Designing

But they don’t dive too deep into more complex sizing concepts, like picking compatible parts for your system and wiring the components together properly.

One common point of confusion is the concept of **string sizing**—how many panels you can wire into a single input on your inverter.

I wanted to write this article to explain the concept of string sizing, and break down the string sizing calculations we do to ensure your panel strings are the proper size to keep you running at maximum efficiency.

It’s worth noting that the grid-tied and off-grid systems we sell already take string sizing into account, so you won’t have to worry about this if you work with one of our designers.

However, we know that many of our readers are heavily inclined toward the DIY approach. Our goal is to equip you with accurate information to make informed decisions during your research and design process.

## What Is String Sizing?

A **panel string** is a group of panels that are wired into a single input on your power inverter. **String sizing** describes the calculations we make to determine how many panels we should plug into one input for optimal efficiency.

For example, this grid-tied system contains 24 Mission Solar 360W panels and one SMA Sunny Boy 7700W inverter. The inverter (appropriately called a string inverter) has three string inputs.

This system is designed to connect three strings of 8 panels each into those inputs (totaling 24 panels).

## Why Does String Sizing Matter?

Inverters operate within a specific input voltage range, called the **operating range**. Your panel strings must output a voltage that falls within that range.

If the panels don’t supply enough voltage, the inverter won’t have enough power to turn on.

If too much voltage is supplied, you can damage your inverter and void the warranty.

The operating range is simply the range in which your inverter will properly function. In this range, your inverter will turn on and deliver power to your appliances.

However, falling within the operating range just means the inverter is working — it doesn’t guarantee you’re getting the most power you possibly can out of it.

To really optimize output, you want to fall within a more narrow voltage range called the **maximum power point (MPP)** range. This is the sweet spot in which your inverter runs at the peak efficiency listed on its spec sheet.

Your goal is to size your panel strings to supply a voltage that falls within this maximum power point range.

Let’s look at how we calculate string size to achieve this goal.

## How To Calculate String Size

String sizing calculations depend on the specific voltage of your panels and inverter, as well as outside factors like temperature.

Each panel has an **output voltage**. This is the voltage the panel sends to the inverter. We’ll need to look at a few different figures:

**Open circuit voltage (Voc):** The voltage supplied when the circuit is open—that is, when current isn’t passing through the circuit. This state occurs when the inverter isn’t powered on.

**Max Power voltage (Vmp): **The voltage of the panel after it is turned on and operating normally under load (current is flowing through the circuit).

Find these numbers on the panel spec sheet. It’s different for every panel.

On the inverter spec sheet, look for the **rated MPP voltage range**.** **This is the sweet spot for ideal operation that I mentioned in the last section.

Also take note of the **max DC input voltage.** We’re especially concerned about this, because if you exceed the max operating voltage, you’ll overload the inverter and potentially fry the equipment. (We’ve seen it, unfortunately.) Going over the max operating voltage will void the warranty on your inverter.

There is also a minimum DC voltage and a startup voltage requirement that needs to be met in order to turn on the inverter. Typically this won’t be an issue, since we want our strings to operate well above the minimum, up in the MPP range where it works at higher efficiency.

Alright, we’ve got our figures and it’s time to do some math. Let’s use that 9 kW grid-tied system I linked earlier as an example.

Mission Solar 360W panels have a Vmp of 39.28 and a Voc of 48.08, as listed on the spec sheet:

The SMA Sunny Boy 7700W inverter has a rated MPP voltage range of 270-480 volts. The operating range is 100-600 volts (look for minimum and maximum DC voltage on the spec sheet):

### Step 1: Find your minimum string size

First we want to calculate the minimum number of panels we should put in a string.

For that, take the low end of the MPP range (in this case 270V) and divide by the Vmp of the panel (39.28).

270V **÷** 39.28V = 6.87

The result is 6.87, which needs to be rounded up to the next whole number (since you can’t put a fraction of a panel on a string). So your minimum string size is **7 panels** before temperature compensation.

### Step 2: Find maximum string size that doesn’t exceed operating voltage

For maximum string size, we want to calculate against the max DC input voltage to make sure we don’t overload the inverter.

For this calculation, take the max DC input (600V) and divide by the Voc of the panel (48.08).

600V **÷** 48.08V = 12.48

This time we need to round the result down, since we’re trying to stay below a maximum threshold. So we come to **12 panels**.

Again, this number is not final because we haven’t corrected for temperature yet.

### Step 3: Check that max string size falls within MPP range

In step 2 we calculated that maximum string size to keep the inverter operational. We want to double check that this falls within our peak efficiency range as well.

For that, take the max string size calculated in step 2 (12 panels) and multiply by the Vmp of the panel (39.28).

12 ∗ 39.28 = 471.36V

We are checking that this falls under the top end of the MPP range (in this example, 480V). Since 471V is below our target 480V, everything checks out here.

If we had arrived at a number above the MPP range in this step, we would knock the max string size down by 1 and recalculate until we successfully fall within the MPP range.

Based on these calculations, we have a string size of **7-12 **panels. But this doesn’t take temperature into account, which can have a significant impact on our figures (colder temperatures lead to a rise in voltages and hotter temperatures will lower voltage).

### Step 4: Account for temperature in your location

We now want to ask the question: “would extreme temperatures cause us to fall outside a safe operating range?”

To do this, I go to Weather Channel’s site, weather.com, and enter the location where the system will be built.

Let’s say we’re in Boise, ID. Search for the location in the search bar:

Use the dropdown to set your units to Celsius. This will match the units on the panel spec sheet.

Then navigate to the Almanac with records and average temps in this location. I want to find the coldest ever day on record (to account for the absolute worst-case scenario). That’s the gray bar:

We find that the absolute coldest day on record in Boise is -33.3° C.

Now we need to go back to the solar panel spec sheet and look for the **temperature coefficient of Voc**, which measures the change in voltage per degree Celsius away from the Normal Operating Cell Temperature (NOCT).

NOCT measures the panel’s voltage at a given temperature, when it’s tested in a climate-controlled environment.

For the Mission Solar 360W panels in our example, the NOCT is 44° C. We take the difference between the NOCT and the coldest day on record (-33.3° C) for a value of 77.3° C below the standard conditions.

The temperature coefficient on these panels is 0.280%/°C. This means that for each degree Celsius away from the NOCT, the panel will produce .28% more voltage.

We first need to multiply the Voc of the panel (48.08) by the temperature coefficient of Voc (.28%). Since the temperature coefficient is a percentage, move the decimal 2 places to the left to account for this in the equation:

48.08 ∗ 0.0028 = 0.134624

This gives the voltage change per degree Celsius, so we need to multiply by the temperature difference we found above (77.3°C):

0.134624 ∗ 77.3 = 10.406V

On a record-cold day in Boise, each panel will produce about 10.406 volts above its rated Voc of 48.08. We need to add those values together to get the true panel voltage on a record cold day:

48.08V + 10.406V = 58.486V

From here, multiply the true panel voltage by the max number of panels in the string (12) we calculated in step 2:

58.486 ∗ 12 = 701.83V

The total voltage of the array can peak at 701.83V on a record cold day! This is well above the max operating voltage of 600V, which means cold temps can push your array into territory that will cause damage to your inverter.

That’s obviously not ideal (did we mention you could fry your system?), so we need to make adjustments to max string size to bring this down to an acceptable level.

You want to start subtracting panels off the string until you fall within the operating range. Take the array voltage (701.83V) and subtract the true panel voltage (58.486V):

701.83V – 58.486V = 643.346V

Not good enough: it’s still above the 600V limit. We need to subtract one more panel:

643.346V – 58.486V = 584.86V

Perfect. We’re under the 600V max input threshold after accounting for the temperature extremes the array could reasonably be exposed to. Since we’ve removed 2 panels from our starting point, **we arrive at a final max string size of 10 panels**.

This is the magic number. Under these conditions, **your string size should be capped at 10 panels**. Any larger has the potential to permanently damage your array in extreme temperatures.

Right about now, hawk-eyed readers may be asking…

**“This accounts for cold temperatures…what about excessively hot temperatures above the NOCT?”**

NOCT tends to be measured at 44-46°C which is around 111-115° Fahrenheit. Most places don’t peak above this, although it certainly happens in some areas, especially close to the Equator.

Regardless, warm temps aren’t as much of a concern because they decrease voltage. Again, our primary concern is staying below the max input voltage so we don’t damage the inverter. Voltage drop due to warm temps just brings us further under the “danger zone.”

Extreme heat will affect minimum string size, though, and you may want to check that your minimum string size still falls within the MPP range for optimal efficiency. To do that, you follow the same calculations as above, but you need to use different values:

- Use the panel
**Vmp**in place of**Voc.** - Use the panel
**Temperature Coefficient of Pmax**in place of**Temperature Coefficient of Voc.** - When it comes to calculating the true voltage of the panel,
**subtract the voltage compensation from the panel Vmp**(instead of adding it to the panel Voc).

For example, the record high in Death Valley, CA is 56.7°C, which is 12.7°C above the NOCT. The Vmp is 39.28V and the Pmax temperature coefficient is -0.377. Here’s how the math would look in this scenario:

**Vmp **∗** temp coefficient of Pmax = voltage change per ° Celsius**

39.28 ∗ 0.00377 = 0.148

**Total voltage difference for 12.7° C above NOCT**

0.148 ∗ 12.7 = 1.8796V

**Subtract from Vmp to arrive at true panel voltage on record-hot day**

39.28 – 1.8796 = 37.4004

**Multiply by minimum string size for total input voltage**

37.4004 ∗ 7 = 261.8028

Way back in Step 1, we cited the low end of the MPP range as 270V and you can see 261.8V falls slightly below that range. The ideal would be to bump the minimum string size up to 8 panels.

However…this is accounting for the absolute hottest day on record in Death Valley, which is a sweltering 134°F! And the consequence here isn’t inverter damage, just a system that operates slightly below peak efficiency in extreme circumstances.

So really, you can see the concern here is pretty much non-existent. 8 panels is technically ideal for minimum string size, but 7 panels is not going to give you any trouble.

## Wrapping Up

Whew…we made it! That’s our exhaustive guide to string sizing, for all you folks who love to get hands-on with your projects.

Remember, our complete system packages are built with proper string size in mind, which takes these complex calculations out of your hands. For help building a system that fits your needs, request a free consultation with our experienced system design team.