The solar module data sheet specifies Voc and Vmp under standard test conditions (STC): cell at 25°C, radiation at 1,000 W/m². Many string calculations stop at that number. However, panels on rooftops rarely sit precisely at 25°C. Cool mornings increase their voltage, while scorching afternoons decrease it, both shifting the number of modules that can be safely connected in series.
There are two limits that are monitored simultaneously. The upper limit protects the inverter. The lower limit ensures the inverter continues to harvest power.
Two limits, two temperatures
| Limit | Voltage Used | Calculation Temperature | Rounding |
|---|---|---|---|
| Maximum modules per string | Voc | lowest temperature at the location | downward |
| Minimum modules per string | Vmp | highest cell temperature | upward |
Voc is used for the upper limit because it is the highest voltage that can come from the module, which occurs when no current is flowing. The data sheet for the Huawei SUN2000-50KTL-M3 states that input voltage above its maximum limit (1,100 V) is likely to damage the inverter. Voltage outside the MPPT range (200 to 1,000 V) causes the inverter to not operate properly.
Why temperature shifts the calculations
According to PVEducation, the solar cell parameter most affected by temperature is the open-circuit voltage. For silicon cells, it decreases by about 2.2 mV per °C for each cell. At the module level, this is expressed as a temperature coefficient. For example, from the LONGi Hi-MO 5 data sheet: Voc coefficient -0.265%/°C, peak power coefficient -0.340%/°C, and short-circuit current coefficient only +0.050%/°C.
The current barely changes, so the power loss when hot is almost entirely due to voltage drop. Therefore, if the data sheet does not list the Vmp coefficient, the power coefficient can be used as a safe estimate.
Cell temperatures are also much higher than air temperatures. PVEducation provides an approximation formula: cell temperature = air temperature + (NOCT - 20) / 80 x S, where S is radiation in mW/cm² (1,000 W/m² = 100). The NOCT of most modules is in the range of 40 to 45°C. Modules mounted on roofs without air gaps can be 10°C hotter. The same formula also shows the opposite side: under weak morning radiation, cell temperature is only a few degrees different from the air.
Example calculation
Suppose a module with Voc 49.5 V and Vmp 41.6 V (STC), coefficients as above, and NOCT 45°C. The inverter has a maximum voltage of 1,100 V with a minimum MPPT of 200 V. These module numbers are illustrative, not specifications for a specific brand.
Upper limit. At 25°C: 1,100 / 49.5 = 22.2, rounded down to 22 modules. Suppose the lowest morning temperature at the location is 18°C. Voc increases by 7 x 0.265% = 1.9%, resulting in 50.4 V per module. The calculation changes: 1,100 / 50.4 = 21.8, meaning 21 modules. If it remains at 22, the string would reach about 1,109 V on a cold morning.
Lower limit. At 25°C: 200 / 41.6 = 4.8, rounded up to 5 modules. Then on a scorching afternoon: air at 34°C, radiation at 1,000 W/m². Cell temperature = 34 + (25 / 80) x 100 = 65°C, or 40°C above STC. Vmp drops by about 13.7%, resulting in 35.9 V per module. Five modules only provide 180 V, below the MPPT threshold. Need 6 modules (215 V). For modules attached to the roof that are 10°C hotter, six modules still provide about 207 V.
| Condition | Voltage per module | Result |
|---|---|---|
| STC, upper limit | Voc 49.5 V | maximum 22 |
| Morning 18°C | Voc 50.4 V | maximum 21 |
| STC, lower limit | Vmp 41.6 V | minimum 5 |
| Afternoon 34°C, cell 65°C | Vmp 35.9 V | minimum 6 |
The safe range in this example is now 6 to 21 modules, not 5 to 22.
What to check before finalizing the design
- Lowest temperature taken from location data, not a guess. Use records from the nearest BMKG station, especially in highland areas where mornings are much cooler.
- Vmp of the string remains below the upper MPPT limit. With 21 modules, 21 x 41.6 = 874 V. On a morning at 18°C, the voltage increases by about 2% to approximately 895 V, still below 1,000 V.
- Current per MPPT. Parallel strings add current. The example inverter limits current to 30 A and short-circuit current to 40 A per MPPT, so the number of parallel strings is calculated separately from the number of series modules.
If you prefer to see the explanation directly, there is a clip. A broader overview of solar power plant design can be found in this article.
Sources
- PVEducation (C. Honsberg and S. Bowden), Nominal Operating Cell Temperature
- PVEducation (C. Honsberg and S. Bowden), Effect of Temperature
- LONGi, Hi-MO 5: Temperature Coefficient (STC test)
- Huawei, SUN2000-50KTL-M3 Datasheet: Technical Specification