4. From Cell to Module to Array

Learning objectives

• Explain how cells combine into modules and modules into arrays.
• Define STC and every core datasheet parameter (Voc, Isc, Vmp, Imp, Pmax).
• Use temperature coefficients to adjust ratings to real conditions.
• Read a module datasheet well enough to begin sizing.

4.1 Cells → modules

A single silicon cell produces only about 0.5–0.6 V regardless of its size (size sets current, not voltage). That’s far too little to be useful, so cells are wired in series inside a module. A traditional 60-cell module yields roughly 60 × 0.5 V ≈ 30+ V open-circuit; 72-cell modules more. (Recall Chapter 1: series adds voltage.) The cells are laminated between glass and a backsheet, framed, and fitted with a junction box and bypass diodes: the package we call a module (panel).

4.2 Modules → arrays

Modules combine the same two ways:

• In series → a string: module voltages add, building the high DC voltage (often 300–600 V residential, up to 1,000–1,500 V utility) that inverters want.
• In parallel → strings combine: currents add.

The full collection is the array. How many modules in series, and how many strings in parallel is the central design decision of Chapter 15. That decision is governed entirely by the datasheet numbers below interacting with temperature and inverter limits.

4.3 Standard Test Conditions (STC)

Modules are rated under a fixed laboratory reference so they can be compared:

STC = 1,000 W/m² irradiance, 25 °C cell temperature, AM1.5 spectrum.

The nameplate watts (e.g., “400 W module”) is the power at STC. ⚠️ Real arrays rarely operate at STC (cells run hotter than 25 °C in sunlight and irradiance varies), so STC ratings are a comparison baseline, not a field prediction. Bridging STC to reality is what derate factors (Chapter 14) and temperature coefficients (4.5) are for. A second reference, NOCT/PTC, estimates more realistic operating output and is often closer to field behavior.

4.4 The core datasheet parameters

Every module datasheet lists these at STC. They are the vocabulary of design:

• Pmax (Pmp): maximum power, the nameplate watts.
• Voc (open-circuit voltage): voltage with no load connected (terminals open). The highest voltage the module reaches. Drives the maximum system voltage calculation.
• Isc (short-circuit current): current with the terminals shorted. The highest current. Drives conductor and OCPD sizing.
• Vmp (voltage at max power): the operating voltage at peak power.
• Imp (current at max power): the operating current at peak power.

The relationship Pmax = Vmp × Imp holds at the max-power point. A module’s I-V curve plots current against voltage across all operating points; Voc and Isc are its endpoints, and Pmax is the “knee” where Vmp × Imp is greatest. The fill factor (how square the curve is) is a quality indicator. Inverter MPPT (Chapter 6) exists to keep the array operating at that knee as conditions shift.

4.5 Temperature coefficients: making the datasheet real

Because temperature changes voltage (Chapter 3.3), datasheets give temperature coefficients, typically:

• β (Voc): %/°C, negative: how much Voc falls per degree above 25 °C (and rises per degree below).
• γ (Pmax): %/°C, negative: how output power changes with temperature.
• α (Isc): %/°C, small and positive.

These let you compute the actual Voc on the coldest expected morning (the maximum voltage case, which must stay under the inverter and equipment limits) and the actual Vmp on the hottest afternoon (the minimum voltage case, which must stay within the inverter’s MPPT window).

Example 4.A (the calculation you’ll do constantly): A module has Voc = 40.0 V and β = −0.28 %/°C. On a record-cold morning of −10 °C, the cell is 35 °C below STC. Voltage rise = 35 × 0.28% = 9.8%. Cold Voc = 40.0 × 1.098 ≈ 43.9 V per module. String ten of these in series and the cold open-circuit string voltage is ~439 V. That number, not the 400 V you’d get from nameplate, is what must stay below your inverter’s maximum input voltage. Undersize for this and cold weather can over-volt and damage the inverter. This single calculation is the backbone of Chapter 15.

4.6 What you can now do

With Chapters 1–4 you can read the four-quadrant logic of any module datasheet, understand what each number physically means, adjust it for temperature, and see how series/parallel choices build an array’s voltage and current. That is precisely the toolkit Part IV turns into complete, code-compliant designs.

4.7 The I-V curve, drawn

 Current (A)
  Isc ┤●─────────────●  ← knee = max power point (Vmp, Imp)
      │              │\
      │   operating  │ \
  Imp ┤   region     │  ●  Pmax = Vmp × Imp  (the area of the
      │              │  │\      biggest rectangle that fits)
      │              │  │ \
    0 ┼──────────────┴──┴──●── Voltage (V)
      0             Vmp   Voc

The curve runs from Isc (left, terminals shorted, zero volts) to Voc (right, open terminals, zero current). Power is V × I at every point; it peaks at the knee (Vmp, Imp), the largest rectangle that fits under the curve. The inverter’s MPPT (Ch 6) constantly hunts for this knee. A “squarer” curve has a higher fill factor and a better-quality cell.

4.8 An annotated datasheet (sample 440 W module)

Every number on a datasheet maps to a downstream decision. The skill of Part IV is reading this table and turning it into a code-compliant array.

4.9 Mini case study: one module, four downstream uses

Take the 440 W module above on a site with a record low of −18 °C and an inverter rated 600 V max, 60–550 V MPPT:

• Max string (cold Voc): Voc(cold) = 49.5 × [1 + (−0.0025)(−18 − 25)] = 49.5 × 1.1075 ≈ 54.8 V. Max modules = 600 ÷ 54.8 = 10.9 → 10 per string.
• Conductor current: 13.85 × 1.56 ≈ 21.6 A minimum ampacity (before derating, Ch 16).
• OCPD: any series fuse must not exceed the 25 A max-series-fuse rating.
• Roof load: the array must stay within the 5,400 Pa front load after the structural calc (Ch 25). One datasheet, four design constraints. We haven’t even left Part I. That is the leverage these four chapters give you.

Chapter 4 summary

Cells series-wire into modules (cell voltage × count); modules series-wire into strings and parallel into arrays (series adds volts, parallel adds amps). STC (1,000 W/m², 25 °C, AM1.5) is the rating baseline; nameplate watts is Pmax at STC. The core parameters (Pmax, Voc, Isc, Vmp, Imp) describe the I-V curve, and temperature coefficients convert them to real cold/hot conditions. The cold-Voc string calculation is the foundational design constraint of the whole trade.

Practice Problems: Chapter 4

1. A module shows Vmp = 41 V and Imp = 10.7 A. What is its Pmax?
2. On the I-V curve, what are the current and voltage at the two endpoints (Isc point and Voc point)?
3. A module has Voc = 50 V and β = −0.27%/°C. Find its Voc on a −20 °C morning (45 °C below STC).
4. With that cold Voc, how many modules can go in series under a 600 V inverter limit?
5. A 12-module string uses modules of Voc(STC) = 45 V. At STC, what is the string Voc? Why is this not the number you size the inverter against?
6. A module’s max series fuse rating is 20 A. You calculate a required OCPD of 22 A. What’s the problem, and the likely fix?
7. Why is nameplate (STC) wattage a poor predictor of a hot-roof afternoon’s output?

Solutions: Chapter 4

1. Pmax = 41 × 10.7 = 438.7 W.
2. Isc point: maximum current, 0 V. Voc point: maximum voltage, 0 A.
3. ΔT = −45 °C; rise = 45 × 0.27% = 12.15%; Voc(cold) = 50 × 1.1215 = 56.1 V.
4. 600 ÷ 56.1 = 10.7 → 10 modules (round down; 11 would exceed 600 V).
5. STC string Voc = 12 × 45 = 540 V. You don’t size to this because cold weather raises Voc above STC, so the relevant ceiling is the higher cold-Voc figure (Ch 15).
6. A 22 A fuse exceeds the module’s 20 A max series fuse rating: not allowed. Fix: reduce the calculated current (e.g., fewer parallel strings on that fuse) or reconfigure so a ≤20 A standard fuse protects the circuit.
7. Because STC assumes a 25 °C cell; a real roof runs far hotter, and the negative power temperature coefficient drops output well below nameplate.

PART I: CONSOLIDATION

You now hold the conceptual core the rest of the primer applies:

• Power vs energy, Ohm’s law, P = V×I, DC vs AC, series/parallel (Ch 1).
• Irradiance vs insolation, peak sun hours, site geometry (Ch 2).
• How a cell makes current, the band gap, why heat hurts (Ch 3).
• Datasheets, STC, the five parameters, temperature math (Ch 4).

Part II opens up the hardware (modules, inverters, racking, BOS, and storage), describing each component against the physics you just learned so that by Part IV you can size and design a complete system from first principles.

Hardware is where physics meets a purchase order. Each chapter ties a component back to the Part I fundamentals, then to the datasheet limits and listing standards that govern how you may legally and safely use it. Listing standards in this part were verified against UL, IEC, and industry sources as of mid-2026; standards revise, so confirm the edition cited on any product before specifying it.