Solar thermal collector field for heat

Guards every division and every clamp denominator against zero.

Market range Not applicable (numerical parameter).

Neutral element used instead of an inline literal in the DSL.

Market range Exact.

Comparison floor used in the input guard and in the efficiency clamp.

Market range Exact.

Converts the percent-scale inputs (utilisation, O&M) into fractions.

Market range Exact.

Upper bound of a percent input and scale factor of the field efficiency output.

Market range Exact.

Converts specific yields and auxiliary electricity from kWh to MWh.

Market range Exact.

Converts annual heat to kWh for the equivalent full-load hours.

Market range Exact.

Converts the peak collector power density from W to kW.

Market range Exact.

The certified efficiency curve is instantaneous and rated at 1000 W/m2. An annual yield must be evaluated at the energy-weighted mean irradiance actually seen by the field; using 1000 W/m2 overstates the annual yield by roughly 35 %.

Rating irradiance of the certified collector curve; used here only to express the field's nominal thermal capacity (eta0 x 1 kW/m2), the basis on which solar thermal capacity is normally quoted.

Market range Exact (standard test condition).

Single annual factor lumping the incidence-angle modifier and soiling. A per-hour incidence model is out of scope for a screening tool.

Collector-loop piping and heat-exchanger losses between the absorber and the delivery point.

Non-ideal flow distribution, transients and unforeseen losses across a large field.

Cap on the thermal-loss load penalty. At an operating temperature high enough to zero the efficiency curve the ratio would diverge; the cap keeps the reported figure finite without touching the yield, which is already clamped at zero.

Market range Not applicable (numerical parameter). It does not bite anywhere in the declared input domain.

Zero-loss efficiency of a high-performing evacuated-tube collector, used for the side-by-side reference efficiency at the same operating temperature.

First-order loss of the reference evacuated-tube collector.

Second-order loss of the reference evacuated-tube collector.

Lower guard rail on the installed specific capex, well below any published field cost.

Market range No published European field has ever been built below ~120 EUR/m2 gross.

Plafond numérique du coût spécifique mis à l'échelle. Il est placé STRICTEMENT au-dessus du maximum atteignable dans la boîte d'entrée déclarée — 800 EUR/m2 de coût spécifique plus 2 000 000 EUR de coût fixe répartis sur 1 000 m2, soit 2 800 — pour qu'il ne morde jamais sur un point que l'utilisateur peut atteindre. À 900 il mordait dès 650 EUR/m2 et gelait la LCOH pendant que le curseur de coût bougeait.

Market range Task 68 (2024) reports 320-700 EUR/m2; small or complex fields can exceed it.

Land footprint for siting: row spacing and access alleys mean a field occupies about three times its collector area.

Diurnal storage volume a field of this kind normally needs. Reported here but deliberately NOT included in the levelized cost, because the cost basis of this model excludes it.

Tank storage cost used to size the separate storage budget the field will also need.

Measured benchmark the model is calibrated against and reported against: the average output of 40 Danish solar heating plants.

Measured annual field efficiency referenced to HORIZONTAL irradiation, which is why this calculator reports its efficiency on the same basis: the output is directly comparable to a published measurement.

Lower edge of the published specific-yield band, used to flag a result that leaves the observed envelope.

Upper edge of the published specific-yield band for Danish conditions.

Published Central-European solar district heat cost, used as the reference the levelized cost is reported against.

Lower bound of the 2024 European supplier range, used to place the modelled installed cost against a current market quote rather than only against 2015 Danish prices.

Default zero-loss efficiency: the flat-plate collector DEA uses as its reference.

Default first-order loss coefficient of the DEA reference flat plate.

Market range 1.0 (high-performing ETC) to 4.0 (medium-performing FPC) per SDH table 7.1.1.

Default second-order loss coefficient of the DEA reference flat plate.

Market range 0.005 (ETC) to 0.015 (reference FPC).

Alternative collector class the user can type in: high-performing flat plate 0.80 / 3.0 / 0.008.

Market range eta0 0.75-0.80, a1 3.0-4.0, a2 0.008-0.010 across the flat-plate classes in table 7.1.1.

Default site irradiation (Wurzburg, Germany), representative of a Central-European district-heating network.

Market range Aarhus 1030, Wurzburg 1225, Graz 1308, Lyon 1419, Sevilla 1908 kWh/m2/yr from the same query.

Default in-plane gain over horizontal for a fixed tilt around 35 deg.

Default mean collector fluid temperature, the low end of the 60-110 degC district-heating / process window this asset targets.

Default share of collected heat actually delivered. A design choice: it stands in for storage sizing and demand matching, which this steady-state model does not simulate.

Size-independent term of the installed-cost regression. It, and not a power law, is what makes the specific cost fall with field size.

Variable term of the installed-cost regression, per gross m2.

Market range 167 EUR/m2 (Denmark, 2015 prices) up to 320-700 EUR/m2 (IEA SHC Task 68, 2024, Central Europe).

Published installed cost at the typical plant size, the point against which the affine form was checked.

Upper bound of the 2024 European supplier range. Documented rather than wired in: it is the value to type into the specific capex input for a pessimistic Central-European case.

Default fixed O&M, set at the LOWER edge of the recommended band on purpose: the measured Danish figure is far lower still, so 1 %/yr is already the conservative reading and 2 %/yr is the defensible pessimistic case.

Default circulation-pump electricity per MWh of heat collected.

Default delivered electricity price for the pumps.

Default real discount rate.

Default technical and economic lifetime.

Instantaneous collector efficiency: eta = eta0 - a1.dT/G - a2.dT^2/G, with dT the difference between the mean fluid and the ambient temperature and G the global in-plane irradiance. Clamped at zero: a field hot enough to zero the curve produces nothing, it does not produce negative heat.

Market range Universal across certified collectors; the parameters, not the form, vary.

Levelized cost of heat = (CRF x installed capex + fixed O&M + auxiliary electricity) / annual delivered heat, with CRF = r(1+r)^N / ((1+r)^N - 1) and a guarded 1/N branch at r = 0.

Market range Standard across levelized-cost studies; the assumptions dropped here are the ones a financier will ask about first.

The size input is GROSS collector area, not aperture area. Every cost and yield figure grounded here is per gross m2, so mixing an aperture-area input with gross-area costs would silently inflate both capex and yield per m2.

Market range Aperture/gross ratio is technology-specific: about 0.93 for large flat plates, and 1.41/1.74 = 0.81 on the measured Apricus evacuated-tube certificate. It must not be hardcoded across both.

Model validation, anchor 1: fed with DEA's own site conditions (GHI 1046 horizontal, tilt gain 1.193 for Aarhus at 40 deg, dT 50 K) and all other defaults, the model returns 453.2 kWh/m2/yr and 43.3 % of GHI.

Market range Second check with PVGIS' own Aarhus GHI (1030) gives 446.3 kWh/m2/yr, still within 1 % of the measurement.

Model validation, anchor 2: with the specific capex moved to 400 EUR/m2 (mid Task 68 range) and no fixed term, the model returns 52.4 EUR/MWh_th.

The default capex is stated in 2015 EUR, the base year of the DEA regression that sets it. Escalate it, or replace it with a current quote, before taking a levelized cost to a lender.

Market range The gap between the two cost worlds is roughly a factor two, which is far larger than any escalation index over the period.

Steady-state annual-average model. No hourly simulation, no storage dynamics, no explicit solar fraction or demand matching; dumping is represented only by the utilisation rate. Incidence angle and soiling are lumped into one annual factor rather than modelled per hour.

Market range A field whose solar fraction is the binding question needs an hourly model; use this one to size the field and bound the cost.

Excluded from the levelized cost: diurnal storage (reported separately), seasonal storage, land (available as an explicit input, zero by default), VAT, and any subsidy.

Market range Diurnal storage adds roughly 27 EUR/m2 of collector at DEA prices, about 14 % on top of the Danish field capex.

Chaining: the single outlet is heat and the single inlet is electricity, so no inlet and outlet of this asset share a commodity and no same-commodity chaining rule is needed. The electricity inlet is driven by an adjustable input, so project mode gets a real knob rather than a read-only link.

Market range Not applicable here.