String design
Minimum modules per string (hot Vmp vs MPPT minimum)
- where
- estimated cell temperature (°C)
- maximum ambient temperature (°C)
- nominal operating cell temperature (°C)
- irradiance on the module (W/m²)
- module Vmp when hot (V)
- module maximum-power voltage at STC (V)
- temperature coefficient of Vmp (%/°C)
- minimum modules per string
- inverter MPPT minimum voltage (V)
Explain this equation
Works out the fewest modules in a string so that, on a hot sunny day, the voltage stays above the inverter's minimum tracking voltage.
NOCT is the cell temperature in standard test conditions of 20 °C air and 800 W/m². The cell runs hotter than the air in proportion to the sunlight, so the rise above air temperature is scaled by G / 800. A hot cell gives less voltage: with a negative γ_V the bracket is less than one. Dividing the inverter minimum by the hot module voltage and rounding up gives the minimum string length.
The cell temperature model is the standard NOCT approximation; the voltage change is linear in temperature.
Sense check: in 35 °C air at full sun a 45 °C NOCT module runs at about 66 °C, and a 32 V module drops to about 27.4 V. A 150 V minimum needs 6 modules.
Watch out: if the string voltage falls below the MPPT minimum the inverter loses output or stops. Leave some margin for degradation and partial shade.
On a hot day module voltage drops. This checks that a string keeps its maximum-power voltage above the inverter's MPPT minimum, so the inverter keeps tracking.
Enter your values to see the result.
Good to know
Cell temperature is estimated from the module NOCT (measured at 800 W/m², 20 °C ambient, 1 m/s wind). Roof-integrated or tightly mounted arrays with little rear ventilation run hotter than NOCT predicts, so allow extra margin. Many datasheets give only Pmax and Voc coefficients; the Pmax coefficient is a reasonable stand-in for Vmp because the current coefficient is small. Also check the inverter start-up voltage.
Common mistake
Using the open-circuit voltage instead of Vmp, or the STC Vmp without a temperature correction, so a short string drops out of the MPPT window in summer.
Limits
Steady-state cell temperature estimate; ignores wind and mounting effects. Partial shading or bypass-diode operation lowers string voltage further.
Sources
- IEC 61215 / IEC 61853 module test conditions: NOCT measured at 800 W/m² irradiance, 20 °C ambient and 1 m/s wind; cell temperature estimate Tc = Ta + (NOCT − 20) × G/800
- Module manufacturer datasheet: STC values (Voc, Vmp, Isc, Imp, Pmax), temperature coefficients of Voc, Pmax and Isc, NOCT/NMOT and dimensions
- IET Code of Practice for Grid-connected Solar Photovoltaic Systems, 2nd edition (2022)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow MCS standards, manufacturer data, BS 7671, the ENA connection rules and Building Regulations. System design and DNO applications need a competent, certified installer.