15. String Sizing & Voltage Windows

Learning objectives

• Execute the cold-Voc maximum and hot-Vmp minimum string calculations.
• Keep a string within the inverter’s absolute-max and MPPT-window limits.
• Source the temperature extremes these calculations require.

This is the single most important calculation in PV design. Get it wrong cold and you over-volt and destroy an inverter. Get it wrong hot and the array falls out of its tracking window and silently underproduces. Master this chapter above all others.

15.1 Why temperature rules stringing

From Chapter 3.3 / 4.5: cold raises module voltage, heat lowers it. Two boundary conditions therefore govern how many modules you may place in a series string:

• Maximum (cold) case: on the record-cold morning, the string’s Voc must stay below the inverter’s maximum DC input voltage.
• Minimum (hot) case: on the hottest operating afternoon, the string’s Vmp must stay above the inverter’s MPPT minimum voltage.

The allowable modules-per-string is the band between these limits.

15.2 The data you need

• Module Voc, Vmp, and temperature coefficients β(Voc) and the Vmp coefficient (from the datasheet, Chapter 5.4).
• Inverter max DC input voltage and MPPT voltage window (Chapter 6.3).
• Record low ambient temperature for the site (ASHRAE “extreme annual mean minimum” is the standard source) for the cold case.

• Maximum expected cell temperature (often ~70 °C cell on a hot roof) for the hot case.

15.3 Maximum string size (cold-Voc)

Adjust Voc upward for cold:

Voc(cold) = Voc(STC) × [1 + β × (T(min) − 25 °C)] (β negative, ΔT negative → product positive → voltage rises)

Then: Max modules per string = Inverter max DC voltage ÷ Voc(cold) (round down).

Example 15.A: Module Voc = 49.5 V, β = −0.25 %/°C. Site record low = −15 °C → ΔT = −40 °C. Voc(cold) = 49.5 × [1 + (−0.0025)(−40)] = 49.5 × 1.10 = 54.45 V/module. Inverter max input = 600 V → 600 ÷ 54.45 = 11.0 → maximum 11 modules per string (at 11, cold-Voc = 599 V, just under the limit; 12 would be 653 V, an inverter-killer).

15.4 Minimum string size (hot-Vmp)

Adjust Vmp downward for heat using the Vmp temperature coefficient (similar magnitude, negative):

Vmp(hot) = Vmp(STC) × [1 + coeff × (T(cell,max) − 25 °C)]

Then: Min modules per string = MPPT minimum voltage ÷ Vmp(hot) (round up).

Example 15.B: Module Vmp = 41.0 V, coeff ≈ −0.34 %/°C, max cell T = 70 °C → ΔT = +45 °C. Vmp(hot) = 41.0 × [1 + (−0.0034)(45)] = 41.0 × 0.847 = 34.7 V/module. Inverter MPPT minimum = 200 V → 200 ÷ 34.7 = 5.76 → minimum 6 modules per string.

15.5 The allowable band

Combining the examples: 6 to 11 modules per string. Any string length in that range is electrically valid. Choose within it to match your module count and parallel-string/MPPT limits (Chapter 16). A 19-module array (Ex 14.A) might wire as two strings of 9 and 10 (both within 6–11), subject to the inverter’s per-MPPT rules.

⚠️ Always use site-specific temperature extremes, never generic ones. A design valid in a mild coastal town can over-volt in a continental cold snap.

15.6 The voltage window, drawn

   Inverter MAX input voltage (e.g., 600 V)  ══════════════════ ← cold-Voc string
                                                                   must stay BELOW
        ▲                                                          this line
        │   ┌──────────────────────────────┐
        │   │   VALID string lengths        │   ← any modules-per-string
        │   │   live in this band           │      whose cold-Voc < max AND
        │   └──────────────────────────────┘      whose hot-Vmp > MPPT min
        │
   MPPT MINIMUM voltage (e.g., 200 V)  ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ─ ← hot-Vmp string
                                                                   must stay ABOVE
                                                                   this line

Too many modules → cold morning pushes Voc through the ceiling → inverter damage. Too few modules → hot afternoon drops Vmp below the floor → array falls out of MPPT and underproduces.

15.7 A second full worked example (different module/inverter)

Module: Voc = 49.5 V, Vmp = 41.2 V, β(Voc) = −0.25%/°C, Vmp coeff ≈ −0.34%/°C. Inverter: max DC input 1,000 V, MPPT window 250–950 V. Site: record low −25 °C (ΔT = −50 °C); hot cell max 70 °C (ΔT = +45 °C).

Cold Voc (max case): Voc(cold) = 49.5 × [1 + (−0.0025)(−50)] = 49.5 × 1.125 = 55.7 V/module. Max modules = 1,000 ÷ 55.7 = 17.9 → 17 per string (17 × 55.7 = 947 V < 1,000 V ✓).

Hot Vmp (min case): Vmp(hot) = 41.2 × [1 + (−0.0034)(45)] = 41.2 × 0.847 = 34.9 V/module. Min modules = 250 ÷ 34.9 = 7.2 → 8 per string (8 × 34.9 = 279 V > 250 V ✓).

Allowable band: 8–17 modules per string. A 30-module array might wire as two strings of 15, each within band. Or wire it as three strings of 10, subject to the inverter’s MPPT/current limits (Ch 16).

⚠️ Notice the 1,000 V inverter allows far longer strings than the 600 V unit in Example 15.A (max 11). Higher system voltage is exactly why commercial/utility designs favor 1,000–1,500 V equipment: fewer strings, less wire.

Chapter 15 summary

Cold sets the ceiling (string Voc(cold) < inverter max V → round modules down); heat sets the floor (string Vmp(hot) > MPPT min → round up). The band between is your legal string length. Use ASHRAE extreme-low and hot-cell temperatures and the datasheet coefficients. This calculation protects the inverter and guarantees the array stays in tracking.

Practice Problems: Chapter 15

Use: Module Voc = 48.0 V, Vmp = 40.0 V, β(Voc) = −0.28%/°C, Vmp coeff = −0.35%/°C. Inverter: max 600 V, MPPT 150–500 V.

1. Site record low = −15 °C. Compute Voc(cold) per module.
2. What is the maximum number of modules per string under the 600 V limit?
3. Hot cell max = 65 °C. Compute Vmp(hot) per module.
4. What is the minimum number of modules per string for the 150 V MPPT floor?
5. State the allowable string-length band.
6. A designer proposes 13 modules per string. Is that legal here? What’s the risk if they’d proposed 14?
7. Conceptually: if you switched to a module with a better (smaller-magnitude) Voc temperature coefficient, would the maximum string length go up or down? Why?

Solutions: Chapter 15

1. ΔT = −15 − 25 = −40 °C; rise = 40 × 0.28% = 11.2%; Voc(cold) = 48.0 × 1.112 = 53.4 V.
2. 600 ÷ 53.4 = 11.2 → 11 modules (11 × 53.4 = 587 V < 600 V ✓; 12 would be 641 V ✗).
3. ΔT = +40 °C; drop = 40 × 0.35% = 14%; Vmp(hot) = 40.0 × 0.86 = 34.4 V.
4. 150 ÷ 34.4 = 4.36 → 5 modules (round up; 5 × 34.4 = 172 V > 150 V ✓).
5. 5 to 11 modules per string.
6. 13 exceeds the max of 11 → not legal (cold-Voc would be 13 × 53.4 = 694 V, well over 600 V). 14 would be even worse (748 V). Both risk over-voltage inverter damage on a cold morning.
7. Up. A smaller-magnitude coefficient means less voltage rise in cold, so each module’s cold-Voc is lower, and more of them fit under the inverter ceiling.