plant on land.

Market range 13.3 EUR/kW/year ground-mount, 15 EUR/kW/year agri-PV.

Reference specific yield of central and eastern Germany at optimal tilt. The site's own full load hours are reported against it, so a capacity factor is never entered blind.

Market range 935 (north Germany) to 1280 (south Germany) kWh/kWp/year.

Radiation reduction level at which the meta-analysis reports its relative crop yields. The shade-sensitivity slope of every crop class is the chord from full light to this point.

Market range The fitted domain runs 0-50% RSR.

Relative yield of maize (C4 row crop) at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range maize (C4 row crop): 45% of the unshaded control at 40% RSR (95% CI 37-56%).

Relative yield of grain legumes at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range grain legumes: 50% of the unshaded control at 40% RSR (CI 41-61%).

Relative yield of leafy vegetables at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range leafy vegetables: 86% of the unshaded control at 40% RSR (CI 61-120%).

Relative yield of forages and grassland at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range forages and grassland: 93% of the unshaded control at 40% RSR (CI 75-117%).

Relative yield of fruity vegetables at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range fruity vegetables: 102% of the unshaded control at 40% RSR (CI 67-156%).

Relative yield of orchard fruits at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range orchard fruits: 113% of the unshaded control at 40% RSR (CI 84-152%).

Relative yield of berries at 40% radiation reduction. Divided by the 0.4 reference it gives the class shade-sensitivity slope used when the override is left at zero.

Market range berries: 114% of the unshaded control at 40% RSR (CI 84-154%).

Relative yield of C3 cereals at 40% radiation reduction, anchored on the only multi-year field measurement available: winter wheat at Heggelbach lost 10.5% on average (-19%, +3%, -28%, +2% over 2017-2020) at a measured 30% reduction of photosynthetically active radiation, i.e. a slope of 0.35, which puts 40% RSR at 86% of the control.

Market range Laub et al. 2022 class C3 cereals as shade tolerant up to 50% RSR, consistent with this slope.

Selector code for maize. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for grain legumes. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for C3 cereals (wheat, barley, rapeseed). The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for leafy vegetables. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for forages and grassland. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for fruity vegetables. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for orchard fruits. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Selector code for berries. The DSL carries no strings, so the crop class is an integer compared against these codes.

Market range Exact.

Maximum share of the plot that the projected area of the panels may cover under the French agrivoltaic decree. It is the binding constraint on density in France, and it is regulatory, not economic.

Market range 40% of the plot area.

Minimum average yield per hectare, relative to a control zone, for the agricultural production to be considered significant under the French decree.

Market range 90% of the control zone yield.

Minimum share of the installation area that must be left as an unshaded control zone, capped at one hectare. Reported for completeness; its production is not deducted in V1.

Market range At least 5% of the area, capped at 1 ha.

Weighted average clearing price of the eighth period of the French PPE2 'PV Sol' tender. Used as the reference remuneration a French agri-PV project can realistically expect to beat.

Market range 34.25 EUR/MWh European solar PPA (Q3 2025) to 79.48 EUR/MWh French tender average.

EU average gross crop output per hectare of utilised agricultural area. The baseline crop revenue entered by the user is reported against it, so an implausible baseline is visible immediately.

Market range 800 EUR/ha (extensive arable) to 6000+ EUR/ha (special crops).

The free sizing lever is the light left to the crop, and the installed capacity is derived from it. Exposing both as independent inputs would let a user sweep capacity while the crop yield stayed frozen - the curve would then show PV revenue rising with no agronomic cost, which is the opposite of the truth. This is why no chart sweeps a capacity here, and why the plot area only scales absolute quantities.

Market range Fraunhofer ISE reports 500-800 kWp/ha for high-mounted agri-PV, 250-430 for ground-level layouts and 700-1100 for conventional ground-mounted PV; the coupling reproduces the high-mounted band at the defaults and lands under the ground-level band at the 90% transmission end.

Light reaching the crop is taken as one minus the projected ground coverage ratio. Calibrated on Heggelbach: a 3.4 m module row on a 9.5 m pitch, about 34% projected coverage, measured photosynthetically active radiation 30% below the reference plot.

Market range Holds for fixed-tilt elevated rows; a tracker or a vertical bifacial layout redistributes light differently.

The crop response is modelled as linear in the radiation reduction, with a slope read as the chord of the Laub et al. estimates to 40% reduction. The underlying response is not linear: maize and grain legumes lose disproportionately from the first percent of shade, while fruits and berries gain up to 25-30% reduction before declining.

Market range Valid over the 0-50% radiation reduction the calculator accepts; wrong beyond 50%, where Laub et al. show every class turning sensitive.

The shade-sensitivity override defaults to zero, which means 'take the benchmark of the crop class selected'. A default frozen on one class would make every other class wrong - maize is four times more sensitive than C3 cereals - and no structural gate can see that error.

Market range Grounded envelope -0.35 (berries) to 1.375 (maize) per unit of radiation reduction.

The yield lost to the uncultivable strips around the posts is a geometric term, kept separate from the shade term and multiplied with it. Heggelbach measures about 8%.

Market range 0-12% depending on post spacing and machinery width.

The baseline crop revenue is gross output per hectare, not a margin. Seed, fertiliser, fuel, machinery and labour are not modelled, so the crop lines are an upper bound on what the crop contributes and must never be netted against a PV cost as if they were profit.

Market range EU average gross crop output 1714 EUR/ha/year of utilised agricultural area.

The crop is deliberately NOT declared as an outlet flow and NOT booked as a negative OPEX line. The project service prices flows by commodity name and there is no crop commodity; a phantom outlet would hand the main product an uncontrolled by-product credit, and a negative OPEX would net gross revenue against a cost, which the scope decision above forbids. The crop therefore lives as a pure economic output on the calculator page, and the asset the project mode sees is an electricity producer.

Market range Not applicable.

Chaining rule for the project mode. This asset has no inlet: it buys nothing, so no upstream link is legitimate or needed, and no commodity appears on both sides. Its single outlet is electricity, resized through the plot area, which scales capacity and generation proportionally while leaving every per-hectare figure and the LCOE untouched. Downstream links to electricity consumers therefore carry a coefficient of 1 and no double-counting is possible.

Market range Not applicable.

The CAPEX build-up is an INSTALLED cost: substructure, site preparation and erection, modules, electrical balance of system and grid connection, excluding VAT. It is not bare equipment. The meta therefore declares an installed battery limit, so the project adds working capital and contingency only - declaring it ex-factory would let the project re-apply the full indirect and owner build-up and overstate the CAPEX by about 77%.

Market range ISE agri-PV 900-1700 EUR/kWp installed; Leitfaden postes are installed costs.

No six-tenths rule is applied to the CAPEX. The ISE band of 900-1700 EUR/kWp already spans 0.5 to 2 MWp, so an exponent on top would double-count the size effect. If one were ever added, it would carry on the TOTAL cost; on a SPECIFIC cost in EUR/kWp the correct exponent is the total exponent minus one, hence negative - a specific cost that rises with plant size is always wrong.

Market range 0.5-2 MWp covered by the published band.

No cost in this calculator is clamped. Every CAPEX poste is a free sum of inputs whose sliders already carry the published band, so there is no guard rail that could bite inside the declared domain and silently freeze a cost while the user moves it. Executed, not asserted: over the 65 536 corners of the input box the built-up CAPEX runs 1047-1580 EUR/kWp, entirely inside the 900-1700 published band.

Market range Not applicable.

The declared output bounds were calibrated by evaluating the DSL on all 65 536 corners of the input box, not on single-variable sweeps. Outputs that are products or ratios of inputs reach their extrema at the corners, never on the axes: the LCOE runs 46.3-202.4 EUR/MWh, the yield retention 39.6-114.0%, the capacity density 190-920 kWp/ha, the land equivalent ratio 0.932-2.454 and the revenue per hectare 6 433-130 146 EUR - all inside the declared bounds, none of them reachable by moving one slider at a time.

Market range Not applicable.

The LCOE denominator is the discounted degraded energy, not the year-one yield. At 0.25%/year over 30 years at 3.5% real this costs 2.9% of the energy - small, but it is the difference between reproducing the ISE band and sitting 3% below it.

Market range 0.2-0.5%/year of module degradation.

Deliberately out of scope: the control zone's lost PV production (reported, not deducted), land lease or concession fees, crop input costs, subsidies and the German agri-PV technology bonus, grid connection beyond the plant gate, trackers and vertical bifacial layouts, hail and storm insurance premia specific to elevated structures, water use and irrigation savings under partial shade, residual value and decommissioning.

Market range Not applicable.