# Array to Inverter Matching

Mastering Manual Design Calculations

With too few modules in series an inverter cannot maintain an array’s MPP under high temperature conditions for the site, sacrificing energy harvest. Too many modules in series results in voltages above 600 Vdc, which can damage equipment, violate the NEC and void the manufacturer’s warranty.

Matching array output to inverter input is a critical step in PV system design. The primary goal of matching an array to an inverter is to ensure that the inverter can capture a high percentage of the available energy that the array produces during all of the environmental conditions anticipated at the site. Often a secondary goal is to maximize the inverter capacity so that the inverter will operate at or near full power during high irradiance periods without power limiting. It is important that power limiting occur only during exceptional or transitory conditions, not under normal operating conditions.

The array in a typical grid-direct PV system consists of one or more strings of five to 20 modules wired in series. The exact number of modules - the number in series and the number of strings - depends on the electrical characteristics of the module, the input voltage and current range of the inverter, and the expected high and low ambient temperatures of the site. In a well designed system, the array’s operating voltage, current and power output will be within the inverter’s operating range at all times.

Inverter manufacturers typically provide string sizing guidelines or online programs to assist in matching a particular array configuration to a specific inverter. The system designer needs to provide the record low and average high temperatures for the site. Some online string sizing calculators generate detailed results that integrators can use to optimize their designs. However, the main function of these programs is to calculate the maximum and minimum number of modules in series, providing designers with a range of acceptable array configurations.

## MANUAL CALCULATIONS

The necessary calculations can also be done manually. This is an important skill to learn, especially for designers. Building integrated products are seldom included in string sizing calculators, and new products on the market may not immediately be added to the inverter manufacturer’s online calculators. On the roof, the ability to manually verify array configurations can avoid costly mistakes. Without wireless laptop connections, crews in the field cannot rely upon online string sizing tools. But solar professionals can, and should, master the steps detailed in this article.

To illustrate how to calculate these configurations manually, the following example assumes:

1. a rooftop PV array mounted at the plane of the roof and elevated by 3–4 inches;
2. an environment with an ambient temperature range of 0°–45°C;
3. a 7 kWac inverter with an input voltage range of 250–600 Vdc, a MPPT range of 250–480 Vdc, a maximum dc input current of 30 amps and a California Energy Commission (CEC) weighted efficiency of 96%; and
4. a crystalline PV module with the specifications listed in Table 1.

## MAXIMUM MODULES IN SERIES

Maximum input voltage for an inverter is a hard stop design limit. Exceeding the maximum inverter operating voltage can result in catastrophic failure of the inverter and could, in some cases, result in NEC violations. Therefore, the maximum open circuit voltage is the most critical value to consider when designing a PV array.

The number of modules in series determines the array open-circuit voltage (Voc). Because voltage is temperature dependent, Voc must be temperature corrected in order to calculate the maximum PV system voltage (see 2008 NEC, Table 690.7 to the right). This temperature corrected Voc will determine the maximum number of modules allowable per series string. Conservative designers will use the record low ambient temperature at their site as the cell temperature for these calculations.

A good first step for designers is to determine the temperature differential for their site, in this case the low temperature differential. In our example the record low temperature for the site is 0°C, which is a differential of -25°C from Standard Test Conditions (STC). As cell temperature drops, output voltage increases. This effect is described by the appropriate temperature coefficient, which in this case is given as a percentage of Voc.

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