Relación célula-módulo para módulos ETFE: ¿Por qué 33 células solares no suman la cantidad nominal indicada en la placa?

An OEM buyer emailed us last quarter with one very good question. His cell spec said 26.2% efficiency. His panel held 33 half-cut cells at roughly 4.37 W each, which multiplies out to 144.2 W. So why did the label say 130 W?

Fourteen watts, apparently missing.

Nothing was wrong with the solar panel. That gap has a name, a formula and a well-mapped set of causes — engineers call it the cell-to-module (CTM) ratio. What follows walks the arithmetic on a real 130 W ETFE back-contact solar module, hands you three checks you can run on any datasheet in a minute, and settles a question we field almost weekly: does the fiberglass layer eat your power?

What CTM actually measures

CTM compares two numbers: the sum of the individual cell powers, flash-tested before lamination, against the finished module’s rated power at STC.

A ratio below 100% is ordinary. Building cells into a module adds film, adhesive, gaps, conductors and resistance, and each charges a small toll.

What surprises buyers is that CTM can climb above 100%. Fraunhofer ISE has built half-cell modules at 104% CTM by deliberately engineering optical gains into the stack. At industry scale the crossover already happened: according to ITRPV data CTM passed the 100% benchmark in 2021, with half-cell designs above 100.5% and three-cut designs near 101%.

A module, in other words, is not a box that loses light. It is an optical system, and parts of it hand power back.

The trap: dividing module efficiency by cell efficiency

One mistake shows up in procurement spreadsheets more than any other. A buyer sees 20.2% module efficiency and 26.2% cell efficiency, divides, lands on 77.1%, and reports that the factory is losing 23% in lamination.

The number is wrong, and the reason is structural rather than arithmetic. Cell efficiency is measured over the cell area; module efficiency is measured over the whole panel. A panel carries edges, cell gaps and routing space — none of it makes power, and none of it belongs in a lamination loss figure.

Split the two effects and the numbers stop looking suspicious. One is geometry, fixed by layout; the other is integration physics, fixed by process. Lumping them together hides the only one you can actually negotiate.

A worked example: 130 W of flexible back contact

Take a real product — a 1090 × 590 mm ETFE back-contact flexible module, 33 half-cut cells in a 3 × 11 array, rated 130 W at STC.

Next, the geometry. Each half-cell measures roughly 91 × 183.75 mm, so 33 of them cover about 0.552 m². The panel spans 0.643 m². Active coverage therefore sits near 85.8%.

Multiply the three together:

We recommend this reconciliation to every buyer, because it is fast and hard to fake. If a supplier’s three numbers refuse to close within a few tenths, something is off — an inflated cell efficiency, a misstated area, or a datasheet borrowed from someone else’s product.

Two more checks, and neither needs a lab

The efficiency reconciliation is the thorough test. These two take a minute and catch fabricated datasheets outright.

Volts per cell. Divide the module voltages by the cell count: 20.13 V ÷ 33 = 0.61 V at maximum power, 23.45 V ÷ 33 = 0.71 V open-circuit. Both land where back-contact silicon belongs. Come out at 0.5 or 0.9 V and either the cell count is wrong or the electrical data was invented.

Current density. Divide short-circuit current by one cell’s active area — in a series string every cell carries the same current. Here: 6.77 A ÷ 167.2 cm² = 40.5 mA/cm².

Treat it as a red line. A datasheet implying more than roughly 43 mA/cm² is not optimistic; it is impossible. We have seen quoted figures clear 46. One caution: where cells sit in parallel groups rather than a single series string, divide module current by the number of parallel strings first.

Where the missing 14 watts actually go

That 9.8% is not one thing. It is at least six, and only some of them involve light at all.

That last row is why you cannot estimate CTM by multiplying transmittance figures off four supplier datasheets. Fraunhofer’s modelling puts gains and losses in the same ledger, not in a chain of subtractions.

Splitting optical loss from electrical loss

Six mechanisms in one number is not much use when you are trying to fix something. The split is easy, though, and it turns on which parameter each mechanism damages. Optical losses cost photons, so they show up in current. Electrical losses cost voltage and fill factor, and leave current largely alone.

So ask for flash data both sides of lamination and compute two ratios:

• Module Isc ÷ cell Isc is your optical CTM. Front-sheet reflection, encapsulant absorption and fiberglass scattering all land here.
• The remainder sits in Voc and fill factor: interconnection resistance, mismatch and cut-edge recombination.

The distinction matters commercially. Mostly optical, and you argue about materials — fiber weight, encapsulant grade, layer count. Mostly electrical, and materials will not save you; the conversation moves to conductor design, binning and separation process. Suppliers who cannot produce both sets of flash data usually do not measure them.

Cutting deserves its own note, because the popular framing gets it backwards. Half-cut construction is a clear net win — halve the current and resistive loss drops fourfold, worth 3 to 5% more power than full-cell equivalents. The real question is how much the separation process hands back. Not much, done well: Fraunhofer ISE reports optimized thermal laser separation costing only slightly above 0.1% absolute in efficiency, with edge passivation recovering roughly 85% of that. Cheaper scribe-and-break routes leave far more damage — damage that surfaces later as cracks under load.

Does fiberglass block your light? The honest answer

Pick up a sheet of dry fiberglass mat and it looks white, cloudy, hopeless. Buyers spot it in a layer diagram and conclude the panel is discarding a tenth of its sunlight. The instinct is reasonable. It is also, in the main, wrong.

Dry fiberglass appears white because the fibers sit surrounded by air — E-glass has a refractive index near 1.56, air is 1.00, and that step scatters light at every one of millions of fiber boundaries. Vacuum lamination changes the arithmetic. Encapsulant floods the space between fibers, and PV-grade EVA and POE land around 1.48. The index step collapses from roughly 0.56 to roughly 0.08, and scattering falls sharply with it.

Translucent, though, is not transparent. That residual 0.08 is exactly why fiber quantity remains the controlling variable. As the EPFL team behind the most-cited study on this put it: even a small mismatch between fiber and matrix reduces transmittance, and the penalty grows with reinforcement weight.

The data: transmittance falls with fiber weight

EPFL researchers encapsulated photovoltaic cells beneath glass-fiber laminates of increasing reinforcement weight, then measured the short-circuit current against bare cells. The pattern is unambiguous.

Fuente: Pascual et al., EPFL, CISBAT 2013. Values are short-circuit-current ratios over 300–800 nm.

Fiber architecture barely registered — weave pattern moved the needle by a few percent, total fiber weight by tens. Cross-ply read slightly below unidirectional, which the authors traced to air pockets trapped where fibers cross.

Note the low end: even at 410 g/m², far heavier than the veils used in flexible PV, transmittance held at 88%. So the useful question was never “does this panel contain fiberglass?” It is how many grams per square meter, on which side, and how completely was it impregnated?

Layer position decides the cost

Most flexible laminates are built symmetrically, the same reinforcement above and below the cell, which keeps the stack balanced and stops the panel curling as it cools. Optically, though, the two layers have almost nothing in common. Only one stands in the sunlight.

Rear layers are not free, but they are cheap — they shape internal reflection rather than intercepting incoming light. When a competitor’s diagram shows heavy reinforcement in front of the cell, that build runs a different optical budget from one carrying its structure behind.

Why flexible modules start a step behind — and it isn’t the fiberglass

Start with the good news, because ETFE genuinely wins one round. Saint-Gobain’s Norton ETFE datasheet lists n = 1.40 and transmission above 95%. Run the Fresnel arithmetic: air-to-ETFE reflects about 2.8%, against roughly 4.3% for bare glass at 1.52. Uncoated for uncoated, ETFE lets more light in.

Now the bad news, twice over. Mainstream glass is not uncoated — an anti-reflective layer pulls it to roughly 2%, erasing ETFE’s advantage against the product it actually competes with. And the second penalty appears on no datasheet at all. Light recycling works by total internal reflection: light that misses a cell scatters off the rear layers, strikes the front sheet from inside, and beyond the critical angle returns for a second pass at the silicon. That angle depends on the front sheet’s index — and here the low index works against you. Glass at 1.52 gives roughly 41°; ETFE at 1.40 gives roughly 46°.

Wider critical angle, wider escape cone, more light lost out the front instead of returned to the cell. The same property that helps on the way in hurts on the way back. It is structural — nothing to do with fiberglass, membrane count or lamination skill — and one honest reason a flexible laminate will not match AR-coated glass on CTM however well it is built. Dense back-contact layouts compound it: with high cell coverage there is little exposed backsheet to scatter from, so a white rear film buys fewer watts here than in a widely spaced module.

Total transmittance is not the number you want

Suppliers quote one figure. For a fiberglass composite, one figure is not enough — a laminate can pass 90% of the light and still look milky, because the light arrives scattered. That is haze, and it gets measured separately.

Scattered light is not automatically lost; a photon reaching the cell makes current whatever path it took. But haze is a reliable tell about process control. EPFL’s work on lightweight glass-free modules found EVA and POE both transmitting around 90% from roughly 350 to 1100 nm, while noting that certain polyolefins turn milky after lamination, cutting transmittance and raising reflectance.

Milky means incomplete impregnation, trapped air, or a lamination recipe that never closed the voids — and in a fiberglass build, any of them restores the glass-to-air interfaces the whole process was meant to eliminate. Ask for the haze number. It tells you about the factory, not just the film.

What good CTM looks like, by format

Benchmarks only mean something within a format. Holding a flexible ETFE laminate against a glass module on CTM alone measures the wrong thing.

Glass-module figures follow ITRPV roadmap data. Flexible ranges reflect our own build data and published module-integration studies — engineering guidance, not certified specifications.

Read the table as a trade-off, not a scoreboard. A flexible module surrenders several points of CTM for weight, bend radius and crack resistance — on an RV roof or a curved deck, that trade is the entire reason the product exists. Around 90% is healthy. A claimed 99% on the same structure should stop you cold.

How to isolate the fiberglass cost yourself

No research lab required — four coupons and a spectrophotometer with an integrating sphere will do. Laminate four cell-free samples using your production recipe:

Measure total transmittance, direct transmittance, haze and reflectance across 300–1200 nm, then weight against your cell’s spectral response. A visible-light average alone misleads, because silicon cares a great deal about the near infrared. The ratio C ÷ B is the figure worth arguing about with a supplier; everything else is opinion.

Twelve questions before you place an OEM order

Question 8 catches more problems than the rest combined — plenty of datasheets still list EVA because nobody updated a template written years ago. Question 2 is the one suppliers least expect, and a vague answer there tells you plenty about everything downstream.

Key takeaways

• CTM compares module power to the sum of cell powers. Below 100% is normal; mainstream glass now runs above it.
• Never divide module efficiency by cell efficiency — that mixes geometry with integration loss.
• Module efficiency = cell efficiency × active coverage × CTM. Use it as a consistency audit.
• Divide module Isc by one cell’s active area. Above ~43 mA/cm² the datasheet is impossible, not optimistic.
• Divide module voltage by cell count. Back-contact silicon gives ~0.61 V at Vmp, ~0.71 V at Voc.
• Isc ratio isolates optical loss; whatever remains sits in Voc and fill factor, and is electrical.
• Roughly 90% CTM is healthy for a reinforced flexible ETFE laminate.
• Fiberglass turns translucent once encapsulant fills the gaps — translucent, not transparent. Areal weight rules; weave pattern barely matters. Only front-side reinforcement costs real light.
• ETFE’s low index cuts first-surface reflection but widens the escape cone, so flexible panels recycle less light than AR glass. That gap is structural.

Frequently asked questions

How do I calculate the cell-to-module ratio?

Divide the module’s rated power at STC by the sum of the flash-tested powers of every cell inside it, then multiply by 100. For the 130 W example here: 130 ÷ 144.2 = 90.2%. Use measured half-cell data where you can; deriving cell power from a headline efficiency figure gives an approximation, not a measurement.

What is a good cell-to-module ratio for a flexible solar panel?

For a reinforced ETFE module, roughly 88–94% is realistic. Glass modules now sit above 100% because AR-coated glass, mature interconnection and better light recycling recover more than they lose. Judge a flexible panel against other flexible panels.

Why is my module efficiency so much lower than the cell efficiency?

Two independent reasons. Part of the panel area holds no silicon, and integration losses reduce the power the silicon does produce. In the worked example above, coverage accounted for about 14% and CTM for about 10%.

Does fiberglass reduce solar panel output?

Front-side fiberglass costs some light. How much depends on areal weight and impregnation quality, not on the mere presence of fiberglass. Rear-side reinforcement carries almost no direct optical cost.

Is a half-cut cell exactly half the power of a full cell?

Close, but no. Cutting creates fresh edges where carriers recombine, so the halves together measure slightly under the original. Optimized thermal laser separation costs around 0.1% absolute in efficiency, and edge passivation recovers most of that.

Is CTM a certified specification?

No. Module power falls under IEC 61215 and cell measurement under IEC 60904, but no standard governs how the ratio gets reported. Treat any CTM figure as a claim to be qualified, not a certified value.

Talk through your own numbers

Every laminate is a negotiation. Fiber weight against crack resistance. Layer count against optical budget. Bend radius against stiffness. There is no universally correct stack — only the right one for how the panel gets mounted and what it has to survive.

Send us a datasheet — anyone’s — and we will run the audit in this article against it. Volts per cell, current density against the physics ceiling, and the efficiency reconciliation. You get three numbers back and our read on whether they close. No obligation, and we will tell you if a competitor’s figures hold up.

Coulee builds ETFE back-contact flexible modules, rigid BC modules and dual-glass BIPV for distributors, installers, OEM buyers and developers across North America and Europe — custom layouts, sizes, voltages, private labelling, low-MOQ trials.

Correo electrónico: info@couleenergy.com
Teléfono: +1 737 702 0119
Web: couleenergy.com

OEM & ODM · Low MOQ · Custom size, power & shape · Fast sampling

Sources and further reading

1. Fraunhofer ISE — CTM 100+: improving module performance by analysis of cell-to-module losses
2. Fraunhofer ISE — SmartCalc.CTM / SmartCalc.Module cell-to-module analysis software
3. Richter, Hermle & Glunz, Revista IEEE de Energía Fotovoltaica (2013) — Reassessment of the limiting efficiency for crystalline silicon solar cells (29.43% and 43.31 mA/cm² intrinsic limits)
4. Saint-Gobain Performance Plastics — Norton® ETFE fluoropolymer film typical properties (refractive index, transmission)
5. Pascual, de Castro, Schueler, Vassilopoulos & Keller (EPFL, CISBAT 2013) — Total light transmittance of glass fiber-reinforced polymer laminates
6. Lisco, Virtuani & Ballif (EPFL, EU PVSEC 2020) — Optimisation of the frontsheet encapsulant for lightweight glass-free PV modules
7. Lohmüller et al. (Fraunhofer ISE, SiliconPV 2025) — Low-loss singulation of TOPCon half solar cells by TLS and Al₂O₃ edge passivation
8. pv magazine — Laser optimization for half-cut solar cells
9. TaiyangNews — Gains and losses at module level (ITRPV cell-to-module data)