# Array Voltage Considerations: Page 5 of 6

### CASE STUDY: EXAMPLE DC VOLTAGE CALCULATIONS

This case study illustrates how to implement the high and low dc voltage recommendations described in this article. It assumes a 50 kW inverter because designers working on smaller arrays, especially those under 10 kW, can be heavily influenced by a desire to fully exploit the available inverter capacity. This often leads to array voltage compromises that are unnecessary in larger systems. The inverter in this case is large enough that its capacity does not drive array voltage design. The relevant design details for this case study are as follows.

Location: Raleigh, NC
Low design temperature: -13°C, per ASHRAE Extreme Annual Mean Minimum Design Dry Bulb Temperature
Record low temperature: -21°C, per Weather.com
High design temperature: 34°C, per ASHRAE 2% Annual Design Dry Bulb Temperature
PV module: Yingli YL230P-29b, 230 W STC, 29.5 Vmp, 7.8 Imp, 37.0 Voc, 8.4 Isc, -0.137 V/°C temperature coefficient of Voc (-0.37%/°C x 37.0 Voc), -0.133 V/°C temperature coefficient of Vmp (based on the published temperature coefficient for Pmp, -0.45%/°C x 29.5 Vmp)
Inverter: Satcon PVS-50, 50 kW, 600 Vdc maximum input, 305–600 Vdc MPPT range

Maximum modules in series. To determine the maximum number of modules in series, first calculate the per-module maximum voltage as follows:

VMAX = VOC + ((TLOW − TREF) × αVOC)

where TLOW is the ASHRAE Extreme Annual Mean Minimum Design Dry Bulb Temperature; TREF is the cell temperature at STC; and αVOC is the temperature coefficient of Voc.

VMAX = 37.0 V + ((-13°C − 25°C) x -0.137 V/°C)
= 37.0 V + (-38°C x -0.137 V/°C)
= 37.0 V + 5.2 V
= 42.2 V

Divide the maximum inverter input voltage by the temperature-corrected open-circuit voltage and round down to the nearest whole number to determine the maximum number of modules in series:

NMAX = 600 Vdc / 42.2 V = 14.2
= 14 modules in series

Minimum modules in series. To determine the minimum number of modules in series, first calculate the per module minimum voltage as follows:

VMIN = (VMP + ((THI + TRISE − TREF) × βVMP))

where THI is the ASHRAE 2% Annual Design Dry Bulb Temperature, TRISE is the rise in cell temperature expected considering array mounting (typically 20°C to 30°C), and βVMP is the temperature coefficient of Vmp.

VMIN = 29.5 V + ((34°C + 20°C − 25°C) x -0.133 V/°C)
= 29.5 V + (29°C x -0.133 V/°C)
= 29.5 V − 3.9 V
= 25.6 V

Select and apply a multiplier to account for the combined effects of high ac grid voltage, array degradation and module voltage tolerance. 0.85 is used in this case:

VMIN = 25.6 V x 0.85 = 21.8 V

Divide the minimum MPPT voltage by the minimum voltage per module and round up to the nearest whole number to determine the minimum number of modules in series:

NMIN = 305 V / 21.8 V = 13.99
= 14 module in series

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