# String Theory

PV Array Voltage Calculations
Intermediate

The Fronius IG 5100 inverter has an operating voltage range between 150 and 450 VDC, and a maximum input voltage of 500 Voc.
The Kaco 3601xi inverter has an operating voltage range between 125 and 300 VDC, and a maximum input voltage of 400 Voc.
The SMA Sunny Boy SB7000US inverter has an operating voltage range between 250 and 480 VDC, and a maximum input voltage of 600 Voc.
The Xantrex GT5.0 inverter has an operating voltage range between 240 and 550 VDC, and a maximum input voltage of 600 Voc.

A decade or so ago, most PVs were designed with battery charging in mind. Module open-circuit and maximum power voltages fit into simple 12-volt nominal building blocks—one or more modules wired in parallel provided ideal voltage for charging a 12 V battery bank. Strings of two modules wired in series charged 24 V battery banks, and “high” voltage systems had four modules in series and operated at 48 V nominal. But as inverter and charge controller designs have evolved, the concept of designing systems in 12 V increments has faded.

Today, grid-direct batteryless inverters are designed for up to 600 volts open circuit (Voc). Several brands of maximum power point tracking (MPPT) charge controllers are able to charge a lower-voltage battery bank (12 to 48 V nominal) from higher-voltage arrays with open-circuit voltages of approximately 150 Voc. Even module design voltages have deviated from the simple 12 V building-block approach. First, 24 V nominal modules hit the market, and now many modules operate at voltages either above or below 24 VDC nominal. In fact, in most systems, the concept of PV array nominal voltage has been left by the wayside. Open-circuit voltage (Voc) and maximum power voltage (Vmp) are now the basis of PV array design.

## String Sizing Considerations

A number of variables affect PV array voltage and performance. Module-specific operating characteristics, the number of modules in series, cell temperature, mount type, inverter or charge controller specifications, and the coldest historical temperature at your site all come into play. Most, if not all, high-voltage-string inverter manufacturers have online calculators to help system designers determine the maximum, minimum, and the ideal number of modules per series string for their equipment. Similar calculators have yet to be developed by all MPPT charge controller manufacturers, so system designers need to run their own calculations to determine an array’s acceptable voltage range. While string-sizing calculators remove much of the math from system design, understanding how the calculations are made will help you better understand how a PV array functions day to day and season to season.

## Temperature Effects & Array Voltage

A PV module’s voltage is directly affected by its operating temperature. As module temperature increases, voltage decreases. PV module manufacturers rate a module’s open-circuit and maximum power voltages at a standard test condition (STC) of 25°C (about 77°F). As module temperature rises above 25°C, the voltage drops. Conversely, if the module’s temperature drops below 25°C, the module’s operating voltage will be greater than its rating at STC.

Because temperature has a significant effect on module output, PV manufacturers specify a module’s temperature coefficient, which is represented as a percentage of voltage loss per 1°C above 25°C. A common temperature coefficient value for crystalline PV modules is -0.38% per degree Celsius; so for every 1°C above 25°C, the module temporarily loses 0.38% of its voltage. And for every 1°C below 25°C, the module voltage will increase by 0.38%.

Another approach to specifying the effect of changing module temperature is a voltage correction value—the number of volts per degree Celsius that the module will lose as its temperature rises above the 25°C reference point. For example, a crystalline module with a maximum power voltage of 34.8 volts might have a temperature correction factor of approximately -0.144 Voc per degree Celsius. These figures are provided on the module’s specification sheets.

It may not sound like much, but when the temperature values are applied, the combined effect can be substantial. For example, on a sunny summer day, module temperatures in a parallel-to-the-roof array installation will typically be about 35ºC (63ºF) above ambient temperature. If the module’s temperature coefficient was -0.38%, for every degree Celsius in temperature rise array voltage will be reduced by this percentage. In this case, if the ambient temperature was 25ºC (77°F), the module temperature would be approximately 60ºC (140ºF), and the actual array voltage would be about 13.3% below its rated value at STC.

## Sizing to the Voltage Window

The power processing equipment connected to a PV array also has an allowable voltage range. This is true of high-voltage string inverters, battery-based MPPT charge controllers, and, less commonly, DC loads, such as well pumps that are directly connected to PV modules.

These components have both maximum Voc and minimum Vmp requirements. Together, these specifications represent the “voltage window” within which the components can operate. For example, a high-voltage grid-direct inverter might have a maximum Voc rating of 600 volts, and an operating voltage range or window between 240 and 550 VDC.

In many cases, inverters and charge controllers can be damaged if the array produces voltage greater than the  maximum value of the equipment, which can happen in cold, sunny weather if the design voltage is too close to the maximum. In turn, if the array voltage drops below the minimum value due to elevated temperatures, inverter or controller power production will stop until the array cools and the voltage rises. Because of this, PV system designers need to account for both extremes of the voltage window to ensure that the PV system will perform in the full range of conditions.

For a particular piece of equipment, voltage correction factors must be applied to the array’s assumed operating temperatures for the system’s site. This information is one piece of the puzzle that will help determine the appropriate number of modules allowed in a series string.

It all boils down to choosing a string size that meets three very important parameters while trying to optimize a few more. You must satisfy a voltage window that, on the high end, is limited by the maximum open-circuit voltage that the inverter or controller can handle before you harm its electronics. On the low end, there are two limiting factors—the minimum MPPT voltage that the inverter can operate at and the minimum start-up voltage the inverter needs to have. If the maximum Voc and minimum Vmp values are correctly calculated and the array designed to these specs, the minimum start-up voltage will always be met.

Once you have satisfied these requirements, you’ll still need to determine the appropriate array wattage to ensure you are using the inverter or controller efficiently. Oversizing an array’s wattage typically won’t damage inverters or controllers, but a portion of the array’s output will be dumped (wasted) as heat, and elevated operating temperatures may lead to shortening the operational life of the equipment. When sizing the array, you’ll also have to stay within the inverter or controller’s amperage limit, and size transmission wiring to keep voltage drop to a minimum. Finally, because PV module output is inherently temperature dependent, all of these parameters are moving targets, with cold and hot weather performance varying greatly, and array output current changing throughout the day as irradiance levels fluctuate.

## Maximum Modules in Series

PV modules reach open-circuit voltage with very little irradiance striking them, approximately 200 watts per square meter. This can often occur within half an hour of sunrise, before the sun has the opportunity to warm the modules. And although the array will be at Voc and not producing any power, that voltage will be applied to whatever component it is connected to.

To determine the maximum number of modules allowable in series for a given piece of equipment, you’ll need to determine array Voc at the coldest historical temperature where the array will be installed (see www.weather.com/common/home/climatology.html). You may need to adjust this value somewhat for your microclimate and elevation. The temperature used in this calculation is most often the record low temperature at the array location. To determine the adjusted open-circuit voltage (Vadj) for the PV module, use the following equation:

Vadj = Voc x {1 + [(Tcell – Tstc) x temperature coefficient]}

Where:

Voc is the STC open-circuit value for the module;

Tcell is the module’s cell temperature in degrees Celsius
(the cell temperature in this situation will be the same as the coldest historical ambient temperature at the site);

Tstc is the STC temperature value for the module,
generally 25°C; and

Temperature coefficient is the percentage loss of voltage specified for the module.

To determine the maximum number of modules allowed for a piece of equipment, the adjusted voltage must be divided into the equipment’s given maximum voltage (Vmax). Round down to the next whole number to ensure the array’s voltage will not exceed the maximum value.

## Minimum Modules Needed Per String

After calculating the maximum number of modules allowable per string, verify the minimum number of modules needed. The array needs to be sized so that when the system is operating at high temperatures, the array voltage remains above the minimum voltage-window threshold to ensure continued operation. To do this, you’ll need to determine the array voltage (Vmp) based on its typical operating temperature during the hot summer months.

## Racking Correction Figures

Two things—array mounts and operating temperatures—are important in evaluating the array’s operating voltage. The type of module mounting used influences heat dissipation—some methods allow for better airflow than others (see “Rack & Stack” in HP123). And although there are methods to estimate the module’s operating temperature based on mounting method and irradiance, it is common to use industry-accepted factors based solely on mounting methods. These values are added to the ambient temperature to estimate the array’s operating temperature.

The racking correction temperatures are applied to the highest average ambient temperature at the array’s location:

• Parallel to roof (<6 in. standoff): +35°C
• Rack-type mount (>6 in. standoff): +30°C
• Top-of-pole mount: +25°C

The highest temperature used is generally the average high temperature during the summer months, although some designers prefer to use the annual record high temperature for this calculation. Using the annual record high temperature for the calculation is a more conservative approach that ensures that the array will operate in all conditions it is subjected to without dropping below the inverter’s voltage window.

After the module’s voltage is corrected for maximum temperature, this value is divided into the component’s minimum voltage window. The result is a fractional value that must be rounded up to the next highest whole number, since at times the array will be operating at temperatures higher than the average value used.

When determining the minimum number of modules in series, designers need to be careful not to design a system that will normally operate at the very bottom of the voltage window. An array’s voltage that consistently drops to or near a component’s minimum window on “average” days increases the possibility of reduced energy output on days that exceed the average temperature. And, while PV modules are built to last, some degradation occurs over time. This is primarily due to moisture ingress that gradually corrodes a module’s internal electrical connections, creating higher resistance that, in turn, results in lower operating voltages. In extreme cases, this voltage degradation could amount to as much a 1% annual drop in module voltage. So you’ll also need to account for this over the array’s lifetime. Given these considerations, designing string sizes well above the minimum acceptable voltage level is sound system design.

## Access

Ryan Mayfield has a degree in environmental engineering from Humboldt State University and lives in Corvallis, Oregon. He teaches PV classes at Lane Community College and Solar Energy International, and is a principal at Renewable Energy Associates, a firm focusing on PV system design, implementation, commissioning, and industry-related training. He holds a Renewable Energy Technician license in Oregon.

Online String Calculators:

Fronius • www.fronius-usa.com

Kaco • www.kacosolar.com

PV Powered • www.pvpowered.com

SMA America • www.sma-america.com

Solectria • www.solren.com (charts only)

Xantrex • www.xantrex.com